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=Riemann Meets COLLADA & Oculus Rift S=
=Riemann Meets COLLADA & Oculus Rift S=
If you want to jump straight to the fun part, copy the ASCII text file that is contained below within the [[#Scroll1|scrollable box]] named, <b>Inertial17.dae</b>, and read the accompanying instructions regarding how to view this example model on a Mac.  A second file &#8212; presenting the same example model, but as viewed from a rotating frame of reference &#8212; can be extracted from a separate [[#Scroll2|scrollable box]] named, <b>MultiLagrange18.dae</b>.


{{LSU_HBook_header}}
{{LSU_HBook_header}}


==Example Model==
==Example Model==
===Key Physical Parameters===


The model that we have chosen to use in our first successful construction of a COLLADA-based, 3D and interactive animation has the following properties; this model has been selected from [[User:Tohline/ThreeDimensionalConfigurations/RiemannStype#Table2|Table 2 of our accompanying discussion of Riemann S-type ellipsoids]]:
The model that we have chosen to use in our first successful construction of a COLLADA-based, 3D and interactive animation has the following properties; this model has been selected from [[User:Tohline/ThreeDimensionalConfigurations/RiemannStype#Table2|Table 2 of our accompanying discussion of Riemann S-type ellipsoids]]:
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<tr>
<tr>
   <td align="right">
   <td align="center" rowspan="6">
<math>~\frac{b}{a}</math>
<b>Figure 1a</b><br />&nbsp;<br />
[[File:B41c385EFEdiagram02.png|325px|EFE Parameter Space]]
  </td>
  <td align="center" rowspan="6" width="2%">
&nbsp;
  </td>
  <td align="center" colspan="3">
<math>~\frac{b}{a} = 0.41</math>
   </td>
   </td>
   <td align="center">
   <td align="center" rowspan="6" width="2%">
<math>~=</math>
&nbsp;
   </td>
   </td>
   <td align="left">
   <td align="center" rowspan="6" bgcolor="lightgrey">
<math>~0.41</math>
<b>Figure 1b</b><br />
[[File:COLLADA3rdViewpoint.png|300px|EFE Model b41c385]]
   </td>
   </td>
</tr>
</tr>


<tr>
<tr>
   <td align="right">
   <td align="center" colspan="3">
<math>~\frac{c}{a}</math>
<math>~\frac{c}{a} = 0.385</math>
   </td>
   </td>
</tr>
<tr>
   <td align="center">
   <td align="center">
<math>~=</math>
''Direct''
   </td>
   </td>
   <td align="left">
   <td align="center" width="2%" rowspan="4">
<math>~0.385</math>
&nbsp;
  </td>  
  <td align="center">
''Adjoint''
   </td>
   </td>
</tr>
</tr>


<tr>
<tr>
   <td align="right">
   <td align="center">
<math>~\Omega_\mathrm{EFE}</math>
<math>~\Omega_\mathrm{EFE} =  0.547874</math>
   </td>
   </td>
   <td align="center">
   <td align="center">
<math>~=</math>
<math>~\Omega_\mathrm{EFE} = - 0.079886</math>
  </td>
  <td align="left">
<math>~ \frac{\omega}{\sqrt\pi } = \frac{0.971082}{\sqrt\pi} = 0.547874</math>
   </td>
   </td>
</tr>
</tr>


<tr>
<tr>
   <td align="right">
   <td align="center">
<math>~\lambda_\mathrm{EFE}</math>
<math>~\lambda_\mathrm{EFE} = 0.079886</math>
   </td>
   </td>
   <td align="center">
   <td align="center">
<math>~=</math>
<math>~\lambda_\mathrm{EFE} = - 0.547874</math>
  </td>
  <td align="left">
<math>~ \frac{0.141594}{\sqrt\pi} = 0.079886</math>
   </td>
   </td>
</tr>
</tr>
</table>
The subscript "EFE" means that the relevant frequency is given in units that have been adopted in [<b>[[User:Tohline/Appendix/References#EFE|<font color="red">EFE</font>]]</b>], that is, in units of <math>~[\pi G\rho]^{1 / 2}</math>.  In Figure 1a, below, the solid purple circular marker (where the pair of purple lines cross) identifies the location of this model in the "c/a versus b/a" diagram that appears as Figure 2 on p. 902 of [http://adsabs.harvard.edu/abs/1965ApJ...142..890C S. Chandrasekhar (1965)]; essentially the same diagram appears in &sect;49 (p. 147) of [<b>[[User:Tohline/Appendix/References#EFE|<font color="red">EFE</font>]]</b>].  In a [[User:Tohline/ThreeDimensionalConfigurations/JacobiEllipsoids#Jacobi_Ellipsoids|separate chapter]] we have discussed various properties of uniformly rotating, ''Jacobi'' ellipsoids; they are equilibrium configurations that lie along the sequence that runs from "M<sub>2</sub>" (on the b/a = 1, Maclaurin sequence) to the origin of this diagram.  Our chosen model lies just above the Jacobi-ellipsoid sequence.


<div align="center">
<table border="1" align="center" cellpadding="8">
<tr>
<tr>
   <th align="center">Figure 1a</th>
   <td align="center">
  <th align="center">Figure 1b</th>
<math>~f = - 0.415418</math>
  <th align="center">Figure 1c</th>
</tr>
<tr>
  <td align="left" bgcolor="white">
[[File:EFE_STypeRiemannDiagram05.png|300px|EFE Parameter Space]]
   </td>
   </td>
   <td align="left" bgcolor="lightgrey">
   <td align="center">
[[File:COLLADA1stViewpoint.png|300px|EFE Model b41c385]]
<math>~f = - 19.53923</math>
  </td>
  <td align="left" bgcolor="lightgrey">
[[File:COLLADA2ndViewpoint.png|250px|EFE Model b41c385]]
   </td>
   </td>
</tr>
</tr>
</table>
</table>
</div>
 
The subscript "EFE" on &Omega; and &lambda; means that the relevant frequency is given in units that have been adopted in [<b>[[User:Tohline/Appendix/References#EFE|<font color="red">EFE</font>]]</b>], that is, in units of <math>~[\pi G\rho]^{1 / 2}</math>.  In Figure 1a, the yellow circular marker, that has been placed where the pair of purple dashed lines cross, identifies the location of this model in the "c/a versus b/a" ''[[User:Tohline/ThreeDimensionalConfigurations/RiemannStype#Fig2|EFE Diagram]]'' that appears as Figure 2 on p. 902 of [http://adsabs.harvard.edu/abs/1965ApJ...142..890C S. Chandrasekhar (1965)]; essentially the same diagram appears in &sect;49 (p. 147) of [<b>[[User:Tohline/Appendix/References#EFE|<font color="red">EFE</font>]]</b>]. 
 
In a [[User:Tohline/ThreeDimensionalConfigurations/JacobiEllipsoids#Jacobi_Ellipsoids|separate chapter]] we have discussed various properties of uniformly rotating, ''Jacobi'' ellipsoids; they are equilibrium configurations that lie along the sequence that runs from "M<sub>2</sub>" (on the b/a = 1, Maclaurin sequence) to the origin of this diagram.  Our chosen model lies off of &#8212; just above &#8212; the Jacobi-ellipsoid sequence, which means that it is not rotating as a solid body.  Instead, as we focus first on the ''direct'' (as opposed to the ''adjoint'') configuration, we appreciate that while the ellipsoid is spinning prograde (counter-clockwise) with a frequency given by |&Omega;<sub>EFE</sub>|, each Lagrangian fluid element inside as well as on the surface of the ellipsoid is traveling retrograde (clockwise) along an elliptical path with a frequency given by |&lambda;<sub>EFE</sub>|.
 
===The COLLADA Code &amp; Initial 3D Scene===
 
The following scrollable box titled, <b>Inertial17.dae</b>, contains an <xml>-formatted [https://www.khronos.org/collada/ COLLADA] code that, when properly executed, uses the interactive, 3D animation capabilities of video game drivers to illustrate, in a quantitatively precise fashion, the dynamical flows that are associated with our chosen example model of an equilibrium S-type Riemann ellipsoid. On a Macintosh computer platform, all of the features of this animated and interactive model can be accessed by simply opening the file using Apple's in-house "Preview" application.  Figure 1b provides a snapshot of the Preview app's window immediately (TIME = 0.0) after the COLLADA code has been read into the app.  More elements of this 3D visual scene will be identified and discussed below, but for now we simply point out that the center of the opaque, purple ellipsoid coincides with the origin of the principal underlying "laboratory" coordinate frame &#8212; that is, at (X<sub>0</sub>, Y<sub>0</sub>, Z<sub>0</sub>) = (0, 0, 0) &#8212; and the ellipsoid has the desired axis ratios (b/a, c/a) = (0.41, 0.385).




<div align="center">
<div align="center" id="Scroll1">
<b>Inertial17.dae</b> &nbsp; &nbsp; &nbsp; a COLLADA code containing 7968 lines of <xml>-formatted ASCII text
<b>Inertial17.dae</b> &nbsp; &nbsp; &hellip; &nbsp; &nbsp; a COLLADA code containing 7968 lines of <xml>-formatted ASCII text
</div>
</div>


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Figure 1 displays a pair of still-frame images of this (purple) ellipsoidal configuration after the ellipsoid has completed precisely five (counter-clockwise) spin cycles.  (The snapshots have been taken at the same point in time, but from two different "camera" viewing angles.) The cycle of the "wall mounted" clock is based on the fundamental, EFE-adopted frequency of [&pi; G &rho;]<sup>½</sup>.  In the left-hand image (labeled Figure 1a), the time on the clock appears to be about 9:08.  This means that as the ellipsoid has completed five spin cycles, the clock has completed approximately [9 + 8/60] &#8776; 9.13 cycles.  In other words, the ratio (ellipsoid-to-clock) of these two frequencies is,
<table border="1" cellpadding="10" align="center" width="100%">
<table border="0" cellpadding="5" align="center">
<tr>
<td align="left">
<b>Instructions for Viewing the Example Model on a Mac:</b>
<br />
<ol>
<li>Click, then drag your cursor down through the scrollable box to highlight and ''select'' all 7968 lines of the COLLADA code.</li>
<li>Make a copy (&#8984;-c) of the entire code.</li>
<li>Paste (&#8984;-v) the code into an empty, plain text file (using, for example, Apple's <font type="Courier">TextEdit</font> app) and save it with the name, <b>Inertial17.dae</b>[NOTE:  ".dae" is the file name suffix that is universally associated with an executable COLLADA file.]</li>
<li>Open this file using Apple's ''Preview'' app; the static 3D model of our (opaque purple) ellipsoid should appear at TIME = 0.0 &#8212; see Figure 1b.</li>
<li>To view the 3D (TIME = 0.0) model from different angles, place your mouse cursor anywhere near the center of the Preview app's image, then click and drag the cursor in different directions.</li>
<li>The play/pause buttons &#8212; shown at the bottom of Figure 1b &#8212; become visible if the cursor is simply placed near the bottom of the image being displayed by the Preview app; the animation will start (on a continuous loop) when the play button is clicked.</li>
</ol>


<tr>
<b>Instructions for Viewing the Example Model on a Windows 10 PC:</b>
  <td align="right">
<br />We have not yet figured out how to similarly (at no cost) view COLLADA-based (.dae) 3D scenes on a PC.  On my Lenovo system, the Windows 10 startup menu includes a "3D Viewer" app, but this app does not recognize .dae-formatted files.  However, the app appears to read .glb-formatted files satisfactorily.  As is [[#Inside_the_Oculus_Rift_S_Environment|discussed below]], the Oculus Rift S system will import our COLLADA-based models only if each model file has been translated from a ".dae" format to a ".glb" format. Hence, after this translation has been made principally to facilitate the importation of our model into the Oculus Rift S virtual-reality environment &#8212; see our description, below, of the [[#Khronos_Group.27s_COLLADA2GLTF_Converter|Khronos Group's COLLADA2GLTF Converter]] &#8212; we have also been able to straightforwardly view the 3D scene on our Lenovo PC using its "3D Viewer" app.
<math>~\frac{\Omega_\mathrm{EFE}}{[\pi G \rho]^{1 / 2}}</math>
</td>
  </td>
  <td align="center">
<math>~\approx</math>
  </td>
  <td align="left">
<math>~\frac{5}{9.13} = 0.548 \, .</math>
  </td>
</tr>
</tr>
</table>
</table>


This matches the tabulated value of <math>~\Omega_\mathrm{EFE}</math> presented above.  Now, let's examine the motion of an example Lagrangian fluid element, which has been marked in the 3D scene by a red "arrow" riding in the equatorial plane and along the surface of the (purple) ellipsoidal figure.  At time zero, the fluid marker was placed at the end of the longest axis of the ellipsoid that was nearest the "wall clock"; then, as time progressed and the ellipsoidal figure turned counter-clockwise, the fluid marker moved clockwise and completed less than one full "orbit" in the same time that the ellipsoidal figure completed five full spin cycles.  In the right-hand image (labeled Figure 1b), we can see that ''relative'' to the ellipsoidal figure, the fluid marker has moved through approximately three-quarters of its assigned elliptical "orbit"; let's say, 73% of one full cycle.  This means that the ratio of the Lagrangian fluid element's orbital frequency to the frequency of the wall-clock is,
<table border="0" cellpadding="5" align="center">


<tr>
At TIME = 0.0 (see, again, Figure 1b), our purple ellipsoid is oriented such that its longest axis (of length, 2a) aligns with the X<sub>0</sub>-axis and such that the small red cubic "fluid marker" at the tip of the ellipsoid lies in the plus-X direction &#8212; initially at location (X<sub>0</sub>, Y<sub>0</sub>, Z<sub>0</sub>) = (+a, 0, 0).  At the opposite end of the ellipsoid &#8212; initially at location (X<sub>0</sub>, Y<sub>0</sub>, Z<sub>0</sub>) = (-a, 0, 0) &#8212; we have attached a stubby black pointer; as the ellipsoid spins, this black pointer will remain affixed to the ellipsoid to aid in counting spin cycles, whereas the red fluid marker will not.  The ellipsoid's shortest axis (length, 2c) aligns with the Z<sub>0</sub>-axis, with straight up being associated with the positive Z direction.  The ellipsoid's intermediate axis (length, 2b) initially aligns with the lab's Y<sub>0</sub>-axis, with the positive direction being defined by the standard "righthand rule."
  <td align="right">
 
<math>~\frac{\lambda_\mathrm{EFE}}{[\pi G \rho]^{1 / 2}}</math>
In addition to displaying an opaque purple Riemann ellipsoid, our COLLADA-defined 3D visual scene contains (see, again, Figure 1b):
  </td>
<ul>
  <td align="center">
<li>A square gray "frame" that lies in the laboratory frame's equatorial, Z<sub>0</sub> = 0.0, plane, just outside of and "framing" the ellipsoid; and a small gray solid rectangle that hovers above the ellipsoid and is affixed to the plus-Z<sub>0</sub> axis, also intended to provide 3D orientation and registration queues.</li>
<math>~\approx</math>
<li>A couple of lines of alpha-numeric characters that has been attached to an imaginary laboratory wall to label/quantify the geometric properties of this ellipsoid.</li>
  </td>
<li>A clock that has been hung on the same imaginary laboratory wall.</li>
  <td align="left">
<li>A yellow-dotted ellipse (comprised of 50 individual small yellow markers) that lies in the equatorial plane and is attached to the ellipsoid, marking the trajectory that will be followed by the red cubic "fluid marker" during the animation sequence.</li>
<math>~\frac{0.73}{9.13} = 0.080 \, .</math>
</ul>
  </td>
 
</tr>
===Animation===
</table>
 
When the "play" button is clicked on the Preview app's control panel (again, reference Figure 1b), the COLLADA-directed scene-animation begins.  Three different characteristic timescales are relevant: 
[[File:ClockImage01.png|175px|right|Clock Image]]<ol>
<li>
We use the motion of the hands on the wall-mounted clock to identify the natural oscillation frequency of the physical system, namely, <math>~\Omega_0 \equiv [\pi G \rho]^{1 / 2}</math>.  More specifically, by declaration, one oscillation period of the red "minute" hand &#8212; that is to say, one wall-clock "hour" &#8212; is <math>~P_0 = 2\pi[\pi G \rho]^{-1 / 2} = [4\pi/(G \rho)]^{1 / 2}</math>.  One full cycle of the wall-clock's black "hour" hand is therefore 12P<sub>0</sub>.  For pedagogical purposes, in all of our COLLADA-driven animations we have equated P<sub>0</sub> with a COLLADA TIME interval of 4.0, which means that during each animation, one wall-clock hour passes every (approximately) 4 seconds of real time.<sup>&Dagger;</sup></li>
<li>The purple ellipsoid spins in a prograde direction about its shortest axis &#8212; that is, about the Z<sub>0</sub>-axis &#8212; on a timescale set by the value of <math>~\Omega_\mathrm{EFE}</math>, which has already been normalized to &Omega;<sub>0</sub>.  Specifically, as viewed from the inertial frame of reference, the ellipsoid will complete one full spin in a time, <math>~P_\mathrm{spin} = |\Omega_\mathrm{EFE}|^{-1} = [0.5479]^{-1} = 1.825</math> wall-clock hours, which is approximately 7.3 seconds of real time.</li>
<li>As viewed from a frame of reference that is spinning with the ellipsoid, each Lagrangian fluid element inside as well as on the surface of the ellipsoid moves in a retro-grade direction along an elliptical trajectory that has the same ellipticity as does the equatorial surface of the 3D ellipsoid.  Each and every Lagrangian fluid element completes one full elliptical orbit in a time, <math>~P_\mathrm{Lagrange} = \lambda_\mathrm{EFE}^{-1} = [0.0799]^{-1} = 12.52</math> wall-clock hours, which is about 50 seconds of real time.
</ol>
 
In the COLLADA-based code (<b>Inertial17.dae</b>) that has been provided above in the scrollable box, we have instructed the animation sequence to follow the system's evolution through five complete spins of the purple ellipsoid.  (Unless the ''pause'' button is clicked, the animation will actually loop repeatedly, but the time on the wall-mounted clock will reset to 0<sup>h</sup>0<sup>m</sup> after every fifth spin period.)  In practice, this animation sequence lasts (5 &times; 1.825) &times; 4 = 36.5 seconds of real time.


This matches the tabulated value of <math>~\lambda_\mathrm{EFE}</math> presented above.
Figure 2 displays a pair of still-frame images of our example (purple) ellipsoidal configuration after the ellipsoid has completed precisely five (counter-clockwise) spin cycles.  (The snapshots have been taken at the same point in time, but from two different camera viewing angles.)  In the left-hand image (Figure 2a),  the time on the clock appears to be about 9<sup>h</sup>8<sup>m</sup>.  This means that as the ellipsoid has completed five spin cycles, the "minute" hand of the clock has completed approximately [9 + 8/60] &#8776; 9.13 cycles.  Dividing this number by 5 gives a value of <math>~P_\mathrm{spin} \approx 1.827</math>, which is indeed the spin period we identified earlier.  This illustrates that the proper physical timescales governing oscillations of the wall-mounted clock and of the spinning ellipsoid have been implemented in a quantitatively accurate manner within the COLLADA code.


==See Also==
 
<div align="center">
<table border="1" align="center" cellpadding="8">
<tr>
  <th align="center">Figure 2a</th>
  <th align="center">Figure 2b</th>
</tr>
<tr>
  <td align="left" bgcolor="lightgrey">
[[File:COLLADA1stViewpoint.png|300px|EFE Model b41c385]]
  </td>
  <td align="left" bgcolor="lightgrey">
[[File:COLLADA4thViewpoint.png|300px|EFE Model b41c385]]
  </td>
</tr>
</table>
</div>
 
 
In Figure 1b, above, we have used a small red cube to mark the Lagrangian fluid element that is initially (TIME = 0.0) located at the end of the longest axis of the ellipsoid (in the +X direction).  In Figure 2b we can see where this fluid element is located after the ellipsoid has completed five complete spins.  After moving in a retrograde (clockwise) direction along its assigned elliptical trajectory while the ellipsoid completed five full spins, we see that the red-tagged Lagrangian fluid element has completed a little less than 3/4 of one full orbit; let's call it 73% of one orbit.  We therefore infer from the COLLADA-driven animation that <math>~0.73 P_\mathrm{Lagrange}\approx~5 P_\mathrm{spin}</math>, that is, <math>~P_\mathrm{Lagrange}\approx 6.849 P_\mathrm{spin}</math>.  This is indeed a proper reflection of the physical properties of our chosen example Riemann S-type ellipsoid, as its mathematically determined equilibrium frequency ratio is, <math>~|\Omega_\mathrm{EFE}|/|\lambda_\mathrm{EFE}| = 6.8582</math>.  This, too, illustrates that the proper physical timescales governing oscillations of our chosen example Riemann ellipsoid have been implemented in a quantitatively accurate manner within the COLLADA code.
 
===Rotating Reference Frame===
 
<table border="0" align="right" cellpadding="8"><tr><td align="center">
<table border="0" align="center"><tr><td align="center" bgcolor="lightgray">&nbsp;<br /><b>Figure 3</b><br />
[[File:COLLADA1stRotatingView.png|300px|Rotating Frame at TIME zero]]
</td></tr></table>
</td></tr></table>
The following scrollable box titled, <b>MultiLagrange18.dae</b>, contains another <xml>-formatted [https://www.khronos.org/collada/ COLLADA] code.  It is identical in most respects to the COLLADA code named <b>Inertial17.dae</b> that has been discussed above in considerable detail.  But there are two key differences:
<ol type="A">
<li>As Figure 3 illustrates, while the surface of the ellipsoid is still colored purple, it has been made partially transparent to reveal the location of three &#8212; rather than only one &#8212; Lagrangian fluid elements.  All three are initially positioned along the plus-X<sub>0</sub> axis, but two are located inside, rather than on the surface of, the ellipsoid.</li>
<li>This new, "MultiLagrange" COLLADA animation presents the system's evolution as viewed from a frame of reference that is spinning with the frequency of the ellipsoid, &Omega;<sub>EFE</sub>. As before, the COLLADA-driven animation is carried through five full ellipsoid spins, but from the perspective of this new rotating frame, the ellipsoid remains stationary and it is the components of the "laboratory" that actually spin; and they spin ''clockwise'' rather than counter-clockwise.</li>
</ol>
 
From the point of view of this rotating reference frame, it is much easier to watch and diagnose the behavior of the fluid motion interior to the surface of the ellipsoid.  Note, in particular, the relative speed and alignment of the three fluid elements at different points along their coordinated orbits. Because Riemann S-type ellipsoids are uniform-density configurations and they are composed of an incompressible fluid, at all points in time and in space (within the volume of the ellipsoid) the divergence of the velocity must be zero.
 
 
<div align="center" id="Scroll2">
<b>MultiLagrange18.dae</b> &nbsp; &nbsp; &hellip; &nbsp; &nbsp; a COLLADA code containing 7994 lines of <xml>-formatted ASCII text
</div>
 
<div style="height: 400px; width: 100%; overflow: scroll;">
<pre>
<?xml version="1.0" encoding="UTF-8" standalone="no" ?>
<COLLADA xmlns="http://www.collada.org/2005/11/COLLADASchema" version="1.4.1">
    <asset>
        <contributor>
            <author>jet53man</author>
            <authoring_tool>Raw XML</authoring_tool>
        </contributor>
        <created>2020-04-28</created>
        <modified>2020-05-10</modified>
        <unit meter="0.0254" name="inch" />
        <up_axis>Z_UP</up_axis>
<!--
This file originally was named FullLast45X.dae ...
here its assigned name is RiemannBuild05.dae (etc.)
we are inserting various objects, drawn from b41c385_DI.dae
 
                <node>        <geometry>      <material>      <effect>
*** firstclock:    ID3    Clock_OuterEdge        ID6            ID5
***          :            Clock_InnerEdge      InnerID6      InnerID5
***  Jetman  :  ArrowID3  Clock_ArrowEdge      ArrowID6      ArrowID5
***  HourHand :  HourID3  Clock_HourEdge        HourID6        HourID5
-->
    </asset>
    <library_effects>
        <effect id="DiffusePurple_00">
            <profile_COMMON>
                <technique sid="COMMON">
                    <phong>
                        <diffuse>
                            <color>0.5 0.0 0.99  1.0</color>
                        </diffuse>
                        <transparency>
              <float sid="transparency">0.6</float>
                        </transparency>
                    </phong>
                </technique>
            </profile_COMMON>
        </effect>
        <effect id="DiffuseRed_EFE">
            <profile_COMMON>
                <technique sid="COMMON">
                    <lambert>
                        <diffuse>
                            <color>1.0 0.0 0.0  1.0</color>
                        </diffuse>
                    </lambert>
                </technique>
            </profile_COMMON>
        </effect>
<!-- effect:  MidPlane Frame -->
        <effect id="MidPlaneID5">
            <profile_COMMON>
                <technique sid="COMMON">
                    <lambert>
                        <diffuse>
                            <color>0.0 0.0 0.6 0.5</color>
                        </diffuse>
                    </lambert>
                </technique>
            </profile_COMMON>
        </effect>
<!-- effect:  Cylindrical Pointer -->
        <effect id="CylID5">
            <profile_COMMON>
                <technique sid="COMMON">
                    <lambert>
                        <diffuse>
                            <color>0.0 0.0 0.0 1.0</color>
                        </diffuse>
                    </lambert>
                </technique>
            </profile_COMMON>
        </effect>
        <effect id="MarkersID5">
          <profile_COMMON>
            <technique sid="COMMON">
              <lambert>
                <diffuse>
                  <color>1 1 0 1</color>
                </diffuse>
              </lambert>
            </technique>
          </profile_COMMON>
        </effect>
<!-- effect:  Letters -->
        <effect id="LettersID5">
            <profile_COMMON>
                <technique sid="COMMON">
                    <lambert>
                        <diffuse>
                            <color>0 0 0 1</color>
                        </diffuse>
                    </lambert>
                </technique>
            </profile_COMMON>
        </effect>
        <effect id="DiagonalID5">
            <profile_COMMON>
                <technique sid="COMMON">
                    <lambert>
                        <diffuse>
                            <color>0 0 1 1</color>
                        </diffuse>
                    </lambert>
                </technique>
            </profile_COMMON>
        </effect>
        <effect id="Black_DiagonalID5">
            <profile_COMMON>
                <technique sid="COMMON">
                    <lambert>
                        <diffuse>
                            <color>0 0 0 1</color>
                        </diffuse>
                    </lambert>
                </technique>
            </profile_COMMON>
        </effect>
<!-- effect:  Four Clock Components -->
        <effect id="ID5">
            <profile_COMMON>
                <technique sid="COMMON">
                    <lambert>
                        <diffuse>
                            <color>0 0 1 1</color>
                        </diffuse>
                    </lambert>
                </technique>
            </profile_COMMON>
        </effect>
        <effect id="InnerID5">
            <profile_COMMON>
                <technique sid="COMMON">
                    <lambert>
                        <diffuse>
                            <color>0.4 0.0 0.7 0.4</color>
                        </diffuse>
                    </lambert>
                </technique>
            </profile_COMMON>
        </effect>
        <effect id="ArrowID5">
            <profile_COMMON>
                <technique sid="COMMON">
                    <lambert>
                        <diffuse>
                            <color>1.0 0.0 0.0 1.0</color>
                        </diffuse>
                    </lambert>
                </technique>
            </profile_COMMON>
        </effect>
        <effect id="HourID5">
            <profile_COMMON>
                <technique sid="COMMON">
                    <lambert>
                        <diffuse>
                            <color>0.0 0.0 0.0 1.0</color>
                        </diffuse>
                    </lambert>
                </technique>
            </profile_COMMON>
        </effect>
    </library_effects>
    <library_materials>
<!-- material:  Four Clock Components -->
        <material id="ID6" name="material">
            <instance_effect url="#ID5" />
        </material>
        <material id="InnerID6" name="Inner_material">
            <instance_effect url="#InnerID5" />
        </material>
        <material id="ArrowID6" name="Arrow_material">
            <instance_effect url="#ArrowID5" />
        </material>
        <material id="HourID6" name="Hour_material">
            <instance_effect url="#HourID5" />
        </material>
        <material id="ID6_EFE" name="material">
            <instance_effect url="#DiffusePurple_00" />
        </material>
<!-- material:  MidPlane Frame -->
        <material id="MidPlaneID6" name="MidPlane_material">
            <instance_effect url="#MidPlaneID5" />
        </material>
<!-- material:  Cylindrical Pointer -->
        <material id="CylID6" name="Cyl_material">
            <instance_effect url="#CylID5" />
        </material>
        <material id="ZupID6" name="Zup_material">
            <instance_effect url="#MidPlaneID5" />
        </material>
        <material id="MarkersID6" name="markers_material">
            <instance_effect url="#MarkersID5" />
        </material>
        <material id="Primary_MarkerID6" name="primary_marker_material">
            <instance_effect url="#DiffuseRed_EFE" />
        </material>
<!-- material:  Letters -->
        <material id="LettersID6" name="material">
            <instance_effect url="#LettersID5" />
        </material>
        <material id="DiagonalID6" name="material">
            <instance_effect url="#DiagonalID5" />
        </material>
        <material id="Black_DiagonalID6" name="material">
            <instance_effect url="#Black_DiagonalID5" />
        </material>
    </library_materials>
    <library_nodes>
<!-- node:  Three clock components -->
        <node id="ID3" name="cube_component">
            <instance_geometry url="#Clock_OuterEdge">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#ID6">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                        </instance_material>
                    </technique_common>
                </bind_material>
            </instance_geometry>
            <instance_geometry url="#Clock_InnerEdge">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#InnerID6">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                        </instance_material>
                    </technique_common>
                </bind_material>
            </instance_geometry>
        </node>
        <node id="ArrowID3" name="cube_component">
            <instance_geometry url="#Clock_ArrowEdge">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#ArrowID6">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                        </instance_material>
                    </technique_common>
                </bind_material>
            </instance_geometry>
        </node>
        <node id="HourID3" name="hour_hand">
            <instance_geometry url="#Clock_HourEdge">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#HourID6">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                        </instance_material>
                    </technique_common>
                </bind_material>
            </instance_geometry>
        </node>
        <node id="ID3_EFE" name="cube_componentEFE">
            <instance_geometry url="#EllipsoidOctant">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#ID6_EFE">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                        </instance_material>
                    </technique_common>
                </bind_material>
            </instance_geometry>
            <instance_geometry url="#ReflectOctant">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#ID6_EFE">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                        </instance_material>
                    </technique_common>
                </bind_material>
            </instance_geometry>
        </node>
<!-- node:  MidPlane Frame -->
        <node id="EqPlane" name="equatorial_plane">
            <instance_geometry url="#EquatorialPlane">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#MidPlaneID6">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                        </instance_material>
                    </technique_common>
                </bind_material>
            </instance_geometry>
        </node>
<!-- node:  Cylindrical Pointer -->
        <node id="CylPointer" name="cylindrical_component">
            <instance_geometry url="#Cylinder">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#CylID6">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                        </instance_material>
                    </technique_common>
                </bind_material>
            </instance_geometry>
        </node>
        <node id="ZupPointer" name="Zup_component">
            <instance_geometry url="#CubeID4">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#ZupID6">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                        </instance_material>
                    </technique_common>
                </bind_material>
            </instance_geometry>
        </node>
        <node id="MarkersID3" name="Lagrange_markers">
          <instance_geometry url="#CubeID4">
            <bind_material>
              <technique_common>
                <instance_material symbol="Material2" target="#MarkersID6">
                  <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                </instance_material>
              </technique_common>
            </bind_material>
          </instance_geometry>
        </node>
        <node id="Primary_MarkerID3" name="Primary_marker">
          <instance_geometry url="#CubeID4">
            <bind_material>
              <technique_common>
                <instance_material symbol="Material2" target="#Primary_MarkerID6">
                  <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                </instance_material>
              </technique_common>
            </bind_material>
          </instance_geometry>
        </node>
<!-- node:  Letters -->
        <node id="LettersID3" name="cube_component">
            <instance_geometry url="#CubeID4">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#LettersID6">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                        </instance_material>
                    </technique_common>
                </bind_material>
            </instance_geometry>
        </node>
        <node id="DiagonalID3" name="diagonal_component">
            <instance_geometry url="#DiagonalID4">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#DiagonalID6">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                        </instance_material>
                    </technique_common>
                </bind_material>
            </instance_geometry>
        </node>
        <node id="Black_DiagonalID3" name="Blackdiagonal_component">
            <instance_geometry url="#DiagonalID4">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#Black_DiagonalID6">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                        </instance_material>
                    </technique_common>
                </bind_material>
            </instance_geometry>
        </node>
    </library_nodes>
    <library_geometries>
<!-- geometry:  Four Clock Components -->
        <geometry id="Clock_OuterEdge">
            <mesh>
<!--
            **********************************************
            *
            *  Insert first portion of clock's structure
            *
            **********************************************
-->
                <source id="Clock_Positions">
                  <float_array id="Coordinates01" count="123"> 0.0  1.0  0.2 1.0  1.0  0.2 1.0  0.0  0.2 1.0 -1.0  0.2 0.0 -1.0  0.2 -1.0 -1.0  0.2 -1.0  0.0  0.2 -1.0  1.0  0.2 0.0  1.0 -0.2 1.0  1.0 -0.2 1.0  0.0 -0.2 1.0 -1.0 -0.2 0.0 -1.0 -0.2 -1.0 -1.0 -0.2 -1.0  0.0 -0.2 -1.0  1.0 -0.2 0.9  0.0  0.2 0.779423 0.45 0.2 0.45 0.779423 0.2 0.0  0.9  0.2 -0.45 0.779423 0.2 -0.779423 0.45 0.2 -0.9 0.0 0.2 -0.779423 -0.45 0.2 -0.45 -0.779423 0.2 0.0 -0.9 0.2 0.45 -0.779423 0.2 0.779423 -0.45 0.2 -0.9  0.0  -0.2 -0.779423 0.45 -0.2 -0.45 0.779423 -0.2 -0.0  0.9  -0.2 0.45 0.779423 -0.2 0.779423 0.45 -0.2 0.9 0.0 -0.2 0.779423 -0.45 -0.2 0.45 -0.779423 -0.2 -0.0 -0.9 -0.2 -0.45 -0.779423 -0.2 -0.779423 -0.45 -0.2  0.0 0.0 -0.2</float_array>
                  <technique_common>
                    <accessor source="#Coordinates01" count="41" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                    </accessor>
                  </technique_common>
                </source>
                <source id="Clock_Normals">
                  <float_array id="InnerNormals01" count="18">
1.0  0.0  0.0
-1.0  0.0  0.0
0.0  1.0  0.0
0.0 -1.0  0.0
0.0  0.0  1.0
0.0  0.0 -1.0
                  </float_array>
                    <technique_common>
                        <accessor source="#InnerNormals01" count="6" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                        </accessor>
                    </technique_common>
                </source>
                <vertices id="Clock_Vertices">
                    <input semantic="POSITION" source="#Clock_Positions" />
                </vertices>
                <polylist count="56" material="Material2">
                    <input semantic="VERTEX" source="#Clock_Vertices" offset="0" />
                    <input semantic="NORMAL" source="#Clock_Normals" offset="1" />
<vcount> 3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3</vcount>
<p> 0 2 1 2 8 2  1 2 9 2 8 2  7 2 0 2 15 2  0 2 8 2 15 2 1 0 2 0 9 0  2 0 10 0 9 0  2 0 3 0 10 0  3 0 11 0 10 0 3 3 4 3 11 3  4 3 12 3 11 3  4 3 5 3 12 3  5 3 13 3 12 3 5 1 6 1 13 1  6 1 14 1 13 1  6 1 7 1 14 1  7 1 15 1 14 1 2 4 17 4 16 4  2 4 1 4 17 4  1 4 18 4 17 4  1 4 0 4 18 4  0 4 19 4 18 4 0 4 20 4 19 4  0 4 7 4 20 4  7 4 21 4 20 4  7 4 6 4 21 4  6 4 22 4 21 4 6 4 23 4 22 4  6 4 5 4 23 4  5 4 24 4 23 4  5 4 4 4 24 4  4 4 25 4 24 4 4 4 26 4 25 4  4 4 3 4 26 4  3 4 27 4 26 4  3 4 2 4 27 4  2 4 16 4 27 4 14 5 29 5 28 5  14 5 15 5 29 5  15 5 30 5 29 5  15 5 8 5 30 5  8 5 31 5 30 5 8 5 32 5 31 5  8 5 9 5 32 5  9 5 33 5 32 5  9 5 10 5 33 5  10 5 34 5 33 5 10 5 35 5 34 5  10 5 11 5 35 5  11 5 36 5 35 5  11 5 12 5 36 5  12 5 37 5 36 5 12 5 38 5 37 5  12 5 13 5 38 5  13 5 39 5 38 5  13 5 14 5 39 5  14 5 28 5 39 5 </p>
                </polylist>
            </mesh>
        </geometry>
        <geometry id="Clock_InnerEdge">
            <mesh>
<!--
            **********************************************
            *
            *  Insert second portion of clock's structure
            *
            **********************************************
-->
                <source id="Clock_InnerPositions">
                  <float_array id="InnerCoordinates01" count="123">
0.0  1.0  0.2 1.0  1.0  0.2 1.0  0.0  0.2 1.0 -1.0  0.2 0.0 -1.0  0.2 -1.0 -1.0  0.2 -1.0  0.0  0.2 -1.0  1.0  0.2 0.0  1.0 -0.2 1.0  1.0 -0.2 1.0  0.0 -0.2 1.0 -1.0 -0.2 0.0 -1.0 -0.2 -1.0 -1.0 -0.2 -1.0  0.0 -0.2 -1.0  1.0 -0.2 0.9  0.0  0.2 0.779423 0.45 0.2 0.45 0.779423 0.2 0.0  0.9  0.2 -0.45 0.779423 0.2 -0.779423 0.45 0.2 -0.9 0.0 0.2 -0.779423 -0.45 0.2 -0.45 -0.779423 0.2 0.0 -0.9 0.2 0.45 -0.779423 0.2 0.779423 -0.45 0.2 -0.9  0.0  -0.2 -0.779423 0.45 -0.2 -0.45 0.779423 -0.2 -0.0  0.9  -0.2 0.45 0.779423 -0.2 0.779423 0.45 -0.2 0.9 0.0 -0.2 0.779423 -0.45 -0.2 0.45 -0.779423 -0.2 -0.0 -0.9 -0.2 -0.45 -0.779423 -0.2 -0.779423 -0.45 -0.2  0.0 0.0 -0.2</float_array>
                  <technique_common>
                    <accessor source="#InnerCoordinates01" count="41" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                    </accessor>
                  </technique_common>
                </source>
                <source id="Clock_InnerNormals">
                  <float_array id="InnerNormals01" count="54">
1.0  0.0  0.0
-1.0  0.0  0.0
0.0  1.0  0.0
0.0 -1.0  0.0
0.0  0.0  1.0
0.0  0.0 -1.0
-0.965926 -0.258819 0.0
-0.707107 -0.707107 0.0
-0.258819 -0.965926 0.0
  0.258819 -0.965926 0.0
  0.707107 -0.707107 0.0
  0.965926 -0.258819 0.0
  0.965926  0.258819 0.0
  0.707107  0.707107 0.0
  0.258819  0.965926 0.0
-0.258819  0.965926 0.0
-0.707107  0.707107 0.0
-0.965926  0.258819 0.0
                  </float_array>
                    <technique_common>
                        <accessor source="#InnerNormals01" count="18" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                        </accessor>
                    </technique_common>
                </source>
                <vertices id="Clock_InnerVertices">
                    <input semantic="POSITION" source="#Clock_InnerPositions" />
                </vertices>
                <polylist count="24" material="Material2">
                    <input semantic="VERTEX" source="#Clock_InnerVertices" offset="0" />
                    <input semantic="NORMAL" source="#Clock_InnerNormals" offset="1"/>
<vcount>4 4 4 4  4 4 4 4  4 4 4 4  3 3 3 3  3 3 3 3  3 3 3 3</vcount>
<p> 16 6 17 6 33 6 34 6 17 7 18 7 32 7 33 7 18 8 19 8 31 8 32 8 19 9 20 9 30 9 31 9 20 10 21 10 29 10 30 10 21 11 22 11 28 11 29 11 22 12 23 12 39 12 28 12 23 13 24 13 38 13 39 13 24 14 25 14 37 14 38 14 25 15 26 15 36 15 37 15 26 16 27 16 35 16 36 16 27 17 16 17 34 17 35 17 28 5 29 5 40 5 29 5 30 5 40 5 30 5 31 5 40 5 31 5 32 5 40 5 32 5 33 5 40 5 33 5 34 5 40 5 34 5 35 5 40 5 35 5 36 5 40 5 36 5 37 5 40 5 37 5 38 5 40 5 38 5 39 5 40 5 39 5 28 5 40 5 </p>
              </polylist>
            </mesh>
        </geometry>
        <geometry id="Clock_ArrowEdge">
            <mesh>
<!--
            **********************************************
            *
            *  Insert arrow portion of clock's structure
            *
            **********************************************
-->
                <source id="Clock_ArrowPositions">
                  <float_array id="ArrowCoordinates01" count="30"> 0.0  0.85 0.25 0.1  0.0 0.25 0.0 -0.2 0.25 -0.1  0.0 0.25 0.0  0.85 0.05 0.1  0.0 0.05 0.0 -0.2 0.05 -0.1  0.0 0.05 0.0  0.0 0.25 0.0  0.0 0.05 </float_array>
                  <technique_common>
                    <accessor source="#ArrowCoordinates01" count="10" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                    </accessor>
                  </technique_common>
                </source>
                <source id="Clock_ArrowNormals">
                  <float_array id="ArrowNormals01" count="18">
0  0  1
0  0 -1
0.993151  0.116841 0.0
0.447214 -0.894427 0.0
-0.447214 -0.894427 0.0
-0.993151  0.116841 0.0
                  </float_array>
                    <technique_common>
                        <accessor source="#ArrowNormals01" count="6" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                        </accessor>
                    </technique_common>
                </source>
                <vertices id="Clock_ArrowVertices">
                    <input semantic="POSITION" source="#Clock_ArrowPositions" />
                </vertices>
                <polylist count="12" material="Material2">
                    <input semantic="VERTEX" source="#Clock_ArrowVertices" offset="0" />
                    <input semantic="NORMAL" source="#Clock_ArrowNormals" offset="1"/>
<vcount>3 3 3 3 3 3 3 3 4 4 4 4</vcount>
<p> 0 0 8 0 1 0 1 0 8 0 2 0 2 0 8 0 3 0 3 0 8 0 0 0 4 1 5 1 9 1 5 1 6 1 9 1 6 1 7 1 9 1 7 1 4 1 9 1 0 2 1 2 5 2 4 2 1 3 2 3 6 3 5 3 2 4 3 4 7 4 6 4 3 5 0 5 4 5 7 5 </p>
              </polylist>
            </mesh>
        </geometry>
        <geometry id="Clock_HourEdge">
            <mesh>
<!--
            **********************************************
            *
            *  Insert hour_hand portion of clock's structure
            *
            **********************************************
-->
                <source id="Clock_HourPositions">
                  <float_array id="HourCoordinates01" count="30"> 0.0  0.85 0.25 0.1  0.0 0.25 0.0 -0.2 0.25 -0.1  0.0 0.25 0.0  0.85 0.05 0.1  0.0 0.05 0.0 -0.2 0.05 -0.1  0.0 0.05 0.0  0.0 0.25 0.0  0.0 0.05 </float_array>
                  <technique_common>
                    <accessor source="#HourCoordinates01" count="10" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                    </accessor>
                  </technique_common>
                </source>
                <source id="Clock_HourNormals">
                  <float_array id="HourNormals01" count="18">
0  0  1
0  0 -1
0.993151  0.116841 0.0
0.447214 -0.894427 0.0
-0.447214 -0.894427 0.0
-0.993151  0.116841 0.0
                  </float_array>
                    <technique_common>
                        <accessor source="#HourNormals01" count="6" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                        </accessor>
                    </technique_common>
                </source>
                <vertices id="Clock_HourVertices">
                    <input semantic="POSITION" source="#Clock_HourPositions" />
                </vertices>
                <polylist count="12" material="Material2">
                    <input semantic="VERTEX" source="#Clock_HourVertices" offset="0" />
                    <input semantic="NORMAL" source="#Clock_HourNormals" offset="1"/>
<vcount>3 3 3 3 3 3 3 3 4 4 4 4</vcount>
<p> 0 0 8 0 1 0 1 0 8 0 2 0 2 0 8 0 3 0 3 0 8 0 0 0 4 1 5 1 9 1 5 1 6 1 9 1 6 1 7 1 9 1 7 1 4 1 9 1 0 2 1 2 5 2 4 2 1 3 2 3 6 3 5 3 2 4 3 4 7 4 6 4 3 5 0 5 4 5 7 5 </p>
              </polylist>
            </mesh>
        </geometry>
<!-- geometry:  Letters -->
        <geometry id="CubeID4">
            <mesh>
                <source id="CubeID7_Positions">
                    <float_array id="CoordinatesID10" count="24">
  -0.5  -0.5  -0.5
  -0.5  -0.5  0.5
  -0.5  0.5  -0.5
  -0.5  0.5  0.5
    0.5  -0.5  -0.5
    0.5  -0.5  0.5
    0.5  0.5  -0.5
    0.5  0.5  0.5
                    </float_array>
                    <technique_common>
                        <accessor source="#CoordinatesID10" count="8" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                        </accessor>
                    </technique_common>
                </source>
                <source id="CubeID8_Normals">
                    <float_array id="NormalsID11" count="18">
    0  0 -1
    0  0  1
    0 -1  0
    0  1  0
  -1  0  0
    1  0  0
                    </float_array>
                    <technique_common>
                        <accessor source="#NormalsID11" count="6" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                        </accessor>
                    </technique_common>
                </source>
                <vertices id="CubeID9_Vertices">
                    <input semantic="POSITION" source="#CubeID7_Positions" />
                </vertices>
                <polylist count="12" material="Material2">
                    <input semantic="VERTEX" source="#CubeID9_Vertices" offset="0" />
                    <input semantic="NORMAL" source="#CubeID8_Normals" offset="1" />
<vcount>3 3 3 3  3 3 3 3  3 3 3 3</vcount>
<p>
0 0 2 0 6 0  0 0 6 0 4 0
1 1 7 1 3 1  1 1 5 1 7 1
0 2 4 2 5 2  0 2 5 2 1 2
2 3 3 3 7 3  2 3 7 3 6 3
0 4 1 4 3 4  0 4 3 4 2 4
4 5 6 5 7 5  4 5 7 5 5 5
</p>
                </polylist>
          </mesh>
        </geometry>
        <geometry id="DiagonalID4">
            <mesh>
                <source id="DiagonalID7_Positions">
                    <float_array id="Diag_CoordinatesID10" count="24">
  -0.5  -0.5  -0.5
  -0.5  -0.5  0.5
  -0.5  0.5  -0.5
  -0.5  0.5  0.5
    0.5  -0.5  -0.5
    0.5  -0.5  0.5
    0.5  0.5  -0.5
    0.5  0.5  0.5
                    </float_array>
                    <technique_common>
                        <accessor source="#Diag_CoordinatesID10" count="8" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                        </accessor>
                    </technique_common>
                </source>
                <source id="DiagonalID8_Normals">
                    <float_array id="Diagonal_NormalsID11" count="21">
    0  0 -1
    0  0  1
    0 -1  0
    0  1  0
  -1  0  0
    1  0  0
    0  -0.707 0.707
                    </float_array>
                    <technique_common>
                        <accessor source="#Diagonal_NormalsID11" count="7" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                        </accessor>
                    </technique_common>
                </source>
                <vertices id="DiagonalID9_Vertices">
                    <input semantic="POSITION" source="#DiagonalID7_Positions" />
                </vertices>
                <polylist count="8" material="Material2">
                    <input semantic="VERTEX" source="#DiagonalID9_Vertices" offset="0" />
                    <input semantic="NORMAL" source="#DiagonalID8_Normals" offset="1" />
<vcount>3 3 3 3  3 3 3 3</vcount>
<p>
0 0 2 0 6 0  0 0 6 0 4 0
2 3 3 3 7 3  2 3 7 3 6 3
0 4 3 4 2 4  4 5 6 5 7 5
0 6 7 6 3 6  0 6 4 6 7 6
</p>
                </polylist>
          </mesh>
        </geometry>
<!-- geometry:  Cubes for Lagrangian Markers -->
        <geometry id="CubeID4">
            <mesh>
                <source id="CubeID7_Positions">
                    <float_array id="CoordinatesID10" count="24">
  -0.5  -0.5  -0.5
  -0.5  -0.5  0.5
  -0.5  0.5  -0.5
  -0.5  0.5  0.5
    0.5  -0.5  -0.5
    0.5  -0.5  0.5
    0.5  0.5  -0.5
    0.5  0.5  0.5
                    </float_array>
                    <technique_common>
                        <accessor source="#CoordinatesID10" count="8" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                        </accessor>
                    </technique_common>
                </source>
                <source id="CubeID8_Normals">
                    <float_array id="NormalsID11" count="18">
    0  0 -1
    0  0  1
    0 -1  0
    0  1  0
  -1  0  0
    1  0  0
                    </float_array>
                    <technique_common>
                        <accessor source="#NormalsID11" count="6" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                        </accessor>
                    </technique_common>
                </source>
                <vertices id="CubeID9_Vertices">
                    <input semantic="POSITION" source="#CubeID7_Positions" />
                </vertices>
                <polylist count="12" material="Material2">
                    <input semantic="VERTEX" source="#CubeID9_Vertices" offset="0" />
                    <input semantic="NORMAL" source="#CubeID8_Normals" offset="1" />
<vcount>3 3 3 3  3 3 3 3  3 3 3 3</vcount>
<p>
0 0 2 0 6 0  0 0 6 0 4 0
1 1 7 1 3 1  1 1 5 1 7 1
0 2 4 2 5 2  0 2 5 2 1 2
2 3 3 3 7 3  2 3 7 3 6 3
0 4 1 4 3 4  0 4 3 4 2 4
4 5 6 5 7 5  4 5 7 5 5 5
</p>
                </polylist>
          </mesh>
        </geometry>
<!-- geometry:  Cylindrical Pointer -->
        <geometry id="Cylinder">
            <mesh>
                <source id="Cyl_Positions">
<float_array id="CylCoords01" count="54">
  -1.0  -0.9239  0.3827
  -1.0  -0.3827  0.9239
  -1.0  0.3827  0.9239
  -1.0  0.9239  0.3827
  -1.0  0.9239  -0.3827
  -1.0  0.3827  -0.9239
  -1.0  -0.3827  -0.9239
  -1.0  -0.9239  -0.3827
  -1.0  0.0000  0.0000
  1.0  -0.9239  0.3827
  1.0  -0.3827  0.9239
  1.0  0.3827  0.9239
  1.0  0.9239  0.3827
  1.0  0.9239  -0.3827
  1.0  0.3827  -0.9239
  1.0  -0.3827  -0.9239
  1.0  -0.9239  -0.3827
  1.5  0.0000  0.0000
</float_array>
                  <technique_common>
                    <accessor source="#CylCoords01" count="18" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                    </accessor>
                  </technique_common>
                </source>
                <source id="Cyl_Normals">
                  <float_array id="CylNormals01" count="54">
    1.0  0.0  0.0
  -1.0  0.0  0.0
    0.0  1.0  0.0
    0.0 -1.0  0.0
    0.0  0.0  1.0
    0.0  0.0 -1.0
    0.0  0.7071  0.7071
    0.0  0.7071 -0.7071
    0.0 -0.7071  0.7071
    0.0 -0.7071 -0.7071
    0.8795  -0.3365  0.3365
    0.8795  0.0000  0.4760
    0.8795  0.3365  0.3365
    0.8795  0.4760  0.0000
    0.8795  0.3365  -0.3365
    0.8795  0.0000  -0.4760
    0.8795  -0.3365  -0.3365
    0.8795  -0.4760  0.0000
                  </float_array>
                    <technique_common>
                        <accessor source="#CylNormals01" count="18" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                        </accessor>
                    </technique_common>
                </source>
                <vertices id="Cyl_Vertices">
                    <input semantic="POSITION" source="#Cyl_Positions" />
                </vertices>
                <polylist count="32" material="Material2">
                    <input semantic="VERTEX" source="#Cyl_Vertices" offset="0" />
                    <input semantic="NORMAL" source="#Cyl_Normals" offset="1" />
<vcount>3 3 3 3  3 3 3 3  3 3 3 3  3 3 3 3  3 3 3 3  3 3 3 3  3 3 3 3  3 3 3 3</vcount>
<p>
  0 1  1 1  8 1
  1 1  2 1  8 1
  2 1  3 1  8 1
  3 1  4 1  8 1
  4 1  5 1  8 1
  5 1  6 1  8 1
  6 1  7 1  8 1
  7 1  0 1  8 1
  10 10  9 10  17 10
  11 11  10 11  17 11
  12 12  11 12  17 12
  13 13  12 13  17 13
  14 14  13 14  17 14
  15 15  14 15  17 15
  16 16  15 16  17 16
  9 17  16 17  17 17
  0 8  9 8  1 8
  1 8  9 8  10 8
  1 4  10 4  2 4
  2 4  10 4  11 4
  2 6  11 6  3 6
  3 6  11 6  12 6
  3 2  12 2  4 2
  4 2  12 2  13 2
  4 7  13 7  5 7
  5 7  13 7  14 7
  5 5  14 5  6 5
  6 5  14 5  15 5
  6 9  15 9  7 9
  7 9  15 9  16 9
  7 3  16 3  0 3
  0 3  16 3  9 3
</p>
                </polylist>
            </mesh>
        </geometry>
<!--
            **********************************************
            *
            *  Insert Geometry of Ellipsoid Octant
            *
            **********************************************
-->
<geometry id="EllipsoidOctant">
  <mesh>
<source id="Ellipsoid_Positions">
<float_array id="Ellipsoid_Coordinates" count=" 1563">
    0.0000    0.0000    0.3850
    0.0000    0.4100    0.0000
    0.0400    0.4097    0.0000
    0.0800    0.4087    0.0000
    0.1200    0.4070    0.0000
    0.1600    0.4047    0.0000
    0.2000    0.4017    0.0000
    0.2400    0.3980    0.0000
    0.2800    0.3936    0.0000
    0.3200    0.3884    0.0000
    0.3600    0.3825    0.0000
    0.4000    0.3758    0.0000
    0.4400    0.3682    0.0000
    0.4800    0.3597    0.0000
    0.5200    0.3502    0.0000
    0.5600    0.3397    0.0000
    0.6000    0.3280    0.0000
    0.6400    0.3150    0.0000
    0.6800    0.3006    0.0000
    0.7200    0.2845    0.0000
    0.7600    0.2665    0.0000
    0.8000    0.2460    0.0000
    0.8400    0.2225    0.0000
    0.8800    0.1947    0.0000
    0.9200    0.1607    0.0000
    0.9600    0.1148    0.0000
    1.0000    0.0000    0.0000
    0.0000    0.4095    0.0192
    0.0399    0.4092    0.0192
    0.0799    0.4082    0.0192
    0.1198    0.4065    0.0192
    0.1598    0.4042    0.0192
    0.1997    0.4012    0.0192
    0.2397    0.3975    0.0192
    0.2796    0.3931    0.0192
    0.3196    0.3880    0.0192
    0.3595    0.3820    0.0192
    0.3995    0.3753    0.0192
    0.4394    0.3677    0.0192
    0.4794    0.3592    0.0192
    0.5193    0.3498    0.0192
    0.5593    0.3393    0.0192
    0.5992    0.3276    0.0192
    0.6392    0.3146    0.0192
    0.6791    0.3002    0.0192
    0.7191    0.2842    0.0192
    0.7590    0.2661    0.0192
    0.7990    0.2457    0.0192
    0.8389    0.2222    0.0192
    0.8789    0.1945    0.0192
    0.9188    0.1605    0.0192
    0.9588    0.1147    0.0192
    0.9987    0.0000    0.0192
    0.0000    0.4079    0.0385
    0.0398    0.4076    0.0385
    0.0796    0.4066    0.0385
    0.1194    0.4050    0.0385
    0.1592    0.4027    0.0385
    0.1990    0.3997    0.0385
    0.2388    0.3960    0.0385
    0.2786    0.3916    0.0385
    0.3184    0.3865    0.0385
    0.3582    0.3806    0.0385
    0.3980    0.3739    0.0385
    0.4378    0.3663    0.0385
    0.4776    0.3579    0.0385
    0.5174    0.3485    0.0385
    0.5572    0.3380    0.0385
    0.5970    0.3264    0.0385
    0.6368    0.3135    0.0385
    0.6766    0.2991    0.0385
    0.7164    0.2831    0.0385
    0.7562    0.2651    0.0385
    0.7960    0.2448    0.0385
    0.8358    0.2213    0.0385
    0.8756    0.1938    0.0385
    0.9154    0.1599    0.0385
    0.9552    0.1142    0.0385
    0.9950    0.0000    0.0385
    0.0000    0.4054    0.0578
    0.0395    0.4050    0.0578
    0.0791    0.4041    0.0578
    0.1186    0.4024    0.0578
    0.1582    0.4001    0.0578
    0.1977    0.3972    0.0578
    0.2373    0.3935    0.0578
    0.2768    0.3891    0.0578
    0.3164    0.3840    0.0578
    0.3559    0.3782    0.0578
    0.3955    0.3715    0.0578
    0.4350    0.3640    0.0578
    0.4746    0.3556    0.0578
    0.5141    0.3462    0.0578
    0.5537    0.3358    0.0578
    0.5932    0.3243    0.0578
    0.6328    0.3115    0.0578
    0.6723    0.2972    0.0578
    0.7119    0.2813    0.0578
    0.7514    0.2635    0.0578
    0.7909    0.2432    0.0578
    0.8305    0.2199    0.0578
    0.8700    0.1925    0.0578
    0.9096    0.1589    0.0578
    0.9491    0.1135    0.0578
    0.9887    0.0000    0.0578
    0.0000    0.4017    0.0770
    0.0392    0.4014    0.0770
    0.0784    0.4004    0.0770
    0.1176    0.3988    0.0770
    0.1568    0.3965    0.0770
    0.1960    0.3936    0.0770
    0.2352    0.3900    0.0770
    0.2743    0.3856    0.0770
    0.3135    0.3806    0.0770
    0.3527    0.3748    0.0770
    0.3919    0.3682    0.0770
    0.4311    0.3607    0.0770
    0.4703    0.3524    0.0770
    0.5095    0.3431    0.0770
    0.5487    0.3328    0.0770
    0.5879    0.3214    0.0770
    0.6271    0.3087    0.0770
    0.6663    0.2945    0.0770
    0.7055    0.2788    0.0770
    0.7446    0.2611    0.0770
    0.7838    0.2410    0.0770
    0.8230    0.2180    0.0770
    0.8622    0.1908    0.0770
    0.9014    0.1574    0.0770
    0.9406    0.1125    0.0770
    0.9798    0.0000    0.0770
    0.0000    0.3970    0.0963
    0.0387    0.3967    0.0963
    0.0775    0.3957    0.0963
    0.1162    0.3941    0.0963
    0.1549    0.3919    0.0963
    0.1936    0.3890    0.0963
    0.2324    0.3854    0.0963
    0.2711    0.3811    0.0963
    0.3098    0.3761    0.0963
    0.3486    0.3704    0.0963
    0.3873    0.3638    0.0963
    0.4260    0.3565    0.0963
    0.4648    0.3483    0.0963
    0.5035    0.3391    0.0963
    0.5422    0.3289    0.0963
    0.5809    0.3176    0.0963
    0.6197    0.3050    0.0963
    0.6584    0.2911    0.0963
    0.6971    0.2755    0.0963
    0.7359    0.2580    0.0963
    0.7746    0.2382    0.0963
    0.8133    0.2154    0.0963
    0.8521    0.1886    0.0963
    0.8908    0.1556    0.0963
    0.9295    0.1112    0.0963
    0.9682    0.0000    0.0963
    0.0000    0.3911    0.1155
    0.0382    0.3908    0.1155
    0.0763    0.3899    0.1155
    0.1145    0.3883    0.1155
    0.1526    0.3861    0.1155
    0.1908    0.3832    0.1155
    0.2289    0.3797    0.1155
    0.2671    0.3755    0.1155
    0.3053    0.3705    0.1155
    0.3434    0.3649    0.1155
    0.3816    0.3585    0.1155
    0.4197    0.3512    0.1155
    0.4579    0.3431    0.1155
    0.4960    0.3341    0.1155
    0.5342    0.3240    0.1155
    0.5724    0.3129    0.1155
    0.6105    0.3005    0.1155
    0.6487    0.2868    0.1155
    0.6868    0.2714    0.1155
    0.7250    0.2542    0.1155
    0.7632    0.2347    0.1155
    0.8013    0.2122    0.1155
    0.8395    0.1858    0.1155
    0.8776    0.1533    0.1155
    0.9158    0.1095    0.1155
    0.9539    0.0000    0.1155
    0.0000    0.3841    0.1348
    0.0375    0.3838    0.1348
    0.0749    0.3828    0.1348
    0.1124    0.3813    0.1348
    0.1499    0.3791    0.1348
    0.1873    0.3763    0.1348
    0.2248    0.3728    0.1348
    0.2623    0.3687    0.1348
    0.2998    0.3639    0.1348
    0.3372    0.3583    0.1348
    0.3747    0.3520    0.1348
    0.4122    0.3449    0.1348
    0.4496    0.3369    0.1348
    0.4871    0.3281    0.1348
    0.5246    0.3182    0.1348
    0.5620    0.3073    0.1348
    0.5995    0.2951    0.1348
    0.6370    0.2816    0.1348
    0.6745    0.2665    0.1348
    0.7119    0.2496    0.1348
    0.7494    0.2304    0.1348
    0.7869    0.2084    0.1348
    0.8243    0.1824    0.1348
    0.8618    0.1505    0.1348
    0.8993    0.1075    0.1348
    0.9367    0.0000    0.1348
    0.0000    0.3758    0.1540
    0.0367    0.3755    0.1540
    0.0733    0.3746    0.1540
    0.1100    0.3731    0.1540
    0.1466    0.3709    0.1540
    0.1833    0.3682    0.1540
    0.2200    0.3648    0.1540
    0.2566    0.3607    0.1540
    0.2933    0.3560    0.1540
    0.3299    0.3506    0.1540
    0.3666    0.3444    0.1540
    0.4033    0.3374    0.1540
    0.4399    0.3297    0.1540
    0.4766    0.3210    0.1540
    0.5132    0.3113    0.1540
    0.5499    0.3006    0.1540
    0.5866    0.2887    0.1540
    0.6232    0.2755    0.1540
    0.6599    0.2608    0.1540
    0.6966    0.2442    0.1540
    0.7332    0.2255    0.1540
    0.7699    0.2039    0.1540
    0.8065    0.1785    0.1540
    0.8432    0.1473    0.1540
    0.8799    0.1052    0.1540
    0.9165    0.0000    0.1540
    0.0000    0.3661    0.1732
    0.0357    0.3658    0.1732
    0.0714    0.3650    0.1732
    0.1072    0.3635    0.1732
    0.1429    0.3614    0.1732
    0.1786    0.3587    0.1732
    0.2143    0.3554    0.1732
    0.2500    0.3515    0.1732
    0.2858    0.3469    0.1732
    0.3215    0.3416    0.1732
    0.3572    0.3356    0.1732
    0.3929    0.3288    0.1732
    0.4287    0.3212    0.1732
    0.4644    0.3127    0.1732
    0.5001    0.3033    0.1732
    0.5358    0.2929    0.1732
    0.5715    0.2813    0.1732
    0.6073    0.2685    0.1732
    0.6430    0.2541    0.1732
    0.6787    0.2380    0.1732
    0.7144    0.2197    0.1732
    0.7501    0.1987    0.1732
    0.7859    0.1739    0.1732
    0.8216    0.1435    0.1732
    0.8573    0.1025    0.1732
    0.8930    0.0000    0.1732
    0.0000    0.3551    0.1925
    0.0346    0.3548    0.1925
    0.0693    0.3539    0.1925
    0.1039    0.3525    0.1925
    0.1386    0.3505    0.1925
    0.1732    0.3479    0.1925
    0.2078    0.3447    0.1925
    0.2425    0.3409    0.1925
    0.2771    0.3364    0.1925
    0.3118    0.3313    0.1925
    0.3464    0.3254    0.1925
    0.3811    0.3189    0.1925
    0.4157    0.3115    0.1925
    0.4503    0.3033    0.1925
    0.4850    0.2942    0.1925
    0.5196    0.2841    0.1925
    0.5543    0.2728    0.1925
    0.5889    0.2603    0.1925
    0.6235    0.2464    0.1925
    0.6582    0.2308    0.1925
    0.6928    0.2130    0.1925
    0.7275    0.1927    0.1925
    0.7621    0.1686    0.1925
    0.7967    0.1392    0.1925
    0.8314    0.0994    0.1925
    0.8660    0.0000    0.1925
    0.0000    0.3424    0.2118
    0.0334    0.3421    0.2118
    0.0668    0.3413    0.2118
    0.1002    0.3399    0.2118
    0.1336    0.3380    0.2118
    0.1670    0.3355    0.2118
    0.2004    0.3324    0.2118
    0.2338    0.3287    0.2118
    0.2673    0.3244    0.2118
    0.3007    0.3195    0.2118
    0.3341    0.3138    0.2118
    0.3675    0.3075    0.2118
    0.4009    0.3004    0.2118
    0.4343    0.2925    0.2118
    0.4677    0.2837    0.2118
    0.5011    0.2739    0.2118
    0.5345    0.2631    0.2118
    0.5679    0.2511    0.2118
    0.6013    0.2376    0.2118
    0.6347    0.2225    0.2118
    0.6681    0.2055    0.2118
    0.7015    0.1858    0.2118
    0.7349    0.1626    0.2118
    0.7684    0.1342    0.2118
    0.8018    0.0959    0.2118
    0.8352    0.0000    0.2118
    0.0000    0.3280    0.2310
    0.0320    0.3277    0.2310
    0.0640    0.3269    0.2310
    0.0960    0.3256    0.2310
    0.1280    0.3238    0.2310
    0.1600    0.3214    0.2310
    0.1920    0.3184    0.2310
    0.2240    0.3149    0.2310
    0.2560    0.3108    0.2310
    0.2880    0.3060    0.2310
    0.3200    0.3006    0.2310
    0.3520    0.2945    0.2310
    0.3840    0.2877    0.2310
    0.4160    0.2802    0.2310
    0.4480    0.2717    0.2310
    0.4800    0.2624    0.2310
    0.5120    0.2520    0.2310
    0.5440    0.2405    0.2310
    0.5760    0.2276    0.2310
    0.6080    0.2132    0.2310
    0.6400    0.1968    0.2310
    0.6720    0.1780    0.2310
    0.7040    0.1558    0.2310
    0.7360    0.1285    0.2310
    0.7680    0.0918    0.2310
    0.8000    0.0000    0.2310
    0.0000    0.3116    0.2502
    0.0304    0.3113    0.2502
    0.0608    0.3106    0.2502
    0.0912    0.3093    0.2502
    0.1216    0.3076    0.2502
    0.1520    0.3053    0.2502
    0.1824    0.3025    0.2502
    0.2128    0.2991    0.2502
    0.2432    0.2952    0.2502
    0.2736    0.2907    0.2502
    0.3040    0.2856    0.2502
    0.3344    0.2798    0.2502
    0.3648    0.2733    0.2502
    0.3952    0.2661    0.2502
    0.4256    0.2581    0.2502
    0.4560    0.2493    0.2502
    0.4864    0.2394    0.2502
    0.5168    0.2284    0.2502
    0.5472    0.2162    0.2502
    0.5775    0.2025    0.2502
    0.6079    0.1869    0.2502
    0.6383    0.1691    0.2502
    0.6687    0.1480    0.2502
    0.6991    0.1221    0.2502
    0.7295    0.0872    0.2502
    0.7599    0.0000    0.2502
    0.0000    0.2928    0.2695
    0.0286    0.2926    0.2695
    0.0571    0.2919    0.2695
    0.0857    0.2907    0.2695
    0.1143    0.2890    0.2695
    0.1428    0.2869    0.2695
    0.1714    0.2842    0.2695
    0.2000    0.2811    0.2695
    0.2285    0.2774    0.2695
    0.2571    0.2732    0.2695
    0.2857    0.2684    0.2695
    0.3142    0.2629    0.2695
    0.3428    0.2569    0.2695
    0.3714    0.2501    0.2695
    0.3999    0.2426    0.2695
    0.4285    0.2342    0.2695
    0.4571    0.2250    0.2695
    0.4856    0.2147    0.2695
    0.5142    0.2032    0.2695
    0.5427    0.1903    0.2695
    0.5713    0.1757    0.2695
    0.5999    0.1589    0.2695
    0.6284    0.1391    0.2695
    0.6570    0.1148    0.2695
    0.6856    0.0820    0.2695
    0.7141    0.0000    0.2695
    0.0000    0.2712    0.2888
    0.0265    0.2710    0.2888
    0.0529    0.2703    0.2888
    0.0794    0.2692    0.2888
    0.1058    0.2677    0.2888
    0.1323    0.2657    0.2888
    0.1587    0.2633    0.2888
    0.1852    0.2603    0.2888
    0.2117    0.2569    0.2888
    0.2381    0.2530    0.2888
    0.2646    0.2485    0.2888
    0.2910    0.2435    0.2888
    0.3175    0.2379    0.2888
    0.3439    0.2316    0.2888
    0.3704    0.2247    0.2888
    0.3969    0.2170    0.2888
    0.4233    0.2084    0.2888
    0.4498    0.1988    0.2888
    0.4762    0.1882    0.2888
    0.5027    0.1763    0.2888
    0.5292    0.1627    0.2888
    0.5556    0.1471    0.2888
    0.5821    0.1288    0.2888
    0.6085    0.1063    0.2888
    0.6350    0.0759    0.2888
    0.6614    0.0000    0.2888
    0.0000    0.2460    0.3080
    0.0240    0.2458    0.3080
    0.0480    0.2452    0.3080
    0.0720    0.2442    0.3080
    0.0960    0.2428    0.3080
    0.1200    0.2410    0.3080
    0.1440    0.2388    0.3080
    0.1680    0.2362    0.3080
    0.1920    0.2331    0.3080
    0.2160    0.2295    0.3080
    0.2400    0.2255    0.3080
    0.2640    0.2209    0.3080
    0.2880    0.2158    0.3080
    0.3120    0.2101    0.3080
    0.3360    0.2038    0.3080
    0.3600    0.1968    0.3080
    0.3840    0.1890    0.3080
    0.4080    0.1804    0.3080
    0.4320    0.1707    0.3080
    0.4560    0.1599    0.3080
    0.4800    0.1476    0.3080
    0.5040    0.1335    0.3080
    0.5280    0.1168    0.3080
    0.5520    0.0964    0.3080
    0.5760    0.0689    0.3080
    0.6000    0.0000    0.3080
    0.0000    0.2160    0.3272
    0.0211    0.2158    0.3272
    0.0421    0.2153    0.3272
    0.0632    0.2144    0.3272
    0.0843    0.2132    0.3272
    0.1054    0.2116    0.3272
    0.1264    0.2097    0.3272
    0.1475    0.2073    0.3272
    0.1686    0.2046    0.3272
    0.1896    0.2015    0.3272
    0.2107    0.1979    0.3272
    0.2318    0.1940    0.3272
    0.2529    0.1895    0.3272
    0.2739    0.1845    0.3272
    0.2950    0.1789    0.3272
    0.3161    0.1728    0.3272
    0.3371    0.1660    0.3272
    0.3582    0.1584    0.3272
    0.3793    0.1499    0.3272
    0.4004    0.1404    0.3272
    0.4214    0.1296    0.3272
    0.4425    0.1172    0.3272
    0.4636    0.1026    0.3272
    0.4846    0.0846    0.3272
    0.5057    0.0605    0.3272
    0.5268    0.0000    0.3272
    0.0000    0.1787    0.3465
    0.0174    0.1786    0.3465
    0.0349    0.1781    0.3465
    0.0523    0.1774    0.3465
    0.0697    0.1764    0.3465
    0.0872    0.1751    0.3465
    0.1046    0.1735    0.3465
    0.1220    0.1716    0.3465
    0.1395    0.1693    0.3465
    0.1569    0.1667    0.3465
    0.1744    0.1638    0.3465
    0.1918    0.1605    0.3465
    0.2092    0.1568    0.3465
    0.2267    0.1527    0.3465
    0.2441    0.1481    0.3465
    0.2615    0.1430    0.3465
    0.2790    0.1373    0.3465
    0.2964    0.1310    0.3465
    0.3138    0.1240    0.3465
    0.3313    0.1162    0.3465
    0.3487    0.1072    0.3465
    0.3661    0.0970    0.3465
    0.3836    0.0849    0.3465
    0.4010    0.0700    0.3465
    0.4185    0.0500    0.3465
    0.4359    0.0000    0.3465
    0.0000    0.1280    0.3658
    0.0125    0.1279    0.3658
    0.0250    0.1276    0.3658
    0.0375    0.1271    0.3658
    0.0500    0.1264    0.3658
    0.0624    0.1254    0.3658
    0.0749    0.1243    0.3658
    0.0874    0.1229    0.3658
    0.0999    0.1213    0.3658
    0.1124    0.1194    0.3658
    0.1249    0.1173    0.3658
    0.1374    0.1150    0.3658
    0.1499    0.1123    0.3658
    0.1624    0.1094    0.3658
    0.1749    0.1061    0.3658
    0.1873    0.1024    0.3658
    0.1998    0.0984    0.3658
    0.2123    0.0939    0.3658
    0.2248    0.0888    0.3658
    0.2373    0.0832    0.3658
    0.2498    0.0768    0.3658
    0.2623    0.0695    0.3658
    0.2748    0.0608    0.3658
    0.2873    0.0502    0.3658
    0.2998    0.0358    0.3658
    0.3122    0.0000    0.3658
</float_array>
<technique_common>
  <accessor source="#Ellipsoid_Coordinates" count="  521" stride="3">
        <param name="X" type="float" />
        <param name="Y" type="float" />
        <param name="Z" type="float" />
  </accessor>
</technique_common>
</source>
<source id="Ellipsoid_Normals">
<float_array id="Ellipsoid_Normals01" count=" 2925">
    0.0012    0.1487    0.9889
    0.0037    0.1485    0.9889
    0.0061    0.1480    0.9890
    0.0085    0.1473    0.9891
    0.0110    0.1463    0.9892
    0.0134    0.1451    0.9893
    0.0159    0.1437    0.9895
    0.0183    0.1420    0.9897
    0.0208    0.1400    0.9899
    0.0232    0.1377    0.9902
    0.0257    0.1352    0.9905
    0.0281    0.1323    0.9908
    0.0306    0.1291    0.9912
    0.0330    0.1255    0.9915
    0.0355    0.1215    0.9920
    0.0380    0.1171    0.9924
    0.0404    0.1122    0.9929
    0.0429    0.1067    0.9934
    0.0454    0.1005    0.9939
    0.0479    0.0935    0.9945
    0.0504    0.0856    0.9951
    0.0529    0.0763    0.9957
    0.0554    0.0651    0.9963
    0.0580    0.0505    0.9970
    0.0615    0.0214    0.9979
    0.0029    0.3550    0.9349
    0.0029    0.3550    0.9349
    0.0087    0.3545    0.9350
    0.0087    0.3545    0.9350
    0.0146    0.3535    0.9353
    0.0146    0.3535    0.9353
    0.0204    0.3519    0.9358
    0.0204    0.3519    0.9358
    0.0263    0.3499    0.9364
    0.0263    0.3499    0.9364
    0.0321    0.3473    0.9372
    0.0321    0.3473    0.9372
    0.0380    0.3441    0.9382
    0.0380    0.3441    0.9382
    0.0439    0.3403    0.9393
    0.0439    0.3403    0.9393
    0.0498    0.3360    0.9406
    0.0498    0.3360    0.9406
    0.0558    0.3309    0.9420
    0.0558    0.3309    0.9420
    0.0617    0.3253    0.9436
    0.0617    0.3253    0.9436
    0.0677    0.3188    0.9454
    0.0677    0.3188    0.9454
    0.0738    0.3116    0.9473
    0.0738    0.3116    0.9473
    0.0799    0.3035    0.9495
    0.0799    0.3035    0.9495
    0.0860    0.2945    0.9518
    0.0860    0.2945    0.9518
    0.0922    0.2844    0.9543
    0.0922    0.2844    0.9543
    0.0984    0.2730    0.9570
    0.0984    0.2730    0.9570
    0.1047    0.2603    0.9598
    0.1047    0.2603    0.9598
    0.1110    0.2459    0.9629
    0.1110    0.2459    0.9629
    0.1175    0.2295    0.9662
    0.1175    0.2295    0.9662
    0.1239    0.2106    0.9697
    0.1239    0.2106    0.9697
    0.1305    0.1884    0.9734
    0.1305    0.1884    0.9734
    0.1372    0.1612    0.9773
    0.1372    0.1612    0.9773
    0.1442    0.1257    0.9815
    0.1442    0.1257    0.9815
    0.1536    0.0535    0.9867
    0.1536    0.0535    0.9867
    0.0038    0.4589    0.8885
    0.0038    0.4589    0.8885
    0.0113    0.4583    0.8887
    0.0113    0.4583    0.8887
    0.0188    0.4571    0.8892
    0.0188    0.4571    0.8892
    0.0264    0.4553    0.8900
    0.0264    0.4553    0.8900
    0.0340    0.4528    0.8910
    0.0340    0.4528    0.8910
    0.0416    0.4497    0.8922
    0.0416    0.4497    0.8922
    0.0492    0.4459    0.8937
    0.0492    0.4459    0.8937
    0.0569    0.4414    0.8955
    0.0569    0.4414    0.8955
    0.0647    0.4361    0.8976
    0.0647    0.4361    0.8976
    0.0725    0.4301    0.8999
    0.0725    0.4301    0.8999
    0.0803    0.4232    0.9025
    0.0803    0.4232    0.9025
    0.0882    0.4153    0.9054
    0.0882    0.4153    0.9054
    0.0963    0.4065    0.9086
    0.0963    0.4065    0.9086
    0.1044    0.3966    0.9120
    0.1044    0.3966    0.9120
    0.1126    0.3854    0.9158
    0.1126    0.3854    0.9158
    0.1209    0.3729    0.9200
    0.1209    0.3729    0.9200
    0.1293    0.3588    0.9244
    0.1293    0.3588    0.9244
    0.1379    0.3428    0.9292
    0.1379    0.3428    0.9292
    0.1466    0.3246    0.9344
    0.1466    0.3246    0.9344
    0.1554    0.3038    0.9400
    0.1554    0.3038    0.9400
    0.1645    0.2795    0.9460
    0.1645    0.2795    0.9460
    0.1737    0.2507    0.9524
    0.1737    0.2507    0.9524
    0.1832    0.2152    0.9592
    0.1832    0.2152    0.9592
    0.1931    0.1683    0.9666
    0.1931    0.1683    0.9666
    0.2067    0.0720    0.9758
    0.2067    0.0720    0.9758
    0.0044    0.5398    0.8418
    0.0044    0.5398    0.8418
    0.0133    0.5391    0.8421
    0.0133    0.5391    0.8421
    0.0222    0.5378    0.8428
    0.0222    0.5378    0.8428
    0.0311    0.5358    0.8437
    0.0311    0.5358    0.8437
    0.0400    0.5332    0.8451
    0.0400    0.5332    0.8451
    0.0490    0.5298    0.8467
    0.0490    0.5298    0.8467
    0.0580    0.5256    0.8487
    0.0580    0.5256    0.8487
    0.0672    0.5207    0.8511
    0.0672    0.5207    0.8511
    0.0764    0.5150    0.8538
    0.0764    0.5150    0.8538
    0.0856    0.5084    0.8569
    0.0856    0.5084    0.8569
    0.0950    0.5008    0.8603
    0.0950    0.5008    0.8603
    0.1046    0.4922    0.8642
    0.1046    0.4922    0.8642
    0.1142    0.4824    0.8685
    0.1142    0.4824    0.8685
    0.1240    0.4714    0.8732
    0.1240    0.4714    0.8732
    0.1340    0.4589    0.8783
    0.1340    0.4589    0.8783
    0.1442    0.4448    0.8839
    0.1442    0.4448    0.8839
    0.1546    0.4288    0.8901
    0.1546    0.4288    0.8901
    0.1652    0.4107    0.8967
    0.1652    0.4107    0.8967
    0.1760    0.3898    0.9039
    0.1760    0.3898    0.9039
    0.1872    0.3657    0.9117
    0.1872    0.3657    0.9117
    0.1986    0.3375    0.9201
    0.1986    0.3375    0.9201
    0.2104    0.3036    0.9293
    0.2104    0.3036    0.9293
    0.2227    0.2616    0.9391
    0.2227    0.2616    0.9391
    0.2356    0.2054    0.9499
    0.2356    0.2054    0.9499
    0.2533    0.0883    0.9634
    0.2533    0.0883    0.9634
    0.0050    0.6072    0.7945
    0.0050    0.6072    0.7945
    0.0150    0.6065    0.7949
    0.0150    0.6065    0.7949
    0.0249    0.6052    0.7957
    0.0249    0.6052    0.7957
    0.0350    0.6031    0.7969
    0.0350    0.6031    0.7969
    0.0451    0.6003    0.7985
    0.0451    0.6003    0.7985
    0.0552    0.5968    0.8005
    0.0552    0.5968    0.8005
    0.0654    0.5926    0.8029
    0.0654    0.5926    0.8029
    0.0758    0.5875    0.8057
    0.0758    0.5875    0.8057
    0.0862    0.5815    0.8090
    0.0862    0.5815    0.8090
    0.0968    0.5746    0.8127
    0.0968    0.5746    0.8127
    0.1076    0.5667    0.8169
    0.1076    0.5667    0.8169
    0.1185    0.5576    0.8216
    0.1185    0.5576    0.8216
    0.1296    0.5473    0.8268
    0.1296    0.5473    0.8268
    0.1410    0.5356    0.8326
    0.1410    0.5356    0.8326
    0.1526    0.5224    0.8390
    0.1526    0.5224    0.8390
    0.1644    0.5073    0.8459
    0.1644    0.5073    0.8459
    0.1766    0.4901    0.8536
    0.1766    0.4901    0.8536
    0.1892    0.4704    0.8619
    0.1892    0.4704    0.8619
    0.2021    0.4477    0.8710
    0.2021    0.4477    0.8710
    0.2155    0.4212    0.8810
    0.2155    0.4212    0.8810
    0.2294    0.3898    0.8918
    0.2294    0.3898    0.8918
    0.2439    0.3519    0.9037
    0.2439    0.3519    0.9037
    0.2590    0.3043    0.9167
    0.2590    0.3043    0.9167
    0.2752    0.2399    0.9310
    0.2752    0.2399    0.9310
    0.2974    0.1036    0.9491
    0.2974    0.1036    0.9491
    0.0055    0.6652    0.7467
    0.0055    0.6652    0.7467
    0.0164    0.6645    0.7471
    0.0164    0.6645    0.7471
    0.0273    0.6631    0.7480
    0.0273    0.6631    0.7480
    0.0383    0.6611    0.7493
    0.0383    0.6611    0.7493
    0.0494    0.6583    0.7511
    0.0494    0.6583    0.7511
    0.0606    0.6548    0.7534
    0.0606    0.6548    0.7534
    0.0718    0.6505    0.7561
    0.0718    0.6505    0.7561
    0.0832    0.6454    0.7593
    0.0832    0.6454    0.7593
    0.0948    0.6394    0.7630
    0.0948    0.6394    0.7630
    0.1065    0.6324    0.7673
    0.1065    0.6324    0.7673
    0.1185    0.6243    0.7721
    0.1185    0.6243    0.7721
    0.1307    0.6151    0.7775
    0.1307    0.6151    0.7775
    0.1432    0.6046    0.7836
    0.1432    0.6046    0.7836
    0.1559    0.5926    0.7902
    0.1559    0.5926    0.7902
    0.1691    0.5789    0.7977
    0.1691    0.5789    0.7977
    0.1826    0.5633    0.8058
    0.1826    0.5633    0.8058
    0.1966    0.5454    0.8148
    0.1966    0.5454    0.8148
    0.2110    0.5247    0.8247
    0.2110    0.5247    0.8247
    0.2260    0.5006    0.8356
    0.2260    0.5006    0.8356
    0.2417    0.4724    0.8476
    0.2417    0.4724    0.8476
    0.2581    0.4386    0.8608
    0.2581    0.4386    0.8608
    0.2754    0.3974    0.8754
    0.2754    0.3974    0.8754
    0.2937    0.3450    0.8915
    0.2937    0.3450    0.8915
    0.3134    0.2732    0.9095
    0.3134    0.2732    0.9095
    0.3406    0.1187    0.9327
    0.3406    0.1187    0.9327
    0.0059    0.7159    0.6982
    0.0059    0.7159    0.6982
    0.0176    0.7152    0.6987
    0.0176    0.7152    0.6987
    0.0294    0.7139    0.6996
    0.0294    0.7139    0.6996
    0.0413    0.7119    0.7011
    0.0413    0.7119    0.7011
    0.0532    0.7092    0.7030
    0.0532    0.7092    0.7030
    0.0653    0.7057    0.7055
    0.0653    0.7057    0.7055
    0.0775    0.7015    0.7084
    0.0775    0.7015    0.7084
    0.0898    0.6965    0.7119
    0.0898    0.6965    0.7119
    0.1024    0.6905    0.7160
    0.1024    0.6905    0.7160
    0.1152    0.6836    0.7207
    0.1152    0.6836    0.7207
    0.1282    0.6757    0.7260
    0.1282    0.6757    0.7260
    0.1416    0.6665    0.7319
    0.1416    0.6665    0.7319
    0.1553    0.6560    0.7386
    0.1553    0.6560    0.7386
    0.1695    0.6439    0.7461
    0.1695    0.6439    0.7461
    0.1840    0.6302    0.7543
    0.1840    0.6302    0.7543
    0.1991    0.6143    0.7635
    0.1991    0.6143    0.7635
    0.2148    0.5960    0.7737
    0.2148    0.5960    0.7737
    0.2312    0.5748    0.7850
    0.2312    0.5748    0.7850
    0.2483    0.5499    0.7975
    0.2483    0.5499    0.7975
    0.2663    0.5204    0.8113
    0.2663    0.5204    0.8113
    0.2853    0.4849    0.8267
    0.2853    0.4849    0.8267
    0.3056    0.4409    0.8439
    0.3056    0.4409    0.8439
    0.3273    0.3844    0.8632
    0.3273    0.3844    0.8632
    0.3510    0.3059    0.8850
    0.3510    0.3059    0.8850
    0.3840    0.1338    0.9136
    0.3840    0.1338    0.9136
    0.0062    0.7607    0.6491
    0.0062    0.7607    0.6491
    0.0187    0.7600    0.6496
    0.0187    0.7600    0.6496
    0.0313    0.7588    0.6506
    0.0313    0.7588    0.6506
    0.0439    0.7568    0.6521
    0.0439    0.7568    0.6521
    0.0566    0.7542    0.6542
    0.0566    0.7542    0.6542
    0.0694    0.7509    0.6567
    0.0694    0.7509    0.6567
    0.0825    0.7468    0.6599
    0.0825    0.7468    0.6599
    0.0957    0.7420    0.6636
    0.0957    0.7420    0.6636
    0.1092    0.7362    0.6679
    0.1092    0.7362    0.6679
    0.1229    0.7295    0.6729
    0.1229    0.7295    0.6729
    0.1370    0.7217    0.6785
    0.1370    0.7217    0.6785
    0.1514    0.7128    0.6849
    0.1514    0.7128    0.6849
    0.1663    0.7024    0.6920
    0.1663    0.7024    0.6920
    0.1817    0.6906    0.7001
    0.1817    0.6906    0.7001
    0.1977    0.6769    0.7090
    0.1977    0.6769    0.7090
    0.2143    0.6611    0.7190
    0.2143    0.6611    0.7190
    0.2317    0.6428    0.7301
    0.2317    0.6428    0.7301
    0.2499    0.6214    0.7425
    0.2499    0.6214    0.7425
    0.2692    0.5961    0.7564
    0.2692    0.5961    0.7564
    0.2896    0.5659    0.7719
    0.2896    0.5659    0.7719
    0.3114    0.5291    0.7894
    0.3114    0.5291    0.7894
    0.3348    0.4831    0.8090
    0.3348    0.4831    0.8090
    0.3603    0.4232    0.8314
    0.3603    0.4232    0.8314
    0.3884    0.3386    0.8570
    0.3884    0.3386    0.8570
    0.4282    0.1492    0.8913
    0.4282    0.1492    0.8913
    0.0066    0.8004    0.5995
    0.0066    0.8004    0.5995
    0.0197    0.7998    0.6000
    0.0197    0.7998    0.6000
    0.0329    0.7986    0.6010
    0.0329    0.7986    0.6010
    0.0462    0.7967    0.6025
    0.0462    0.7967    0.6025
    0.0596    0.7943    0.6046
    0.0596    0.7943    0.6046
    0.0732    0.7911    0.6073
    0.0732    0.7911    0.6073
    0.0869    0.7872    0.6105
    0.0869    0.7872    0.6105
    0.1009    0.7826    0.6143
    0.1009    0.7826    0.6143
    0.1152    0.7771    0.6188
    0.1152    0.7771    0.6188
    0.1298    0.7707    0.6239
    0.1298    0.7707    0.6239
    0.1449    0.7632    0.6297
    0.1449    0.7632    0.6297
    0.1603    0.7546    0.6364
    0.1603    0.7546    0.6364
    0.1763    0.7446    0.6438
    0.1763    0.7446    0.6438
    0.1929    0.7331    0.6522
    0.1929    0.7331    0.6522
    0.2102    0.7198    0.6616
    0.2102    0.7198    0.6616
    0.2283    0.7043    0.6722
    0.2283    0.7043    0.6722
    0.2473    0.6862    0.6841
    0.2473    0.6862    0.6841
    0.2674    0.6650    0.6974
    0.2674    0.6650    0.6974
    0.2888    0.6397    0.7123
    0.2888    0.6397    0.7123
    0.3117    0.6091    0.7292
    0.3117    0.6091    0.7292
    0.3364    0.5716    0.7484
    0.3364    0.5716    0.7484
    0.3632    0.5241    0.7703
    0.3632    0.5241    0.7703
    0.3928    0.4614    0.7955
    0.3928    0.4614    0.7955
    0.4260    0.3714    0.8250
    0.4260    0.3714    0.8250
    0.4736    0.1650    0.8651
    0.4736    0.1650    0.8651
    0.0069    0.8356    0.5493
    0.0069    0.8356    0.5493
    0.0206    0.8351    0.5498
    0.0206    0.8351    0.5498
    0.0344    0.8339    0.5508
    0.0344    0.8339    0.5508
    0.0483    0.8322    0.5523
    0.0483    0.8322    0.5523
    0.0623    0.8299    0.5544
    0.0623    0.8299    0.5544
    0.0765    0.8269    0.5571
    0.0765    0.8269    0.5571
    0.0909    0.8233    0.5603
    0.0909    0.8233    0.5603
    0.1056    0.8189    0.5641
    0.1056    0.8189    0.5641
    0.1206    0.8137    0.5686
    0.1206    0.8137    0.5686
    0.1361    0.8076    0.5738
    0.1361    0.8076    0.5738
    0.1519    0.8005    0.5797
    0.1519    0.8005    0.5797
    0.1683    0.7923    0.5864
    0.1683    0.7923    0.5864
    0.1854    0.7828    0.5940
    0.1854    0.7828    0.5940
    0.2031    0.7718    0.6026
    0.2031    0.7718    0.6026
    0.2216    0.7589    0.6123
    0.2216    0.7589    0.6123
    0.2412    0.7440    0.6232
    0.2412    0.7440    0.6232
    0.2618    0.7264    0.6355
    0.2618    0.7264    0.6355
    0.2838    0.7055    0.6494
    0.2838    0.7055    0.6494
    0.3073    0.6806    0.6651
    0.3073    0.6806    0.6651
    0.3327    0.6502    0.6831
    0.3327    0.6502    0.6831
    0.3604    0.6124    0.7037
    0.3604    0.6124    0.7037
    0.3908    0.5640    0.7275
    0.3908    0.5640    0.7275
    0.4249    0.4991    0.7552
    0.4249    0.4991    0.7552
    0.4638    0.4043    0.7883
    0.4638    0.4043    0.7883
    0.5205    0.1813    0.8344
    0.5205    0.1813    0.8344
    0.0071    0.8668    0.4985
    0.0071    0.8668    0.4985
    0.0214    0.8663    0.4990
    0.0214    0.8663    0.4990
    0.0357    0.8653    0.5000
    0.0357    0.8653    0.5000
    0.0501    0.8637    0.5016
    0.0501    0.8637    0.5016
    0.0646    0.8615    0.5036
    0.0646    0.8615    0.5036
    0.0794    0.8588    0.5062
    0.0794    0.8588    0.5062
    0.0944    0.8554    0.5094
    0.0944    0.8554    0.5094
    0.1098    0.8513    0.5131
    0.1098    0.8513    0.5131
    0.1255    0.8464    0.5175
    0.1255    0.8464    0.5175
    0.1416    0.8407    0.5226
    0.1416    0.8407    0.5226
    0.1583    0.8341    0.5285
    0.1583    0.8341    0.5285
    0.1756    0.8263    0.5351
    0.1756    0.8263    0.5351
    0.1935    0.8173    0.5427
    0.1935    0.8173    0.5427
    0.2123    0.8069    0.5513
    0.2123    0.8069    0.5513
    0.2321    0.7947    0.5610
    0.2321    0.7947    0.5610
    0.2529    0.7803    0.5719
    0.2529    0.7803    0.5719
    0.2751    0.7634    0.5844
    0.2751    0.7634    0.5844
    0.2989    0.7432    0.5985
    0.2989    0.7432    0.5985
    0.3246    0.7189    0.6147
    0.3246    0.7189    0.6147
    0.3525    0.6889    0.6333
    0.3525    0.6889    0.6333
    0.3833    0.6513    0.6549
    0.3833    0.6513    0.6549
    0.4176    0.6026    0.6801
    0.4176    0.6026    0.6801
    0.4565    0.5362    0.7100
    0.4565    0.5362    0.7100
    0.5018    0.4374    0.7462
    0.5018    0.4374    0.7462
    0.5690    0.1982    0.7981
    0.5690    0.1982    0.7981
    0.0073    0.8943    0.4474
    0.0073    0.8943    0.4474
    0.0220    0.8938    0.4478
    0.0220    0.8938    0.4478
    0.0368    0.8929    0.4488
    0.0368    0.8929    0.4488
    0.0517    0.8914    0.4503
    0.0517    0.8914    0.4503
    0.0667    0.8894    0.4522
    0.0667    0.8894    0.4522
    0.0820    0.8869    0.4547
    0.0820    0.8869    0.4547
    0.0976    0.8837    0.4577
    0.0976    0.8837    0.4577
    0.1135    0.8799    0.4613
    0.1135    0.8799    0.4613
    0.1298    0.8754    0.4656
    0.1298    0.8754    0.4656
    0.1466    0.8701    0.4705
    0.1466    0.8701    0.4705
    0.1640    0.8640    0.4761
    0.1640    0.8640    0.4761
    0.1820    0.8567    0.4826
    0.1820    0.8567    0.4826
    0.2009    0.8483    0.4899
    0.2009    0.8483    0.4899
    0.2207    0.8385    0.4983
    0.2207    0.8385    0.4983
    0.2415    0.8270    0.5077
    0.2415    0.8270    0.5077
    0.2637    0.8134    0.5185
    0.2637    0.8134    0.5185
    0.2874    0.7973    0.5308
    0.2874    0.7973    0.5308
    0.3129    0.7779    0.5449
    0.3129    0.7779    0.5449
    0.3406    0.7544    0.5611
    0.3406    0.7544    0.5611
    0.3711    0.7252    0.5799
    0.3711    0.7252    0.5799
    0.4050    0.6882    0.6019
    0.4050    0.6882    0.6019
    0.4433    0.6397    0.6279
    0.4433    0.6397    0.6279
    0.4874    0.5725    0.6593
    0.4874    0.5725    0.6593
    0.5397    0.4705    0.6981
    0.5397    0.4705    0.6981
    0.6190    0.2157    0.7552
    0.6190    0.2157    0.7552
    0.0075    0.9183    0.3958
    0.0075    0.9183    0.3958
    0.0226    0.9179    0.3962
    0.0226    0.9179    0.3962
    0.0378    0.9170    0.3971
    0.0378    0.9170    0.3971
    0.0531    0.9156    0.3985
    0.0531    0.9156    0.3985
    0.0686    0.9138    0.4003
    0.0686    0.9138    0.4003
    0.0843    0.9115    0.4026
    0.0843    0.9115    0.4026
    0.1003    0.9086    0.4054
    0.1003    0.9086    0.4054
    0.1167    0.9051    0.4088
    0.1167    0.9051    0.4088
    0.1336    0.9010    0.4128
    0.1336    0.9010    0.4128
    0.1510    0.8961    0.4174
    0.1510    0.8961    0.4174
    0.1690    0.8904    0.4227
    0.1690    0.8904    0.4227
    0.1878    0.8837    0.4288
    0.1878    0.8837    0.4288
    0.2074    0.8758    0.4358
    0.2074    0.8758    0.4358
    0.2281    0.8667    0.4437
    0.2281    0.8667    0.4437
    0.2500    0.8559    0.4527
    0.2500    0.8559    0.4527
    0.2733    0.8431    0.4631
    0.2733    0.8431    0.4631
    0.2984    0.8279    0.4749
    0.2984    0.8279    0.4749
    0.3256    0.8095    0.4885
    0.3256    0.8095    0.4885
    0.3554    0.7870    0.5043
    0.3554    0.7870    0.5043
    0.3883    0.7589    0.5228
    0.3883    0.7589    0.5228
    0.4254    0.7228    0.5446
    0.4254    0.7228    0.5446
    0.4677    0.6749    0.5708
    0.4677    0.6749    0.5708
    0.5172    0.6076    0.6028
    0.5172    0.6076    0.6028
    0.5772    0.5032    0.6432
    0.5772    0.5032    0.6432
    0.6702    0.2335    0.7045
    0.6702    0.2335    0.7045
    0.0077    0.9390    0.3438
    0.0077    0.9390    0.3438
    0.0231    0.9386    0.3442
    0.0231    0.9386    0.3442
    0.0387    0.9378    0.3450
    0.0387    0.9378    0.3450
    0.0543    0.9366    0.3462
    0.0543    0.9366    0.3462
    0.0702    0.9349    0.3479
    0.0702    0.9349    0.3479
    0.0863    0.9328    0.3500
    0.0863    0.9328    0.3500
    0.1027    0.9301    0.3526
    0.1027    0.9301    0.3526
    0.1195    0.9269    0.3557
    0.1195    0.9269    0.3557
    0.1369    0.9231    0.3593
    0.1369    0.9231    0.3593
    0.1548    0.9186    0.3635
    0.1548    0.9186    0.3635
    0.1734    0.9134    0.3684
    0.1734    0.9134    0.3684
    0.1928    0.9072    0.3740
    0.1928    0.9072    0.3740
    0.2131    0.8999    0.3804
    0.2131    0.8999    0.3804
    0.2346    0.8914    0.3877
    0.2346    0.8914    0.3877
    0.2574    0.8814    0.3961
    0.2574    0.8814    0.3961
    0.2818    0.8695    0.4057
    0.2818    0.8695    0.4057
    0.3082    0.8552    0.4167
    0.3082    0.8552    0.4167
    0.3370    0.8378    0.4295
    0.3370    0.8378    0.4295
    0.3686    0.8164    0.4444
    0.3686    0.8164    0.4444
    0.4040    0.7895    0.4620
    0.4040    0.7895    0.4620
    0.4441    0.7546    0.4830
    0.4441    0.7546    0.4830
    0.4905    0.7077    0.5085
    0.4905    0.7077    0.5085
    0.5455    0.6408    0.5401
    0.5455    0.6408    0.5401
    0.6136    0.5349    0.5808
    0.6136    0.5349    0.5808
    0.7219    0.2515    0.6446
    0.7219    0.2515    0.6446
    0.0078    0.9565    0.2915
    0.0078    0.9565    0.2915
    0.0236    0.9562    0.2918
    0.0236    0.9562    0.2918
    0.0394    0.9554    0.2925
    0.0394    0.9554    0.2925
    0.0553    0.9543    0.2936
    0.0553    0.9543    0.2936
    0.0715    0.9528    0.2951
    0.0715    0.9528    0.2951
    0.0879    0.9508    0.2969
    0.0879    0.9508    0.2969
    0.1047    0.9484    0.2992
    0.1047    0.9484    0.2992
    0.1219    0.9455    0.3020
    0.1219    0.9455    0.3020
    0.1397    0.9420    0.3052
    0.1397    0.9420    0.3052
    0.1580    0.9379    0.3089
    0.1580    0.9379    0.3089
    0.1771    0.9330    0.3132
    0.1771    0.9330    0.3132
    0.1970    0.9273    0.3182
    0.1970    0.9273    0.3182
    0.2180    0.9206    0.3239
    0.2180    0.9206    0.3239
    0.2402    0.9128    0.3304
    0.2402    0.9128    0.3304
    0.2639    0.9034    0.3379
    0.2639    0.9034    0.3379
    0.2893    0.8923    0.3465
    0.2893    0.8923    0.3465
    0.3168    0.8790    0.3565
    0.3168    0.8790    0.3565
    0.3469    0.8626    0.3681
    0.3469    0.8626    0.3681
    0.3804    0.8424    0.3817
    0.3804    0.8424    0.3817
    0.4179    0.8167    0.3978
    0.4179    0.8167    0.3978
    0.4609    0.7832    0.4172
    0.4609    0.7832    0.4172
    0.5112    0.7376    0.4411
    0.5112    0.7376    0.4411
    0.5718    0.6716    0.4712
    0.5718    0.6716    0.4712
    0.6481    0.5650    0.5106
    0.6481    0.5650    0.5106
    0.7730    0.2693    0.5745
    0.7730    0.2693    0.5745
    0.0080    0.9710    0.2389
    0.0080    0.9710    0.2389
    0.0239    0.9707    0.2392
    0.0239    0.9707    0.2392
    0.0400    0.9700    0.2398
    0.0400    0.9700    0.2398
    0.0562    0.9690    0.2407
    0.0562    0.9690    0.2407
    0.0726    0.9676    0.2419
    0.0726    0.9676    0.2419
    0.0893    0.9658    0.2435
    0.0893    0.9658    0.2435
    0.1064    0.9636    0.2454
    0.1064    0.9636    0.2454
    0.1239    0.9609    0.2477
    0.1239    0.9609    0.2477
    0.1420    0.9577    0.2505
    0.1420    0.9577    0.2505
    0.1607    0.9539    0.2536
    0.1607    0.9539    0.2536
    0.1802    0.9494    0.2573
    0.1802    0.9494    0.2573
    0.2006    0.9441    0.2615
    0.2006    0.9441    0.2615
    0.2221    0.9379    0.2664
    0.2221    0.9379    0.2664
    0.2449    0.9306    0.2720
    0.2449    0.9306    0.2720
    0.2693    0.9220    0.2784
    0.2693    0.9220    0.2784
    0.2955    0.9116    0.2858
    0.2955    0.9116    0.2858
    0.3240    0.8991    0.2944
    0.3240    0.8991    0.2944
    0.3554    0.8837    0.3044
    0.3554    0.8837    0.3044
    0.3904    0.8646    0.3163
    0.3904    0.8646    0.3163
    0.4300    0.8402    0.3304
    0.4300    0.8402    0.3304
    0.4756    0.8081    0.3476
    0.4756    0.8081    0.3476
    0.5295    0.7640    0.3688
    0.5295    0.7640    0.3688
    0.5952    0.6992    0.3960
    0.5952    0.6992    0.3960
    0.6797    0.5925    0.4323
    0.6797    0.5925    0.4323
    0.8216    0.2863    0.4930
    0.8216    0.2863    0.4930
    0.0081    0.9825    0.1860
    0.0081    0.9825    0.1860
    0.0242    0.9822    0.1863
    0.0242    0.9822    0.1863
    0.0405    0.9816    0.1868
    0.0405    0.9816    0.1868
    0.0569    0.9806    0.1875
    0.0569    0.9806    0.1875
    0.0735    0.9793    0.1885
    0.0735    0.9793    0.1885
    0.0904    0.9777    0.1897
    0.0904    0.9777    0.1897
    0.1077    0.9756    0.1913
    0.1077    0.9756    0.1913
    0.1255    0.9731    0.1931
    0.1255    0.9731    0.1931
    0.1438    0.9701    0.1953
    0.1438    0.9701    0.1953
    0.1629    0.9666    0.1978
    0.1629    0.9666    0.1978
    0.1827    0.9625    0.2008
    0.1827    0.9625    0.2008
    0.2035    0.9576    0.2042
    0.2035    0.9576    0.2042
    0.2254    0.9518    0.2081
    0.2254    0.9518    0.2081
    0.2487    0.9450    0.2126
    0.2487    0.9450    0.2126
    0.2736    0.9369    0.2177
    0.2736    0.9369    0.2177
    0.3005    0.9272    0.2237
    0.3005    0.9272    0.2237
    0.3299    0.9154    0.2307
    0.3299    0.9154    0.2307
    0.3623    0.9009    0.2389
    0.3623    0.9009    0.2389
    0.3986    0.8828    0.2485
    0.3986    0.8828    0.2485
    0.4398    0.8596    0.2602
    0.4398    0.8596    0.2602
    0.4877    0.8288    0.2743
    0.4877    0.8288    0.2743
    0.5448    0.7861    0.2921
    0.5448    0.7861    0.2921
    0.6152    0.7227    0.3150
    0.6152    0.7227    0.3150
    0.7072    0.6165    0.3462
    0.7072    0.6165    0.3462
    0.8656    0.3016    0.3997
    0.8656    0.3016    0.3997
    0.0081    0.9911    0.1330
    0.0081    0.9911    0.1330
    0.0244    0.9908    0.1332
    0.0244    0.9908    0.1332
    0.0408    0.9902    0.1335
    0.0408    0.9902    0.1335
    0.0574    0.9893    0.1341
    0.0574    0.9893    0.1341
    0.0741    0.9881    0.1348
    0.0741    0.9881    0.1348
    0.0912    0.9865    0.1357
    0.0912    0.9865    0.1357
    0.1087    0.9846    0.1368
    0.1087    0.9846    0.1368
    0.1267    0.9823    0.1382
    0.1267    0.9823    0.1382
    0.1452    0.9795    0.1398
    0.1452    0.9795    0.1398
    0.1645    0.9762    0.1416
    0.1645    0.9762    0.1416
    0.1845    0.9723    0.1438
    0.1845    0.9723    0.1438
    0.2056    0.9676    0.1462
    0.2056    0.9676    0.1462
    0.2279    0.9622    0.1491
    0.2279    0.9622    0.1491
    0.2515    0.9558    0.1524
    0.2515    0.9558    0.1524
    0.2769    0.9481    0.1562
    0.2769    0.9481    0.1562
    0.3044    0.9389    0.1606
    0.3044    0.9389    0.1606
    0.3344    0.9278    0.1657
    0.3344    0.9278    0.1657
    0.3676    0.9140    0.1718
    0.3676    0.9140    0.1718
    0.4049    0.8967    0.1789
    0.4049    0.8967    0.1789
    0.4474    0.8744    0.1876
    0.4474    0.8744    0.1876
    0.4971    0.8447    0.1982
    0.4971    0.8447    0.1982
    0.5567    0.8033    0.2116
    0.5567    0.8033    0.2116
    0.6310    0.7412    0.2290
    0.6310    0.7412    0.2290
    0.7293    0.6357    0.2531
    0.7293    0.6357    0.2531
    0.9022    0.3144    0.2953
    0.9022    0.3144    0.2953
    0.0082    0.9968    0.0799
    0.0082    0.9968    0.0799
    0.0246    0.9965    0.0800
    0.0246    0.9965    0.0800
    0.0410    0.9959    0.0802
    0.0410    0.9959    0.0802
    0.0577    0.9951    0.0805
    0.0577    0.9951    0.0805
    0.0746    0.9939    0.0809
    0.0746    0.9939    0.0809
    0.0918    0.9924    0.0815
    0.0918    0.9924    0.0815
    0.1094    0.9906    0.0822
    0.1094    0.9906    0.0822
    0.1275    0.9884    0.0830
    0.1275    0.9884    0.0830
    0.1461    0.9857    0.0840
    0.1461    0.9857    0.0840
    0.1655    0.9825    0.0851
    0.1655    0.9825    0.0851
    0.1858    0.9788    0.0864
    0.1858    0.9788    0.0864
    0.2070    0.9744    0.0879
    0.2070    0.9744    0.0879
    0.2295    0.9692    0.0896
    0.2295    0.9692    0.0896
    0.2534    0.9630    0.0917
    0.2534    0.9630    0.0917
    0.2791    0.9557    0.0940
    0.2791    0.9557    0.0940
    0.3069    0.9468    0.0967
    0.3069    0.9468    0.0967
    0.3374    0.9361    0.0998
    0.3374    0.9361    0.0998
    0.3711    0.9228    0.1035
    0.3711    0.9228    0.1035
    0.4091    0.9061    0.1079
    0.4091    0.9061    0.1079
    0.4526    0.8845    0.1133
    0.4526    0.8845    0.1133
    0.5035    0.8556    0.1199
    0.5035    0.8556    0.1199
    0.5649    0.8151    0.1282
    0.5649    0.8151    0.1282
    0.6419    0.7540    0.1391
    0.6419    0.7540    0.1391
    0.7448    0.6492    0.1543
    0.7448    0.6492    0.1543
    0.9286    0.3236    0.1815
    0.9286    0.3236    0.1815
    0.0082    0.9996    0.0266
    0.0082    0.9996    0.0266
    0.0246    0.9993    0.0267
    0.0246    0.9993    0.0267
    0.0412    0.9988    0.0267
    0.0412    0.9988    0.0267
    0.0579    0.9980    0.0268
    0.0579    0.9980    0.0268
    0.0748    0.9968    0.0270
    0.0748    0.9968    0.0270
    0.0921    0.9954    0.0272
    0.0921    0.9954    0.0272
    0.1097    0.9936    0.0274
    0.1097    0.9936    0.0274
    0.1279    0.9914    0.0277
    0.1279    0.9914    0.0277
    0.1466    0.9888    0.0280
    0.1466    0.9888    0.0280
    0.1661    0.9857    0.0284
    0.1661    0.9857    0.0284
    0.1864    0.9821    0.0288
    0.1864    0.9821    0.0288
    0.2077    0.9777    0.0293
    0.2077    0.9777    0.0293
    0.2303    0.9727    0.0299
    0.2303    0.9727    0.0299
    0.2544    0.9666    0.0306
    0.2544    0.9666    0.0306
    0.2802    0.9594    0.0314
    0.2802    0.9594    0.0314
    0.3082    0.9508    0.0323
    0.3082    0.9508    0.0323
    0.3389    0.9402    0.0333
    0.3389    0.9402    0.0333
    0.3729    0.9272    0.0346
    0.3729    0.9272    0.0346
    0.4113    0.9108    0.0361
    0.4113    0.9108    0.0361
    0.4552    0.8896    0.0379
    0.4552    0.8896    0.0379
    0.5068    0.8611    0.0401
    0.5068    0.8611    0.0401
    0.5691    0.8212    0.0429
    0.5691    0.8212    0.0429
    0.6475    0.7606    0.0466
    0.6475    0.7606    0.0466
    0.7528    0.6562    0.0519
    0.7528    0.6562    0.0519
    0.9425    0.3284    0.0612
    0.9425    0.3284    0.0612
</float_array>
<technique_common>
  <accessor source="#Ellipsoid_Normals01" count="  975" stride="3">
        <param name="X" type="float" />
        <param name="Y" type="float" />
        <param name="Z" type="float" />
  </accessor>
</technique_common>
</source>
<vertices id="Ellipsoid_Vertices">
  <input semantic="POSITION" source="#Ellipsoid_Positions" />
</vertices>
<polylist count="  975" material="Material2">
  <input semantic="VERTEX" source="#Ellipsoid_Vertices" offset="0" />
  <input semantic="NORMAL" source="#Ellipsoid_Normals" offset="1" />
<vcount>
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
</vcount>
<p>
    0    0  496    0  495    0
    0    1  497    1  496    1
    0    2  498    2  497    2
    0    3  499    3  498    3
    0    4  500    4  499    4
    0    5  501    5  500    5
    0    6  502    6  501    6
    0    7  503    7  502    7
    0    8  504    8  503    8
    0    9  505    9  504    9
    0  10  506  10  505  10
    0  11  507  11  506  11
    0  12  508  12  507  12
    0  13  509  13  508  13
    0  14  510  14  509  14
    0  15  511  15  510  15
    0  16  512  16  511  16
    0  17  513  17  512  17
    0  18  514  18  513  18
    0  19  515  19  514  19
    0  20  516  20  515  20
    0  21  517  21  516  21
    0  22  518  22  517  22
    0  23  519  23  518  23
    0  24  520  24  519  24
  495  25  470  25  469  25
  495  26  496  26  470  26
  496  27  471  27  470  27
  496  28  497  28  471  28
  497  29  472  29  471  29
  497  30  498  30  472  30
  498  31  473  31  472  31
  498  32  499  32  473  32
  499  33  474  33  473  33
  499  34  500  34  474  34
  500  35  475  35  474  35
  500  36  501  36  475  36
  501  37  476  37  475  37
  501  38  502  38  476  38
  502  39  477  39  476  39
  502  40  503  40  477  40
  503  41  478  41  477  41
  503  42  504  42  478  42
  504  43  479  43  478  43
  504  44  505  44  479  44
  505  45  480  45  479  45
  505  46  506  46  480  46
  506  47  481  47  480  47
  506  48  507  48  481  48
  507  49  482  49  481  49
  507  50  508  50  482  50
  508  51  483  51  482  51
  508  52  509  52  483  52
  509  53  484  53  483  53
  509  54  510  54  484  54
  510  55  485  55  484  55
  510  56  511  56  485  56
  511  57  486  57  485  57
  511  58  512  58  486  58
  512  59  487  59  486  59
  512  60  513  60  487  60
  513  61  488  61  487  61
  513  62  514  62  488  62
  514  63  489  63  488  63
  514  64  515  64  489  64
  515  65  490  65  489  65
  515  66  516  66  490  66
  516  67  491  67  490  67
  516  68  517  68  491  68
  517  69  492  69  491  69
  517  70  518  70  492  70
  518  71  493  71  492  71
  518  72  519  72  493  72
  519  73  494  73  493  73
  519  74  520  74  494  74
  469  75  444  75  443  75
  469  76  470  76  444  76
  470  77  445  77  444  77
  470  78  471  78  445  78
  471  79  446  79  445  79
  471  80  472  80  446  80
  472  81  447  81  446  81
  472  82  473  82  447  82
  473  83  448  83  447  83
  473  84  474  84  448  84
  474  85  449  85  448  85
  474  86  475  86  449  86
  475  87  450  87  449  87
  475  88  476  88  450  88
  476  89  451  89  450  89
  476  90  477  90  451  90
  477  91  452  91  451  91
  477  92  478  92  452  92
  478  93  453  93  452  93
  478  94  479  94  453  94
  479  95  454  95  453  95
  479  96  480  96  454  96
  480  97  455  97  454  97
  480  98  481  98  455  98
  481  99  456  99  455  99
  481  100  482  100  456  100
  482  101  457  101  456  101
  482  102  483  102  457  102
  483  103  458  103  457  103
  483  104  484  104  458  104
  484  105  459  105  458  105
  484  106  485  106  459  106
  485  107  460  107  459  107
  485  108  486  108  460  108
  486  109  461  109  460  109
  486  110  487  110  461  110
  487  111  462  111  461  111
  487  112  488  112  462  112
  488  113  463  113  462  113
  488  114  489  114  463  114
  489  115  464  115  463  115
  489  116  490  116  464  116
  490  117  465  117  464  117
  490  118  491  118  465  118
  491  119  466  119  465  119
  491  120  492  120  466  120
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  387  320  388  320  362  320
  388  321  363  321  362  321
  388  322  389  322  363  322
  389  323  364  323  363  323
  389  324  390  324  364  324
  339  325  314  325  313  325
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  340  328  341  328  315  328
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  342  331  317  331  316  331
  342  332  343  332  317  332
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  348  344  349  344  323  344
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  359  365  334  365  333  365
  359  366  360  366  334  366
  360  367  335  367  334  367
  360  368  361  368  335  368
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  287  425  262  425  261  425
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  291  434  292  434  266  434
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  263  480  264  480  238  480
  264  481  239  481  238  481
  264  482  265  482  239  482
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  269  491  244  491  243  491
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  285  523  260  523  259  523
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  242  540  243  540  217  540
  243  541  218  541  217  541
  243  542  244  542  218  542
  244  543  219  543  218  543
  244  544  245  544  219  544
  245  545  220  545  219  545
  245  546  246  546  220  546
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  246  548  247  548  221  548
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  251  558  252  558  226  558
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  254  563  229  563  228  563
  254  564  255  564  229  564
  255  565  230  565  229  565
  255  566  256  566  230  566
  256  567  231  567  230  567
  256  568  257  568  231  568
  257  569  232  569  231  569
  257  570  258  570  232  570
  258  571  233  571  232  571
  258  572  259  572  233  572
  259  573  234  573  233  573
  259  574  260  574  234  574
  209  575  184  575  183  575
  209  576  210  576  184  576
  210  577  185  577  184  577
  210  578  211  578  185  578
  211  579  186  579  185  579
  211  580  212  580  186  580
  212  581  187  581  186  581
  212  582  213  582  187  582
  213  583  188  583  187  583
  213  584  214  584  188  584
  214  585  189  585  188  585
  214  586  215  586  189  586
  215  587  190  587  189  587
  215  588  216  588  190  588
  216  589  191  589  190  589
  216  590  217  590  191  590
  217  591  192  591  191  591
  217  592  218  592  192  592
  218  593  193  593  192  593
  218  594  219  594  193  594
  219  595  194  595  193  595
  219  596  220  596  194  596
  220  597  195  597  194  597
  220  598  221  598  195  598
  221  599  196  599  195  599
  221  600  222  600  196  600
  222  601  197  601  196  601
  222  602  223  602  197  602
  223  603  198  603  197  603
  223  604  224  604  198  604
  224  605  199  605  198  605
  224  606  225  606  199  606
  225  607  200  607  199  607
  225  608  226  608  200  608
  226  609  201  609  200  609
  226  610  227  610  201  610
  227  611  202  611  201  611
  227  612  228  612  202  612
  228  613  203  613  202  613
  228  614  229  614  203  614
  229  615  204  615  203  615
  229  616  230  616  204  616
  230  617  205  617  204  617
  230  618  231  618  205  618
  231  619  206  619  205  619
  231  620  232  620  206  620
  232  621  207  621  206  621
  232  622  233  622  207  622
  233  623  208  623  207  623
  233  624  234  624  208  624
  183  625  158  625  157  625
  183  626  184  626  158  626
  184  627  159  627  158  627
  184  628  185  628  159  628
  185  629  160  629  159  629
  185  630  186  630  160  630
  186  631  161  631  160  631
  186  632  187  632  161  632
  187  633  162  633  161  633
  187  634  188  634  162  634
  188  635  163  635  162  635
  188  636  189  636  163  636
  189  637  164  637  163  637
  189  638  190  638  164  638
  190  639  165  639  164  639
  190  640  191  640  165  640
  191  641  166  641  165  641
  191  642  192  642  166  642
  192  643  167  643  166  643
  192  644  193  644  167  644
  193  645  168  645  167  645
  193  646  194  646  168  646
  194  647  169  647  168  647
  194  648  195  648  169  648
  195  649  170  649  169  649
  195  650  196  650  170  650
  196  651  171  651  170  651
  196  652  197  652  171  652
  197  653  172  653  171  653
  197  654  198  654  172  654
  198  655  173  655  172  655
  198  656  199  656  173  656
  199  657  174  657  173  657
  199  658  200  658  174  658
  200  659  175  659  174  659
  200  660  201  660  175  660
  201  661  176  661  175  661
  201  662  202  662  176  662
  202  663  177  663  176  663
  202  664  203  664  177  664
  203  665  178  665  177  665
  203  666  204  666  178  666
  204  667  179  667  178  667
  204  668  205  668  179  668
  205  669  180  669  179  669
  205  670  206  670  180  670
  206  671  181  671  180  671
  206  672  207  672  181  672
  207  673  182  673  181  673
  207  674  208  674  182  674
  157  675  132  675  131  675
  157  676  158  676  132  676
  158  677  133  677  132  677
  158  678  159  678  133  678
  159  679  134  679  133  679
  159  680  160  680  134  680
  160  681  135  681  134  681
  160  682  161  682  135  682
  161  683  136  683  135  683
  161  684  162  684  136  684
  162  685  137  685  136  685
  162  686  163  686  137  686
  163  687  138  687  137  687
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<technique_common>
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</technique_common>
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    0.3327  -0.6502    0.6831
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    0.3604  -0.6124    0.7037
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    0.3908  -0.5640    0.7275
    0.3908  -0.5640    0.7275
    0.4249  -0.4991    0.7552
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    0.4638  -0.4043    0.7883
    0.4638  -0.4043    0.7883
    0.5205  -0.1813    0.8344
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    0.0214  -0.8663    0.4990
    0.0214  -0.8663    0.4990
    0.0357  -0.8653    0.5000
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    0.0646  -0.8615    0.5036
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    0.0368  -0.8929    0.4488
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    0.0517  -0.8914    0.4503
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    0.0820  -0.8869    0.4547
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    0.1135  -0.8799    0.4613
    0.1135  -0.8799    0.4613
    0.1298  -0.8754    0.4656
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    0.1640  -0.8640    0.4761
    0.1640  -0.8640    0.4761
    0.1820  -0.8567    0.4826
    0.1820  -0.8567    0.4826
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    0.2207  -0.8385    0.4983
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    0.2637  -0.8134    0.5185
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    0.3711  -0.7252    0.5799
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    0.4433  -0.6397    0.6279
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    0.6190  -0.2157    0.7552
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    0.0843  -0.9115    0.4026
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    0.1878  -0.8837    0.4288
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    0.2281  -0.8667    0.4437
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    0.2500  -0.8559    0.4527
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    0.2984  -0.8279    0.4749
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    0.1928  -0.9072    0.3740
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    0.3804  -0.8424    0.3817
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    0.5718  -0.6716    0.4712
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    0.7730  -0.2693    0.5745
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    0.0080  -0.9710    0.2389
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    0.4877  -0.8288    0.2743
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    0.8656  -0.3016    0.3997
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    0.2515  -0.9558    0.1524
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    0.4049  -0.8967    0.1789
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    0.4474  -0.8744    0.1876
    0.4474  -0.8744    0.1876
    0.4971  -0.8447    0.1982
    0.4971  -0.8447    0.1982
    0.5567  -0.8033    0.2116
    0.5567  -0.8033    0.2116
    0.6310  -0.7412    0.2290
    0.6310  -0.7412    0.2290
    0.7293  -0.6357    0.2531
    0.7293  -0.6357    0.2531
    0.9022  -0.3144    0.2953
    0.9022  -0.3144    0.2953
    0.0082  -0.9968    0.0799
    0.0082  -0.9968    0.0799
    0.0246  -0.9965    0.0800
    0.0246  -0.9965    0.0800
    0.0410  -0.9959    0.0802
    0.0410  -0.9959    0.0802
    0.0577  -0.9951    0.0805
    0.0577  -0.9951    0.0805
    0.0746  -0.9939    0.0809
    0.0746  -0.9939    0.0809
    0.0918  -0.9924    0.0815
    0.0918  -0.9924    0.0815
    0.1094  -0.9906    0.0822
    0.1094  -0.9906    0.0822
    0.1275  -0.9884    0.0830
    0.1275  -0.9884    0.0830
    0.1461  -0.9857    0.0840
    0.1461  -0.9857    0.0840
    0.1655  -0.9825    0.0851
    0.1655  -0.9825    0.0851
    0.1858  -0.9788    0.0864
    0.1858  -0.9788    0.0864
    0.2070  -0.9744    0.0879
    0.2070  -0.9744    0.0879
    0.2295  -0.9692    0.0896
    0.2295  -0.9692    0.0896
    0.2534  -0.9630    0.0917
    0.2534  -0.9630    0.0917
    0.2791  -0.9557    0.0940
    0.2791  -0.9557    0.0940
    0.3069  -0.9468    0.0967
    0.3069  -0.9468    0.0967
    0.3374  -0.9361    0.0998
    0.3374  -0.9361    0.0998
    0.3711  -0.9228    0.1035
    0.3711  -0.9228    0.1035
    0.4091  -0.9061    0.1079
    0.4091  -0.9061    0.1079
    0.4526  -0.8845    0.1133
    0.4526  -0.8845    0.1133
    0.5035  -0.8556    0.1199
    0.5035  -0.8556    0.1199
    0.5649  -0.8151    0.1282
    0.5649  -0.8151    0.1282
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    0.6419  -0.7540    0.1391
    0.7448  -0.6492    0.1543
    0.7448  -0.6492    0.1543
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    0.9286  -0.3236    0.1815
    0.0082  -0.9996    0.0266
    0.0082  -0.9996    0.0266
    0.0246  -0.9993    0.0267
    0.0246  -0.9993    0.0267
    0.0412  -0.9988    0.0267
    0.0412  -0.9988    0.0267
    0.0579  -0.9980    0.0268
    0.0579  -0.9980    0.0268
    0.0748  -0.9968    0.0270
    0.0748  -0.9968    0.0270
    0.0921  -0.9954    0.0272
    0.0921  -0.9954    0.0272
    0.1097  -0.9936    0.0274
    0.1097  -0.9936    0.0274
    0.1279  -0.9914    0.0277
    0.1279  -0.9914    0.0277
    0.1466  -0.9888    0.0280
    0.1466  -0.9888    0.0280
    0.1661  -0.9857    0.0284
    0.1661  -0.9857    0.0284
    0.1864  -0.9821    0.0288
    0.1864  -0.9821    0.0288
    0.2077  -0.9777    0.0293
    0.2077  -0.9777    0.0293
    0.2303  -0.9727    0.0299
    0.2303  -0.9727    0.0299
    0.2544  -0.9666    0.0306
    0.2544  -0.9666    0.0306
    0.2802  -0.9594    0.0314
    0.2802  -0.9594    0.0314
    0.3082  -0.9508    0.0323
    0.3082  -0.9508    0.0323
    0.3389  -0.9402    0.0333
    0.3389  -0.9402    0.0333
    0.3729  -0.9272    0.0346
    0.3729  -0.9272    0.0346
    0.4113  -0.9108    0.0361
    0.4113  -0.9108    0.0361
    0.4552  -0.8896    0.0379
    0.4552  -0.8896    0.0379
    0.5068  -0.8611    0.0401
    0.5068  -0.8611    0.0401
    0.5691  -0.8212    0.0429
    0.5691  -0.8212    0.0429
    0.6475  -0.7606    0.0466
    0.6475  -0.7606    0.0466
    0.7528  -0.6562    0.0519
    0.7528  -0.6562    0.0519
    0.9425  -0.3284    0.0612
    0.9425  -0.3284    0.0612
</float_array>
<technique_common>
  <accessor source="#Reflect_Normals01" count="  975" stride="3">
        <param name="X" type="float" />
        <param name="Y" type="float" />
        <param name="Z" type="float" />
  </accessor>
</technique_common>
</source>
<vertices id="Reflect_Vertices">
  <input semantic="POSITION" source="#Reflect_Positions" />
</vertices>
<polylist count="  975" material="Material2">
  <input semantic="VERTEX" source="#Reflect_Vertices" offset="0" />
  <input semantic="NORMAL" source="#Reflect_Normals" offset="1" />
<vcount>
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
</vcount>
<p>
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    0    1  496    1  497    1
    0    2  497    2  498    2
    0    3  498    3  499    3
    0    4  499    4  500    4
    0    5  500    5  501    5
    0    6  501    6  502    6
    0    7  502    7  503    7
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  495  25  469  25  470  25
  495  26  470  26  496  26
  496  27  470  27  471  27
  496  28  471  28  497  28
  497  29  471  29  472  29
  497  30  472  30  498  30
  498  31  472  31  473  31
  498  32  473  32  499  32
  499  33  473  33  474  33
  499  34  474  34  500  34
  500  35  474  35  475  35
  500  36  475  36  501  36
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  506  47  480  47  481  47
  506  48  481  48  507  48
  507  49  481  49  482  49
  507  50  482  50  508  50
  508  51  482  51  483  51
  508  52  483  52  509  52
  509  53  483  53  484  53
  509  54  484  54  510  54
  510  55  484  55  485  55
  510  56  485  56  511  56
  511  57  485  57  486  57
  511  58  486  58  512  58
  512  59  486  59  487  59
  512  60  487  60  513  60
  513  61  487  61  488  61
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  514  63  488  63  489  63
  514  64  489  64  515  64
  515  65  489  65  490  65
  515  66  490  66  516  66
  516  67  490  67  491  67
  516  68  491  68  517  68
  517  69  491  69  492  69
  517  70  492  70  518  70
  518  71  492  71  493  71
  518  72  493  72  519  72
  519  73  493  73  494  73
  519  74  494  74  520  74
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  470  77  444  77  445  77
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  474  85  448  85  449  85
  474  86  449  86  475  86
  475  87  449  87  450  87
  475  88  450  88  476  88
  476  89  450  89  451  89
  476  90  451  90  477  90
  477  91  451  91  452  91
  477  92  452  92  478  92
  478  93  452  93  453  93
  478  94  453  94  479  94
  479  95  453  95  454  95
  479  96  454  96  480  96
  480  97  454  97  455  97
  480  98  455  98  481  98
  481  99  455  99  456  99
  481  100  456  100  482  100
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  482  102  457  102  483  102
  483  103  457  103  458  103
  483  104  458  104  484  104
  484  105  458  105  459  105
  484  106  459  106  485  106
  485  107  459  107  460  107
  485  108  460  108  486  108
  486  109  460  109  461  109
  486  110  461  110  487  110
  487  111  461  111  462  111
  487  112  462  112  488  112
  488  113  462  113  463  113
  488  114  463  114  489  114
  489  115  463  115  464  115
  489  116  464  116  490  116
  490  117  464  117  465  117
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  491  119  465  119  466  119
  491  120  466  120  492  120
  492  121  466  121  467  121
  492  122  467  122  493  122
  493  123  467  123  468  123
  493  124  468  124  494  124
  443  125  417  125  418  125
  443  126  418  126  444  126
  444  127  418  127  419  127
  444  128  419  128  445  128
  445  129  419  129  420  129
  445  130  420  130  446  130
  446  131  420  131  421  131
  446  132  421  132  447  132
  447  133  421  133  422  133
  447  134  422  134  448  134
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  449  137  423  137  424  137
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  452  144  427  144  453  144
  453  145  427  145  428  145
  453  146  428  146  454  146
  454  147  428  147  429  147
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  455  149  429  149  430  149
  455  150  430  150  456  150
  456  151  430  151  431  151
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  464  167  438  167  439  167
  464  168  439  168  465  168
  465  169  439  169  440  169
  465  170  440  170  466  170
  466  171  440  171  441  171
  466  172  441  172  467  172
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  417  175  391  175  392  175
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  423  187  397  187  398  187
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  385  315  359  315  360  315
  385  316  360  316  386  316
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  183  625  157  625  158  625
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  184  628  159  628  185  628
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  185  630  160  630  186  630
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  186  632  161  632  187  632
  187  633  161  633  162  633
  187  634  162  634  188  634
  188  635  162  635  163  635
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  189  638  164  638  190  638
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  190  640  165  640  191  640
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  194  648  169  648  195  648
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  195  650  170  650  196  650
  196  651  170  651  171  651
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  200  660  175  660  201  660
  201  661  175  661  176  661
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  202  663  176  663  177  663
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  203  666  178  666  204  666
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  205  669  179  669  180  669
  205  670  180  670  206  670
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  206  672  181  672  207  672
  207  673  181  673  182  673
  207  674  182  674  208  674
  157  675  131  675  132  675
  157  676  132  676  158  676
  158  677  132  677  133  677
  158  678  133  678  159  678
  159  679  133  679  134  679
  159  680  134  680  160  680
  160  681  134  681  135  681
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  168  697  142  697  143  697
  168  698  143  698  169  698
  169  699  143  699  144  699
  169  700  144  700  170  700
  170  701  144  701  145  701
  170  702  145  702  171  702
  171  703  145  703  146  703
  171  704  146  704  172  704
  172  705  146  705  147  705
  172  706  147  706  173  706
  173  707  147  707  148  707
  173  708  148  708  174  708
  174  709  148  709  149  709
  174  710  149  710  175  710
  175  711  149  711  150  711
  175  712  150  712  176  712
  176  713  150  713  151  713
  176  714  151  714  177  714
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  180  721  154  721  155  721
  180  722  155  722  181  722
  181  723  155  723  156  723
  181  724  156  724  182  724
  131  725  105  725  106  725
  131  726  106  726  132  726
  132  727  106  727  107  727
  132  728  107  728  133  728
  133  729  107  729  108  729
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  142  747  116  747  117  747
  142  748  117  748  143  748
  143  749  117  749  118  749
  143  750  118  750  144  750
  144  751  118  751  119  751
  144  752  119  752  145  752
  145  753  119  753  120  753
  145  754  120  754  146  754
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  152  768  127  768  153  768
  153  769  127  769  128  769
  153  770  128  770  154  770
  154  771  128  771  129  771
  154  772  129  772  155  772
  155  773  129  773  130  773
  155  774  130  774  156  774
  105  775  79  775  80  775
  105  776  80  776  106  776
  106  777  80  777  81  777
  106  778  81  778  107  778
  107  779  81  779  82  779
  107  780  82  780  108  780
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  112  790  87  790  113  790
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  113  792  88  792  114  792
  114  793  88  793  89  793
  114  794  89  794  115  794
  115  795  89  795  90  795
  115  796  90  796  116  796
  116  797  90  797  91  797
  116  798  91  798  117  798
  117  799  91  799  92  799
  117  800  92  800  118  800
  118  801  92  801  93  801
  118  802  93  802  119  802
  119  803  93  803  94  803
  119  804  94  804  120  804
  120  805  94  805  95  805
  120  806  95  806  121  806
  121  807  95  807  96  807
  121  808  96  808  122  808
  122  809  96  809  97  809
  122  810  97  810  123  810
  123  811  97  811  98  811
  123  812  98  812  124  812
  124  813  98  813  99  813
  124  814  99  814  125  814
  125  815  99  815  100  815
  125  816  100  816  126  816
  126  817  100  817  101  817
  126  818  101  818  127  818
  127  819  101  819  102  819
  127  820  102  820  128  820
  128  821  102  821  103  821
  128  822  103  822  129  822
  129  823  103  823  104  823
  129  824  104  824  130  824
  79  825  53  825  54  825
  79  826  54  826  80  826
  80  827  54  827  55  827
  80  828  55  828  81  828
  81  829  55  829  56  829
  81  830  56  830  82  830
  82  831  56  831  57  831
  82  832  57  832  83  832
  83  833  57  833  58  833
  83  834  58  834  84  834
  84  835  58  835  59  835
  84  836  59  836  85  836
  85  837  59  837  60  837
  85  838  60  838  86  838
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  86  840  61  840  87  840
  87  841  61  841  62  841
  87  842  62  842  88  842
  88  843  62  843  63  843
  88  844  63  844  89  844
  89  845  63  845  64  845
  89  846  64  846  90  846
  90  847  64  847  65  847
  90  848  65  848  91  848
  91  849  65  849  66  849
  91  850  66  850  92  850
  92  851  66  851  67  851
  92  852  67  852  93  852
  93  853  67  853  68  853
  93  854  68  854  94  854
  94  855  68  855  69  855
  94  856  69  856  95  856
  95  857  69  857  70  857
  95  858  70  858  96  858
  96  859  70  859  71  859
  96  860  71  860  97  860
  97  861  71  861  72  861
  97  862  72  862  98  862
  98  863  72  863  73  863
  98  864  73  864  99  864
  99  865  73  865  74  865
  99  866  74  866  100  866
  100  867  74  867  75  867
  100  868  75  868  101  868
  101  869  75  869  76  869
  101  870  76  870  102  870
  102  871  76  871  77  871
  102  872  77  872  103  872
  103  873  77  873  78  873
  103  874  78  874  104  874
  53  875  27  875  28  875
  53  876  28  876  54  876
  54  877  28  877  29  877
  54  878  29  878  55  878
  55  879  29  879  30  879
  55  880  30  880  56  880
  56  881  30  881  31  881
  56  882  31  882  57  882
  57  883  31  883  32  883
  57  884  32  884  58  884
  58  885  32  885  33  885
  58  886  33  886  59  886
  59  887  33  887  34  887
  59  888  34  888  60  888
  60  889  34  889  35  889
  60  890  35  890  61  890
  61  891  35  891  36  891
  61  892  36  892  62  892
  62  893  36  893  37  893
  62  894  37  894  63  894
  63  895  37  895  38  895
  63  896  38  896  64  896
  64  897  38  897  39  897
  64  898  39  898  65  898
  65  899  39  899  40  899
  65  900  40  900  66  900
  66  901  40  901  41  901
  66  902  41  902  67  902
  67  903  41  903  42  903
  67  904  42  904  68  904
  68  905  42  905  43  905
  68  906  43  906  69  906
  69  907  43  907  44  907
  69  908  44  908  70  908
  70  909  44  909  45  909
  70  910  45  910  71  910
  71  911  45  911  46  911
  71  912  46  912  72  912
  72  913  46  913  47  913
  72  914  47  914  73  914
  73  915  47  915  48  915
  73  916  48  916  74  916
  74  917  48  917  49  917
  74  918  49  918  75  918
  75  919  49  919  50  919
  75  920  50  920  76  920
  76  921  50  921  51  921
  76  922  51  922  77  922
  77  923  51  923  52  923
  77  924  52  924  78  924
  27  925    1  925    2  925
  27  926    2  926  28  926
  28  927    2  927    3  927
  28  928    3  928  29  928
  29  929    3  929    4  929
  29  930    4  930  30  930
  30  931    4  931    5  931
  30  932    5  932  31  932
  31  933    5  933    6  933
  31  934    6  934  32  934
  32  935    6  935    7  935
  32  936    7  936  33  936
  33  937    7  937    8  937
  33  938    8  938  34  938
  34  939    8  939    9  939
  34  940    9  940  35  940
  35  941    9  941  10  941
  35  942  10  942  36  942
  36  943  10  943  11  943
  36  944  11  944  37  944
  37  945  11  945  12  945
  37  946  12  946  38  946
  38  947  12  947  13  947
  38  948  13  948  39  948
  39  949  13  949  14  949
  39  950  14  950  40  950
  40  951  14  951  15  951
  40  952  15  952  41  952
  41  953  15  953  16  953
  41  954  16  954  42  954
  42  955  16  955  17  955
  42  956  17  956  43  956
  43  957  17  957  18  957
  43  958  18  958  44  958
  44  959  18  959  19  959
  44  960  19  960  45  960
  45  961  19  961  20  961
  45  962  20  962  46  962
  46  963  20  963  21  963
  46  964  21  964  47  964
  47  965  21  965  22  965
  47  966  22  966  48  966
  48  967  22  967  23  967
  48  968  23  968  49  968
  49  969  23  969  24  969
  49  970  24  970  50  970
  50  971  24  971  25  971
  50  972  25  972  51  972
  51  973  25  973  26  973
  51  974  26  974  52  974
</p>
</polylist>
  </mesh>
</geometry>
<!-- EquatorialPlane (begin) -->
<geometry id="EquatorialPlane">
  <mesh>
<source id="EquatorialPlane_Positions">
<float_array id="EquatorialPlane_Coordinates" count="48">
  -5.5000    -5.5000    0.2000
    5.5000    -5.5000    0.2000
    5.5000    5.5000    0.2000
  -5.5000    5.5000    0.2000
  -5.7500    -5.7500    0.2000
    5.7500    -5.7500    0.2000
    5.7500    5.7500    0.2000
  -5.7500    5.7500    0.2000
  -5.5000    -5.5000  -0.2000
    5.5000    -5.5000  -0.2000
    5.5000    5.5000  -0.2000
  -5.5000    5.5000  -0.2000
  -5.7500    -5.7500  -0.2000
    5.7500    -5.7500  -0.2000
    5.7500    5.7500  -0.2000
  -5.7500    5.7500  -0.2000
</float_array>
<technique_common>
  <accessor source="#EquatorialPlane_Coordinates" count="  16" stride="3">
        <param name="X" type="float" />
        <param name="Y" type="float" />
        <param name="Z" type="float" />
  </accessor>
</technique_common>
</source>
<source id="EquatorialPlane_Normals">
<float_array id="EquatorialPlane_Normals01" count="18">
    0.0000    0.0000    1.0000
    0.0000    0.0000    -1.0000
    0.0000  -1.0000    0.0000
    0.0000    1.0000    0.0000
  -1.0000    0.0000    0.0000
    1.0000    0.0000    0.0000
</float_array>
<technique_common>
  <accessor source="#EquatorialPlane_Normals01" count="6" stride="3">
        <param name="X" type="float" />
        <param name="Y" type="float" />
        <param name="Z" type="float" />
  </accessor>
</technique_common>
</source>
<vertices id="EquatorialPlane_Vertices">
  <input semantic="POSITION" source="#EquatorialPlane_Positions" />
</vertices>
<polylist count="  12" material="Material2">
  <input semantic="VERTEX" source="#EquatorialPlane_Vertices" offset="0" />
  <input semantic="NORMAL" source="#EquatorialPlane_Normals" offset="1" />
<vcount>
4 4 4 4
4 4 4 4
4 4 4 4
</vcount>
<p>
4 0  5 0  1 0  0 0
5 0  6 0  2 0  1 0
6 0  7 0  3 0  2 0
7 0  4 0  0 0  3 0
8 1  9 1  13 1  12 1
9 1  10 1  14 1  13 1
10 1  11 1  15 1  14 1
11 1  8 1  12 1  15 1
12 2  13 2  5 2  4 2
14 3  15 3  7 3  6 3
15 4  12 4  4 4  7 4
13 5  14 5  6 5  5 5
</p>
</polylist>
  </mesh>
</geometry>
<!-- EquatorialPlane (end)  -->
    </library_geometries>
    <library_animations>
  <animation id="First_rotation_euler_Z">
<!-- for EFE/Ou model b41c385, clockstop = 36.5047 and anglestop = 1800.0 -->
<!-- this means that one 360 degree turn of the ellipsoid takes 7.3009 clock units -->
    <source id="First_rotation_euler_Z-input">
      <float_array id="First_rotation_euler_Z-input-array" count="31">
  0.00
  1.22
  2.43
  3.65
  4.87
  6.08
  7.30
  8.52
  9.73
  10.95
  12.17
  13.39
  14.60
  15.82
  17.04
  18.25
  19.47
  20.69
  21.90
  23.12
  24.34
  25.55
  26.77
  27.99
  29.20
  30.42
  31.64
  32.85
  34.07
  35.29
  36.50
      </float_array>
      <technique_common>
          <accessor source="#First_rotation_euler_Z-input-array" count="31" stride="1">
            <param name="TIME" type="float"/>
          </accessor>
      </technique_common>
    </source>
<!-- This sets the spin rate of the "Entire" ellipsoid -->
    <source id="First_rotation_euler_Z-output">
      <float_array id="First_rotation_euler_Z-output-array" count="31">
    5.0
    5.0
    5.0
    5.0
    5.0
    5.0
    5.0
    5.0
    5.0
    5.0
    5.0
    5.0
    5.0
    5.0
    5.0
    5.0
    5.0
    5.0
    5.0
    5.0
    5.0
    5.0
    5.0
    5.0
    5.0
    5.0
    5.0
    5.0
    5.0
    5.0
    5.0
      </float_array>
      <technique_common>
          <accessor source="#First_rotation_euler_Z-output-array" count="31" stride="1">
            <param name="ANGLE" type="float"/>
          </accessor>
      </technique_common>
    </source>
<!-- This sets the spin rate of the "MidPlane" Frame of reference -->
    <source id="Frame_rotation_euler_Z-output">
      <float_array id="Frame_rotation_euler_Z-output-array" count="31">
  1803.0
  1743.0
  1683.0
  1623.0
  1563.0
  1503.0
  1443.0
  1383.0
  1323.0
  1263.0
  1203.0
  1143.0
  1083.0
  1023.0
  963.0
  903.0
  843.0
  783.0
  723.0
  663.0
  603.0
  543.0
  483.0
  423.0
  363.0
  303.0
  243.0
  183.0
  123.0
    63.0
    3.0
      </float_array>
      <technique_common>
          <accessor source="#Frame_rotation_euler_Z-output-array" count="31" stride="1">
            <param name="ANGLE" type="float"/>
          </accessor>
      </technique_common>
    </source>
    <sampler id="First_rotation_euler_Z-sampler">
      <input semantic="INPUT" source="#First_rotation_euler_Z-input"/>
      <input semantic="OUTPUT" source="#First_rotation_euler_Z-output"/>
    </sampler>
    <sampler id="Frame_rotation_euler_Z-sampler">
      <input semantic="INPUT" source="#First_rotation_euler_Z-input"/>
      <input semantic="OUTPUT" source="#Frame_rotation_euler_Z-output"/>
    </sampler>
    <channel source="#First_rotation_euler_Z-sampler" target="EntireEllipsoid/rotationZ.ANGLE"/>
    <channel source="#Frame_rotation_euler_Z-sampler" target="Inertial/rotationZ.ANGLE"/>
  </animation>
<!-- FLUID ELEMENT 1 -->
  <animation id="FluidElement1_location">
    <source id="Lagrange1_location_X-input">
      <float_array id="Lagrange1_location_X-input-array" count="  37">
  0.0000
  1.0014
  2.0029
  3.0043
  4.0057
  5.0071
  6.0086
  7.0100
  8.0114
  9.0129
10.0143
11.0157
12.0171
13.0186
14.0200
15.0214
16.0229
17.0243
18.0257
19.0271
20.0286
21.0300
22.0314
23.0329
24.0343
25.0357
26.0371
27.0386
28.0400
29.0414
30.0429
31.0443
32.0457
33.0472
34.0486
35.0500
36.0514
      </float_array>
      <technique_common>
          <accessor source="#Lagrange1_location_X-input-array" count="  37" stride="1">
            <param name="TIME" type="float"/>
          </accessor>
      </technique_common>
    </source>
    <source id="Lagrange1_location_X-output">
      <float_array id="Lagrange1_location_X-output-array" count="  37">
  1.0000
  0.9921
  0.9686
  0.9298
  0.8763
  0.8090
  0.7290
  0.6374
  0.5358
  0.4258
  0.3090
  0.1874
  0.0628
-0.0628
-0.1874
-0.3090
-0.4258
-0.5358
-0.6374
-0.7290
-0.8090
-0.8763
-0.9298
-0.9686
-0.9921
-1.0000
-0.9921
-0.9686
-0.9298
-0.8763
-0.8090
-0.7290
-0.6374
-0.5358
-0.4258
-0.3090
-0.1874
      </float_array>
      <technique_common>
          <accessor source="#Lagrange1_location_X-output-array" count="  37" stride="1">
            <param name="X" type="float"/>
          </accessor>
      </technique_common>
    </source>
    <sampler id="Lagrange1_location_X-sampler">
      <input semantic="INPUT" source="#Lagrange1_location_X-input"/>
      <input semantic="OUTPUT" source="#Lagrange1_location_X-output"/>
    </sampler>
    <source id="Lagrange1_location_Y-output">
      <float_array id="Lagrange1_location_Y-output-array" count="  37">
-0.0000
-0.0514
-0.1020
-0.1509
-0.1975
-0.2410
-0.2807
-0.3159
-0.3462
-0.3710
-0.3899
-0.4027
-0.4092
-0.4092
-0.4027
-0.3899
-0.3710
-0.3462
-0.3159
-0.2807
-0.2410
-0.1975
-0.1509
-0.1020
-0.0514
  0.0000
  0.0514
  0.1020
  0.1509
  0.1975
  0.2410
  0.2807
  0.3159
  0.3462
  0.3710
  0.3899
  0.4027
      </float_array>
      <technique_common>
          <accessor source="#Lagrange1_location_Y-output-array" count="  37" stride="1">
            <param name="Y" type="float"/>
          </accessor>
      </technique_common>
    </source>
    <sampler id="Lagrange1_location_Y-sampler">
      <input semantic="INPUT" source="#Lagrange1_location_X-input"/>
      <input semantic="OUTPUT" source="#Lagrange1_location_Y-output"/>
    </sampler>
    <channel source="#Lagrange1_location_X-sampler" target="Lagrange01/location.X"/>
    <channel source="#Lagrange1_location_Y-sampler" target="Lagrange01/location.Y"/>
    <channel source="#Lagrange1_location_X-sampler" target="Lagrange02/location.X"/>
    <channel source="#Lagrange1_location_Y-sampler" target="Lagrange02/location.Y"/>
    <channel source="#Lagrange1_location_X-sampler" target="Lagrange03/location.X"/>
    <channel source="#Lagrange1_location_Y-sampler" target="Lagrange03/location.Y"/>
</animation>
<!-- CLOCK (clockstop = 36.5047)
    One spin of ellipsoid (or frame) is 1.8252 EFE sqrt(pi * G * rho) units;
    Want 1 EFE unit to take 4.0 seconds of TIME;
    Hence, one spin of ellipsoid (360 degrees) is 7.3009 seconds of TIME;
            and 5 ellipsoid spins is 36.5047 seconds of TIME.
    Divide one spin (360) into 12 pieces
    ==> 30 degrees = 1 timestep = 4 x 0.1521 = 0.6084 seconds of TIME.
-->
  <animation id="Cube_quaternion_Z">
    <source id="Cube_quaternion_Z-input">
      <float_array id="Cube_quaternion_Z-input-array" count=" 147">
    0.00  0.25  0.50  0.75  1.00  1.25  1.50  1.75  2.00  2.25  2.50  2.75  3.00  3.25  3.50  3.75
    4.00  4.25  4.50  4.75  5.00  5.25  5.50  5.75  6.00  6.25  6.50  6.75  7.00  7.25  7.50  7.75
    8.00  8.25  8.50  8.75  9.00  9.25  9.50  9.75 10.00 10.25 10.50 10.75 11.00 11.25 11.50 11.75
    12.00 12.25 12.50 12.75 13.00 13.25 13.50 13.75 14.00 14.25 14.50 14.75 15.00 15.25 15.50 15.75
    16.00 16.25 16.50 16.75 17.00 17.25 17.50 17.75 18.00 18.25 18.50 18.75 19.00 19.25 19.50 19.75
    20.00 20.25 20.50 20.75 21.00 21.25 21.50 21.75 22.00 22.25 22.50 22.75 23.00 23.25 23.50 23.75
    24.00 24.25 24.50 24.75 25.00 25.25 25.50 25.75 26.00 26.25 26.50 26.75 27.00 27.25 27.50 27.75
    28.00 28.25 28.50 28.75 29.00 29.25 29.50 29.75 30.00 30.25 30.50 30.75 31.00 31.25 31.50 31.75
    32.00 32.25 32.50 32.75 33.00 33.25 33.50 33.75 34.00 34.25 34.50 34.75 35.00 35.25 35.50 35.75
    36.00 36.25 36.50
      </float_array>
      <technique_common>
          <accessor source="#Cube_quaternion_Z-input-array" count="  147" stride="1">
            <param name="TIME" type="float"/>
          </accessor>
      </technique_common>
    </source>
    <source id="Cube_quaternion_Z-output">
      <float_array id="Cube_quaternion_Z-output-array" count="2352">
  0.000  0.000 -1.00  0.00  -1.0000  0.0000  0.000  0.000  0.0000  1.0000  0.000  0.00  0.000  0.000  0.000  1.000
  0.000  0.000 -1.00  0.00  -0.9239 -0.3827  0.000  0.000  -0.3827  0.9239  0.000  0.00  0.000  0.000  0.000  1.000
  0.000  0.000 -1.00  0.00  -0.7071 -0.7071  0.000  0.000  -0.7071  0.7071  0.000  0.00  0.000  0.000  0.000  1.000
  0.000  0.000 -1.00  0.00  -0.3827 -0.9239  0.000  0.000  -0.9239  0.3827  0.000  0.00  0.000  0.000  0.000  1.000
  0.000  0.000 -1.00  0.00  0.0000 -1.0000  0.000  0.000  -1.0000  0.0000  0.000  0.00  0.000  0.000  0.000  1.000
  0.000  0.000 -1.00  0.00  0.3827 -0.9239  0.000  0.000  -0.9239 -0.3827  0.000  0.00  0.000  0.000  0.000  1.000
  0.000  0.000 -1.00  0.00  0.7071 -0.7071  0.000  0.000  -0.7071 -0.7071  0.000  0.00  0.000  0.000  0.000  1.000
  0.000  0.000 -1.00  0.00  0.9239 -0.3827  0.000  0.000  -0.3827 -0.9239  0.000  0.00  0.000  0.000  0.000  1.000
  0.000  0.000 -1.00  0.00  1.0000  0.0000  0.000  0.000  0.0000 -1.0000  0.000  0.00  0.000  0.000  0.000  1.000
  0.000  0.000 -1.00  0.00  0.9239  0.3827  0.000  0.000  0.3827 -0.9239  0.000  0.00  0.000  0.000  0.000  1.000
  0.000  0.000 -1.00  0.00  0.7071  0.7071  0.000  0.000  0.7071 -0.7071  0.000  0.00  0.000  0.000  0.000  1.000
  0.000  0.000 -1.00  0.00  0.3827  0.9239  0.000  0.000  0.9239 -0.3827  0.000  0.00  0.000  0.000  0.000  1.000
  0.000  0.000 -1.00  0.00  0.0000  1.0000  0.000  0.000  1.0000  0.0000  0.000  0.00  0.000  0.000  0.000  1.000
  0.000  0.000 -1.00  0.00  -0.3827  0.9239  0.000  0.000  0.9239  0.3827  0.000  0.00  0.000  0.000  0.000  1.000
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  0.000  0.000 -1.00  0.00  -0.3827 -0.9239  0.000  0.000  -0.9239  0.3827  0.000  0.00  0.000  0.000  0.000  1.000
  0.000  0.000 -1.00  0.00  0.0000 -1.0000  0.000  0.000  -1.0000  0.0000  0.000  0.00  0.000  0.000  0.000  1.000
  0.000  0.000 -1.00  0.00  0.3827 -0.9239  0.000  0.000  -0.9239 -0.3827  0.000  0.00  0.000  0.000  0.000  1.000
  0.000  0.000 -1.00  0.00  0.7071 -0.7071  0.000  0.000  -0.7071 -0.7071  0.000  0.00  0.000  0.000  0.000  1.000
  0.000  0.000 -1.00  0.00  0.9239 -0.3827  0.000  0.000  -0.3827 -0.9239  0.000  0.00  0.000  0.000  0.000  1.000
  0.000  0.000 -1.00  0.00  1.0000  0.0000  0.000  0.000  0.0000 -1.0000  0.000  0.00  0.000  0.000  0.000  1.000
  0.000  0.000 -1.00  0.00  0.9239  0.3827  0.000  0.000  0.3827 -0.9239  0.000  0.00  0.000  0.000  0.000  1.000
  0.000  0.000 -1.00  0.00  0.7071  0.7071  0.000  0.000  0.7071 -0.7071  0.000  0.00  0.000  0.000  0.000  1.000
  0.000  0.000 -1.00  0.00  0.3827  0.9239  0.000  0.000  0.9239 -0.3827  0.000  0.00  0.000  0.000  0.000  1.000
  0.000  0.000 -1.00  0.00  0.0000  1.0000  0.000  0.000  1.0000  0.0000  0.000  0.00  0.000  0.000  0.000  1.000
  0.000  0.000 -1.00  0.00  -0.3827  0.9239  0.000  0.000  0.9239  0.3827  0.000  0.00  0.000  0.000  0.000  1.000
  0.000  0.000 -1.00  0.00  -0.7071  0.7071  0.000  0.000  0.7071  0.7071  0.000  0.00  0.000  0.000  0.000  1.000
  0.000  0.000 -1.00  0.00  -0.9239  0.3827  0.000  0.000  0.3827  0.9239  0.000  0.00  0.000  0.000  0.000  1.000
  0.000  0.000 -1.00  0.00  -1.0000  0.0000  0.000  0.000  0.0000  1.0000  0.000  0.00  0.000  0.000  0.000  1.000
  0.000  0.000 -1.00  0.00  -0.9239 -0.3827  0.000  0.000  -0.3827  0.9239  0.000  0.00  0.000  0.000  0.000  1.000
  0.000  0.000 -1.00  0.00  -0.7071 -0.7071  0.000  0.000  -0.7071  0.7071  0.000  0.00  0.000  0.000  0.000  1.000
      </float_array>
      <technique_common>
          <accessor source="#Cube_quaternion_Z-output-array" count="  147" stride="16">
            <param name="TRANSFORM" type="float4x4"/>
          </accessor>
      </technique_common>
    </source>
    <sampler id="Cube_quaternion_Z-sampler">
      <input semantic="INPUT" source="#Cube_quaternion_Z-input"/>
      <input semantic="OUTPUT" source="#Cube_quaternion_Z-output"/>
    </sampler>
    <channel source="#Cube_quaternion_Z-sampler" target="Jetman/transformation"/>
  </animation>
<!-- HOURHAND (clockstop =    36.5047) -->
  <animation id="HourHand_euler_Z">
    <source id="HourHand_euler_Z-input">
      <float_array id="HourHand_euler_Z-input-array" count="  147">
    0.00  0.25  0.50  0.75  1.00  1.25  1.50  1.75  2.00  2.25  2.50  2.75  3.00  3.25  3.50  3.75
    4.00  4.25  4.50  4.75  5.00  5.25  5.50  5.75  6.00  6.25  6.50  6.75  7.00  7.25  7.50  7.75
    8.00  8.25  8.50  8.75  9.00  9.25  9.50  9.75 10.00 10.25 10.50 10.75 11.00 11.25 11.50 11.75
    12.00 12.25 12.50 12.75 13.00 13.25 13.50 13.75 14.00 14.25 14.50 14.75 15.00 15.25 15.50 15.75
    16.00 16.25 16.50 16.75 17.00 17.25 17.50 17.75 18.00 18.25 18.50 18.75 19.00 19.25 19.50 19.75
    20.00 20.25 20.50 20.75 21.00 21.25 21.50 21.75 22.00 22.25 22.50 22.75 23.00 23.25 23.50 23.75
    24.00 24.25 24.50 24.75 25.00 25.25 25.50 25.75 26.00 26.25 26.50 26.75 27.00 27.25 27.50 27.75
    28.00 28.25 28.50 28.75 29.00 29.25 29.50 29.75 30.00 30.25 30.50 30.75 31.00 31.25 31.50 31.75
    32.00 32.25 32.50 32.75 33.00 33.25 33.50 33.75 34.00 34.25 34.50 34.75 35.00 35.25 35.50 35.75
    36.00 36.25 36.50
      </float_array>
      <technique_common>
          <accessor source="#HourHand_euler_Z-input-array" count="  147" stride="1">
            <param name="TIME" type="float"/>
          </accessor>
      </technique_common>
    </source>
    <source id="HourHand_euler_Z-output">
      <float_array id="HourHand_euler_Z-output-array" count="  147">
  270.0
  268.125
  266.25
  264.375
  262.5
  260.625
  258.75
  256.875
  255.0
  253.125
  251.25
  249.375
  247.5
  245.625
  243.75
  241.875
  240.0
  238.125
  236.25
  234.375
  232.5
  230.625
  228.75
  226.875
  225.0
  223.125
  221.25
  219.375
  217.5
  215.625
  213.75
  211.875
  210.0
  208.125
  206.25
  204.375
  202.5
  200.625
  198.75
  196.875
  195.0
  193.125
  191.25
  189.375
  187.5
  185.625
  183.75
  181.875
  180.0
  178.125
  176.25
  174.375
  172.5
  170.625
  168.75
  166.875
  165.0
  163.125
  161.25
  159.375
  157.5
  155.625
  153.75
  151.875
  150.0
  148.125
  146.25
  144.375
  142.5
  140.625
  138.75
  136.875
  135.0
  133.125
  131.25
  129.375
  127.5
  125.625
  123.75
  121.875
  120.0
  118.125
  116.25
  114.375
  112.5
  110.625
  108.75
  106.875
  105.0
  103.125
  101.25
  99.375
  97.5
  95.625
  93.75
  91.875
  90.0
  88.125
  86.25
  84.375
  82.5
  80.625
  78.75
  76.875
  75.0
  73.125
  71.25
  69.375
  67.5
  65.625
  63.75
  61.875
  60.0
  58.125
  56.25
  54.375
  52.5
  50.625
  48.75
  46.875
  45.0
  43.125
  41.25
  39.375
  37.5
  35.625
  33.75
  31.875
  30.0
  28.125
  26.25
  24.375
  22.5
  20.625
  18.75
  16.875
  15.0
  13.125
  11.25
    9.375
    7.5
    5.625
    3.75
    1.875
    0.0
  -1.875
  -3.75
      </float_array>
      <technique_common>
          <accessor source="#HourHand_euler_Z-output-array" count="  147" stride="1">
            <param name="ANGLE" type="float"/>
          </accessor>
      </technique_common>
    </source>
    <sampler id="HourHand_euler_Z-sampler">
      <input semantic="INPUT" source="#HourHand_euler_Z-input"/>
      <input semantic="OUTPUT" source="#HourHand_euler_Z-output"/>
    </sampler>
    <channel source="#HourHand_euler_Z-sampler" target="HourHand/rotationZ.ANGLE"/>
  </animation>
    </library_animations>
    <library_controllers/>
    <library_visual_scenes>
        <visual_scene id="ID1">
            <node id="EntireEllipsoid" name="OculusRift_EFE">
            <translate>0.0 0.0 0.0</translate>
            <rotate sid="rotationX">1.0 0.0 0.0  0.0</rotate>
            <rotate sid="rotationY">0.0 1.0 0.0  0.0</rotate>
            <rotate sid="rotationZ">0.0 0.0 1.0  5.0</rotate>
            <scale sid="scale">5.0 5.0 5.0</scale>
                <node id="First" name="First_instance_EFE">
                  <translate>0.0 0.0 0.0</translate>
                  <rotate sid="rotationX">1.0 0.0 0.0  0.0</rotate>
                  <rotate sid="rotationY">0.0 1.0 0.0  0.0</rotate>
                  <rotate sid="rotationZ">0.0 0.0 1.0  0.0</rotate>
                  <scale sid="scale">1.0 1.0 1.0</scale>
                  <instance_node url="#ID3_EFE" />
                </node>
                <node id="Second" name="Second_instance_EFE">
                  <translate>0.0 0.0 0.0</translate>
                  <rotate sid="rotationX">1.0 0.0 0.0  180.0</rotate>
                  <rotate sid="rotationY">0.0 1.0 0.0    0.0</rotate>
                  <rotate sid="rotationZ">0.0 0.0 1.0    0.0</rotate>
                  <scale sid="scale">1.0 1.0 1.0</scale>
                  <instance_node url="#ID3_EFE" />
                </node>
                <node id="Third" name="Third_instance_EFE">
                  <translate>0.0 0.0 0.0</translate>
                  <rotate sid="rotationX">1.0 0.0 0.0    0.0</rotate>
                  <rotate sid="rotationY">0.0 1.0 0.0  180.0</rotate>
                  <rotate sid="rotationZ">0.0 0.0 1.0    0.0</rotate>
                  <scale sid="scale">1.0 1.0 1.0</scale>
                  <instance_node url="#ID3_EFE" />
                </node>
                <node id="Fourth" name="Fourth_instance_EFE">
                  <translate>0.0 0.0 0.0</translate>
                  <rotate sid="rotationX">1.0 0.0 0.0  180.0</rotate>
                  <rotate sid="rotationY">0.0 1.0 0.0  180.0</rotate>
                  <rotate sid="rotationZ">0.0 0.0 1.0    0.0</rotate>
                  <scale sid="scale">1.0 1.0 1.0</scale>
                  <instance_node url="#ID3_EFE" />
                </node>
<!-- instance:  Cylindrical Pointer -->
                <node id="CylinderPointer" name="instance_cylinder"> 
                  <translate sid="location">-1.0 0.0 0.0</translate>
                    <rotate sid="rotationX">1 0 0 0</rotate>
                    <rotate sid="rotationY">0 1 0 0</rotate>
                    <rotate sid="rotationZ">0 0 1 180</rotate>
                  <scale sid="scale">0.05 0.025 0.025</scale>
                  <instance_node url="#CylPointer" />
                </node>                                       
<!-- Begin LAGRANGE markers -->
              <node id="Lagrange01" name="instance_Lagrange01">
                  <translate sid="location">1.0000 0.0000 0.0</translate>
                  <rotate sid="rotationX">1.0 0.0 0.0  0.0</rotate>
                  <rotate sid="rotationY">0.0 1.0 0.0  0.0</rotate>
                  <rotate sid="rotationZ">0.0 0.0 1.0  0.0</rotate>
                  <scale sid="scale">0.06 0.06 0.06</scale>
                <instance_node url="#Primary_MarkerID3" />
              </node>
            <node id="Shrink02" name="instance_Shrink02">
              <scale sid="scale">0.8 0.8 0.8</scale>
              <node id="Lagrange02" name="instance_Lagrange02">
                  <translate sid="location">1.0000 0.0000 0.0</translate>
                  <rotate sid="rotationX">1.0 0.0 0.0  0.0</rotate>
                  <rotate sid="rotationY">0.0 1.0 0.0  0.0</rotate>
                  <rotate sid="rotationZ">0.0 0.0 1.0  0.0</rotate>
                  <scale sid="scale">0.075 0.075 0.075</scale>
                <instance_node url="#Primary_MarkerID3" />
              </node>
            </node>
            <node id="Shrink03" name="instance_Shrink03">
              <scale sid="scale">0.6 0.6 0.6</scale>
              <node id="Lagrange03" name="instance_Lagrange03">
                  <translate sid="location">1.0000 0.0000 0.0</translate>
                  <rotate sid="rotationX">1.0 0.0 0.0  0.0</rotate>
                  <rotate sid="rotationY">0.0 1.0 0.0  0.0</rotate>
                  <rotate sid="rotationZ">0.0 0.0 1.0  0.0</rotate>
                  <scale sid="scale">0.1 0.1 0.1</scale>
                <instance_node url="#Primary_MarkerID3" />
              </node>
            </node>
              <node id="Marker01" name="instance_marker01">
                <matrix>0.025 0.0 0.0 1.0000  0.0 0.025 0.0 -0.0000  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker02" name="instance_marker02">
                <matrix>0.025 0.0 0.0 0.9921  0.0 0.025 0.0 -0.0514  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker03" name="instance_marker03">
                <matrix>0.025 0.0 0.0 0.9686  0.0 0.025 0.0 -0.1020  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker04" name="instance_marker04">
                <matrix>0.025 0.0 0.0 0.9298  0.0 0.025 0.0 -0.1509  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker05" name="instance_marker05">
                <matrix>0.025 0.0 0.0 0.8763  0.0 0.025 0.0 -0.1975  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker06" name="instance_marker06">
                <matrix>0.025 0.0 0.0 0.8090  0.0 0.025 0.0 -0.2410  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker07" name="instance_marker07">
                <matrix>0.025 0.0 0.0 0.7290  0.0 0.025 0.0 -0.2807  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker08" name="instance_marker08">
                <matrix>0.025 0.0 0.0 0.6374  0.0 0.025 0.0 -0.3159  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker09" name="instance_marker09">
                <matrix>0.025 0.0 0.0 0.5358  0.0 0.025 0.0 -0.3462  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker10" name="instance_marker10">
                <matrix>0.025 0.0 0.0 0.4258  0.0 0.025 0.0 -0.3710  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker11" name="instance_marker11">
                <matrix>0.025 0.0 0.0 0.3090  0.0 0.025 0.0 -0.3899  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker12" name="instance_marker12">
                <matrix>0.025 0.0 0.0 0.1874  0.0 0.025 0.0 -0.4027  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker13" name="instance_marker13">
                <matrix>0.025 0.0 0.0 0.0628  0.0 0.025 0.0 -0.4092  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker14" name="instance_marker14">
                <matrix>0.025 0.0 0.0 -0.0628  0.0 0.025 0.0 -0.4092  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker15" name="instance_marker15">
                <matrix>0.025 0.0 0.0 -0.1874  0.0 0.025 0.0 -0.4027  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker16" name="instance_marker16">
                <matrix>0.025 0.0 0.0 -0.3090  0.0 0.025 0.0 -0.3899  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker17" name="instance_marker17">
                <matrix>0.025 0.0 0.0 -0.4258  0.0 0.025 0.0 -0.3710  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker18" name="instance_marker18">
                <matrix>0.025 0.0 0.0 -0.5358  0.0 0.025 0.0 -0.3462  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker19" name="instance_marker19">
                <matrix>0.025 0.0 0.0 -0.6374  0.0 0.025 0.0 -0.3159  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker20" name="instance_marker20">
                <matrix>0.025 0.0 0.0 -0.7290  0.0 0.025 0.0 -0.2807  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker21" name="instance_marker21">
                <matrix>0.025 0.0 0.0 -0.8090  0.0 0.025 0.0 -0.2410  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker22" name="instance_marker22">
                <matrix>0.025 0.0 0.0 -0.8763  0.0 0.025 0.0 -0.1975  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker23" name="instance_marker23">
                <matrix>0.025 0.0 0.0 -0.9298  0.0 0.025 0.0 -0.1509  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker24" name="instance_marker24">
                <matrix>0.025 0.0 0.0 -0.9686  0.0 0.025 0.0 -0.1020  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker25" name="instance_marker25">
                <matrix>0.025 0.0 0.0 -0.9921  0.0 0.025 0.0 -0.0514  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker26" name="instance_marker26">
                <matrix>0.025 0.0 0.0 -1.0000  0.0 0.025 0.0 -0.0000  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
<!-- Second Half -->
              <node id="Marker28" name="instance_marker28">
                <matrix>0.025 0.0 0.0 -0.9921  0.0 0.025 0.0 0.0514  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker29" name="instance_marker29">
                <matrix>0.025 0.0 0.0 -0.9686  0.0 0.025 0.0 0.1020  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker30" name="instance_marker30">
                <matrix>0.025 0.0 0.0 -0.9298  0.0 0.025 0.0 0.1509  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker31" name="instance_marker31">
                <matrix>0.025 0.0 0.0 -0.8763  0.0 0.025 0.0 0.1975  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker32" name="instance_marker32">
                <matrix>0.025 0.0 0.0 -0.8090  0.0 0.025 0.0 0.2410  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker33" name="instance_marker33">
                <matrix>0.025 0.0 0.0 -0.7290  0.0 0.025 0.0 0.2807  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker34" name="instance_marker34">
                <matrix>0.025 0.0 0.0 -0.6374  0.0 0.025 0.0 0.3159  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker35" name="instance_marker35">
                <matrix>0.025 0.0 0.0 -0.5358  0.0 0.025 0.0 0.3462  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker36" name="instance_marker36">
                <matrix>0.025 0.0 0.0 -0.4258  0.0 0.025 0.0 0.3710  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker37" name="instance_marker37">
                <matrix>0.025 0.0 0.0 -0.3090  0.0 0.025 0.0 0.3899  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker38" name="instance_marker38">
                <matrix>0.025 0.0 0.0 -0.1874  0.0 0.025 0.0 0.4027  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker39" name="instance_marker39">
                <matrix>0.025 0.0 0.0 -0.0628  0.0 0.025 0.0 0.4092  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker40" name="instance_marker40">
                <matrix>0.025 0.0 0.0 0.0628  0.0 0.025 0.0 0.4092  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker41" name="instance_marker41">
                <matrix>0.025 0.0 0.0 0.1874  0.0 0.025 0.0 0.4027  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker42" name="instance_marker42">
                <matrix>0.025 0.0 0.0 0.3090  0.0 0.025 0.0 0.3899  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker43" name="instance_marker43">
                <matrix>0.025 0.0 0.0 0.4258  0.0 0.025 0.0 0.3710  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker44" name="instance_marker44">
                <matrix>0.025 0.0 0.0 0.5358  0.0 0.025 0.0 0.3462  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker45" name="instance_marker45">
                <matrix>0.025 0.0 0.0 0.6374  0.0 0.025 0.0 0.3159  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker46" name="instance_marker46">
                <matrix>0.025 0.0 0.0 0.7290  0.0 0.025 0.0 0.2807  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker47" name="instance_marker47">
                <matrix>0.025 0.0 0.0 0.8090  0.0 0.025 0.0 0.2410  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker48" name="instance_marker48">
                <matrix>0.025 0.0 0.0 0.8763  0.0 0.025 0.0 0.1975  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker49" name="instance_marker49">
                <matrix>0.025 0.0 0.0 0.9298  0.0 0.025 0.0 0.1509  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker50" name="instance_marker50">
                <matrix>0.025 0.0 0.0 0.9686  0.0 0.025 0.0 0.1020  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker51" name="instance_marker51">
                <matrix>0.025 0.0 0.0 0.9921  0.0 0.025 0.0 0.0514  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
<!-- End LAGRANGE markers -->
            </node>                          <!-- END EntireEllipsoid -->
          <node id="Inertial" name="instance_inertial">  <!-- Start Inertial Grouping of Objects -->
            <translate>0.0 0.0 0.0</translate>
            <rotate sid="rotationX">1.0 0.0 0.0  0.0</rotate>
            <rotate sid="rotationY">0.0 1.0 0.0  0.0</rotate>
            <rotate sid="rotationZ">0.0 0.0 1.0  1803.0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
            <node id="Zup_Pointer" name="instance_zupPointer"> 
              <translate>0.0 0.0 5.0</translate>
                <rotate sid="rotationX">1 0 0  0.0</rotate>
                <rotate sid="rotationY">0 1 0  0.0</rotate>
                <rotate sid="rotationZ">0 0 1  0.0</rotate>
              <scale sid="scale">0.125 0.5 1.5</scale>
              <instance_node url="#ZupPointer" />
            </node>                                       
<!-- instance:  MidPlane Frame (MidPlane flips with rotationX = 180 for clockwise spin)-->
            <node id="MidPlane" name="instance_MidPlane"> 
              <translate>0.0 0.0 0.0</translate>
                  <rotate sid="rotationX">1.0 0.0 0.0  0.0</rotate>
                  <rotate sid="rotationY">0.0 1.0 0.0  0.0</rotate>
                  <rotate sid="rotationZ">0.0 0.0 1.0  0.0</rotate>
              <scale sid="scale">1.25 1.25 1.25</scale>
              <instance_node url="#EqPlane" />
            </node>
<!-- BEGIN LABELING HERE -->
          <node name="Labels">
          <translate>7.0 -2.0 5.0</translate>
          <rotate sid="rotationX">1 0 0 0.0</rotate>
          <rotate sid="rotationY">0 1 0 0</rotate>
          <rotate sid="rotationZ">0 0 1 180</rotate>
          <scale sid="scale">0.1 0.1 0.1</scale>
<!--  Equals sign #1  -->
            <node name="Equals1">
            <translate>0.0 15.0 1.0</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
                <node id="IDd51" name="instance_51">
                    <matrix>0.25  0 0 0.0  0 1  0 0.0  0 0 1 2.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDd52" name="instance_52">
                    <matrix>0.25  0 0 0.0  0 1  0 1.1  0 0 1 2.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDd53" name="instance_53">
                    <matrix>0.25  0 0 0.0  0 1  0 2.2  0 0 1 2.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDd55" name="instance_55">
                    <matrix>0.25  0 0 0.0  0 1  0 0.0  0 0 1 4.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDd56" name="instance_56">
                    <matrix>0.25  0 0 0.0  0 1  0 1.1  0 0 1 4.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDd57" name="instance_57">
                    <matrix>0.25  0 0 0.0  0 1  0 2.2  0 0 1 4.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
            </node>
<!--  Equals sign #2  -->
            <node name="Equals2">
            <translate>0.0 15.0 -8.5</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
                <node id="IDd51" name="instance_51">
                    <matrix>0.25  0 0 0.0  0 1  0 0.0  0 0 1 2.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDd52" name="instance_52">
                    <matrix>0.25  0 0 0.0  0 1  0 1.1  0 0 1 2.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDd53" name="instance_53">
                    <matrix>0.25  0 0 0.0  0 1  0 2.2  0 0 1 2.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDd55" name="instance_55">
                    <matrix>0.25  0 0 0.0  0 1  0 0.0  0 0 1 4.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDd56" name="instance_56">
                    <matrix>0.25  0 0 0.0  0 1  0 1.1  0 0 1 4.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDd57" name="instance_57">
                    <matrix>0.25  0 0 0.0  0 1  0 2.2  0 0 1 4.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
          </node>
<!--  Division sign #1  -->
            <node name="Divide1">
            <translate>0.0 4.4 1.0</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 0.75 1.0</scale>
                <node id="IDd21" name="instance_21">
                    <matrix>0.25  0 0 0.0  0 1  0 0.0  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
                <node id="IDd22" name="instance_22">
                    <matrix>0.25  0 0 0.0  0 -1  0 1.1  0 0 -1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
                <node id="IDd23" name="instance_23">
                    <matrix>0.25  0 0 0.0  0 1  0 1.1  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
                <node id="IDd24" name="instance_24">
                    <matrix>0.25  0 0 0.0  0 -1  0 2.2  0 0 -1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
                <node id="IDd25" name="instance_25">
                    <matrix>0.25  0 0 0.0  0 1  0 2.2  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
                <node id="IDd26" name="instance_26">
                    <matrix>0.25  0 0 0.0  0 -1  0 3.3  0 0 -1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
                <node id="IDd27" name="instance_27">
                    <matrix>0.25  0 0 0.0  0 1  0 3.3  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
            </node>
<!--  Division sign #2  -->
            <node name="Divide2">
            <translate>0.0 4.4 -8.5</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 0.75 1.0</scale>
                <node id="IDd21" name="instance_21">
                    <matrix>0.25  0 0 0.0  0 1  0 0.0  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
                <node id="IDd22" name="instance_22">
                    <matrix>0.25  0 0 0.0  0 -1  0 1.1  0 0 -1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
                <node id="IDd23" name="instance_23">
                    <matrix>0.25  0 0 0.0  0 1  0 1.1  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
                <node id="IDd24" name="instance_24">
                    <matrix>0.25  0 0 0.0  0 -1  0 2.2  0 0 -1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
                <node id="IDd25" name="instance_25">
                    <matrix>0.25  0 0 0.0  0 1  0 2.2  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
                <node id="IDd26" name="instance_26">
                    <matrix>0.25  0 0 0.0  0 -1  0 3.3  0 0 -1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
                <node id="IDd27" name="instance_27">
                    <matrix>0.25  0 0 0.0  0 1  0 3.3  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
            </node>
<!--  Letter "a" #1  -->
            <node name="Letter_a1">
            <translate>0.0 8.0 1.0</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
                <node id="IDa01" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa06" name="instance_6">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa07" name="instance_7">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa10" name="instance_10">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa11" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa18" name="instance_18">
                    <matrix>0.25  0 0 0.0  0 1 0 0.0  0 0  1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDa19" name="instance_19">
                    <matrix>0.25  0 0 0.0  0 0 1 4.4  0 -1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDa19" name="instance_19">
                    <matrix>0.25  0 0 0.0  0 0 -1 3.3  0 1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDa11" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa31" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa20" name="instance_20">
                    <matrix>0.25  0 0 0.0  0 0 1 3.3  0 -1 0 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDa21" name="instance_21">
                    <matrix>0.25  0 0 0.0  0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
            </node>
<!--  Letter "a" #2  -->
            <node name="Letter_a2">
            <translate>0.0 8.0 -8.5</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
                <node id="IDa01" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa06" name="instance_6">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa07" name="instance_7">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa10" name="instance_10">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa11" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa18" name="instance_18">
                    <matrix>0.25  0 0 0.0  0 1 0 0.0  0 0  1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDa19" name="instance_19">
                    <matrix>0.25  0 0 0.0  0 0 1 4.4  0 -1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDa19" name="instance_19">
                    <matrix>0.25  0 0 0.0  0 0 -1 3.3  0 1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDa11" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa31" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa20" name="instance_20">
                    <matrix>0.25  0 0 0.0  0 0 1 3.3  0 -1 0 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDa21" name="instance_21">
                    <matrix>0.25  0 0 0.0  0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
            </node>
<!--  Letter "a" #2  -->
            <node name="Letter_a2">
            <translate>0.0 8.0 -8.5</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
                <node id="IDa01" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa06" name="instance_6">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa07" name="instance_7">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa10" name="instance_10">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa11" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa18" name="instance_18">
                    <matrix>0.25  0 0 0.0  0 1 0 0.0  0 0  1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDa19" name="instance_19">
                    <matrix>0.25  0 0 0.0  0 0 1 4.4  0 -1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDa19" name="instance_19">
                    <matrix>0.25  0 0 0.0  0 0 -1 3.3  0 1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDa11" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa31" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa20" name="instance_20">
                    <matrix>0.25  0 0 0.0  0 0 1 3.3  0 -1 0 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDa21" name="instance_21">
                    <matrix>0.25  0 0 0.0  0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
            </node>
<!--  Letter "c"  -->
            <node name="Letter_c">
            <translate>0.0 0.0 -8.5</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
                <node id="ID001" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID002" name="instance_2">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID006" name="instance_6">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID007" name="instance_7">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID010" name="instance_10">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID011" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID018" name="instance_18">
                    <matrix>0.25  0 0 0.0  0 1 0 0.0  0 0  1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="ID019" name="instance_19">
                    <matrix>0.25  0 0 0.0  0 -1 0 3.3  0 0  -1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="ID020" name="instance_20">
                    <matrix>0.25  0 0 0.0  0 0 1 3.3  0 -1 0 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="ID021" name="instance_21">
                    <matrix>0.25  0 0 0.0  0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
            </node>
<!--  Letter "b"  ... has 8 + (4 x 15) = 68 lines -->
            <node name="Letter_b">
            <translate>0.0 0.0 1.0</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
                <node id="IDb01" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb02" name="instance_2">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb03" name="instance_3">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb04" name="instance_4">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 4.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb05" name="instance_5">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 5.5  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb12" name="instance_12">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb06" name="instance_6">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb07" name="instance_7">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb08" name="instance_8">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb09" name="instance_9">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb10" name="instance_10">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb11" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb19" name="instance_19">
                    <matrix>0.25  0 0 0.0  0 -1 0 3.3  0 0  -1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDb20" name="instance_20">
                    <matrix>0.25  0 0 0.0  0 0 1 3.3  0 -1 0 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDb21" name="instance_21">
                    <matrix>0.25  0 0 0.0  0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
            </node>
<!-- DECIMAL POINTS -->
                <node id="IDD01" name="Decimal_1">
                    <matrix>0.25 0 0 0.0  0 1 0 25.0  0 0 1 1.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDD02" name="Decimal_2">
                    <matrix>0.25 0 0 0.0  0 1 0 25.0  0 0 1 -8.5  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
<!--  Number "0" #1  ... has 8 + (4 x 18) = 80 lines -->
            <node name="Number_0">
            <translate>0.0 20.0 1.0</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
                <node id="IDb01" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb02" name="instance_2">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb03" name="instance_3">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb04" name="instance_4">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 4.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb05" name="instance_5">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 5.5  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDz19" name="instance_z19">
                    <matrix>0.25  0 0 0.0  0 1 0 0.0  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDb06" name="instance_6">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb07" name="instance_7">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb08" name="instance_8">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb09" name="instance_9">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb10" name="instance_10">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb11" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb19" name="instance_19">
                    <matrix>0.25  0 0 0.0  0 -1 0 3.3  0 0  -1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDb20" name="instance_20">
                    <matrix>0.25  0 0 0.0  0 0 1 3.3  0 -1 0 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDb21" name="instance_21">
                    <matrix>0.25  0 0 0.0  0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDz11" name="instance_z11">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDz12" name="instance_z12">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 4.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDz13" name="instance_z13">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 5.5  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
            </node>
<!--  Number "0" #2  ... has 8 + (4 x 18) = 80 lines -->
            <node name="Number_0b">
            <translate>0.0 20.0 -8.5</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
                <node id="IDb01" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb02" name="instance_2">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb03" name="instance_3">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb04" name="instance_4">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 4.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb05" name="instance_5">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 5.5  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDz19" name="instance_z19">
                    <matrix>0.25  0 0 0.0  0 1 0 0.0  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDb06" name="instance_6">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb07" name="instance_7">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb08" name="instance_8">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb09" name="instance_9">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb10" name="instance_10">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb11" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb19" name="instance_19">
                    <matrix>0.25  0 0 0.0  0 -1 0 3.3  0 0  -1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDb20" name="instance_20">
                    <matrix>0.25  0 0 0.0  0 0 1 3.3  0 -1 0 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDb21" name="instance_21">
                    <matrix>0.25  0 0 0.0  0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDz11" name="instance_z11">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDz12" name="instance_z12">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 4.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDz13" name="instance_z13">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 5.5  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
            </node>
<!--  Number "1" ... has 8 + (4 x 8) = 40 lines -->
<!--  Number "2" #1 ... has 8 + (4 x 17) = 76 lines -->
<!--  Number "2" #2 ... has 8 + (4 x 17) = 76 lines -->
<!--  Number "3"  ... has 8 + (4 x 18) = 80 lines -->
<!--  Number "4" ... has 8 + (4 x 13) = 60 lines -->
<!--  Number "5"  ... has 8 + (4 x 17) = 76 lines -->
<!--  Number "6" ... has 8 + (4 x 18) = 80 lines -->
<!--  Number "7" ... has 8 + (4 x 14) = 64 lines -->
<!--  Number "8" ... has 8 + (4 x 22) = 96 lines -->
<!--  Number "9"  ... has 8 + (4 x 15) = 68 lines -->
<!-- bovera_Digit1 is "4" -->
            <node name="bovera_Digit1">
            <translate>0.0 26.8 1.0</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
<!--  Number "4" ... has 8 + (4 x 13) = 60 lines -->
                <node id="IDe01" name="instance_e01">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDe02" name="instance_e02">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDe02" name="instance_e02">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb04" name="instance_4">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 4.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb05" name="instance_5">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 5.5  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb06" name="instance_6">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb08" name="instance_8">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb09" name="instance_9">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDn09" name="instance_9">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDf12" name="instance_n12">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDn12" name="instance_n12">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDz12" name="instance_z12">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 4.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDz13" name="instance_z13">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 5.5  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
            </node>
<!-- bovera_Digit2 is "1" -->
            <node name="bovera_Digit2">
            <translate>0.0 31.8 1.0</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
<!--  Number "1" ... has 8 + (4 x 8) = 40 lines -->
                <node id="ID101" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID102" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID103" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID104" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID105" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 4.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID106" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 5.5  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID107" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID109" name="instance_z19">
                    <matrix>0.25  0 0 0.0  0 1 0 1.1  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
            </node>
<!-- covera_Digit1 is "3" -->
            <node name="covera_Digit1">
            <translate>0.0 26.8 -8.5</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
<!--  Number "3"  ... has 8 + (4 x 18) = 80 lines -->
                <node id="ID301" name="instance_e01">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID302" name="instance_e02">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID303" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID304" name="instance_5">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 5.5  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID305" name="instance_z19">
                    <matrix>0.25  0 0 0.0  0 1 0 0.0  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="ID306" name="instance_6">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID307" name="instance_7">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID308" name="instance_8">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID309" name="instance_9">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID310" name="instance_10">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID311" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID312" name="instance_19">
                    <matrix>0.25  0 0 0.0  0 -1 0 3.3  0 0  -1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="ID313" name="instance_20">
                    <matrix>0.25  0 0 0.0  0 0 1 3.3  0 -1 0 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="ID314" name="instance_21">
                    <matrix>0.25  0 0 0.0  0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
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              <translate>0.0 0.0 0.0</translate>
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              <scale sid="scale">0.75 0.75 0.75</scale>
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          </node>
<!-- END CLOCK  -->
          </node> <!-- End Inertial Grouping of Objects -->
        </visual_scene>
    </library_visual_scenes>
    <scene>
        <instance_visual_scene url="#ID1" />
    </scene>
</COLLADA>
 
</pre>
</div>
 
==Inside the Oculus Rift S Environment==
 
===Introduction===
 
The [https://www.oculus.com/rift-s/ Oculus Rift S] will import user-constructed 3D objects and allow you to place those objects in a high-quality, interactive virtual reality (VR) environment.  But the Oculus system does not accept COLLADA-formatted files directly.  Instead, it is set up to import files that are in a ".glb" format, which is the binary version of a "GL Transmission Format" ([https://www.khronos.org/gltf/ glTF]) file.  My original expectation was that, after I learned how to construct some intricate and astrophysically interesting 3D visual scenes using COLLADA &#8212; successfully accomplished (!) as illustrated above &#8212; all I would need to do is find a community tool that could translate a COLLADA (.dae) file into glTF (.glb).
 
Here are a few discoveries I made along the way:
<ul>
<li>The Windows 10 startup menu includes a "3D Viewer" app but, at least on my Lenova PC, it does not recognize .dae-formatted files.</li>
<li>The Windows 10 startup menu includes a "Paint 3D" application.  Using this app, it was very easy to "draw" some simple 3D geometric objects &#8212; such as a cube or a torus &#8212; and it was straightforward to export each object to a .glb-formatted file.</li>
<li>[https://www.adobe.com/products/photoshop.html Adobe Photoshop] can read in a COLLADA (.dae) file and it is capable of exporting a 3D scene in .glb format.</li>
<li>[https://blackthread.io BlackThread.io] offers a browser-based tool, named "glTF Converter", that can ostensibly translate .dae-formatted files into .glb-formatted files.</li>
<li>The [https://www.khronos.org Khronos Group]'s "COLLADA to glTF" conversion tool can be located under [https://github.com/KhronosGroup/COLLADA2GLTF/ the group's name on GitHub].</li>
</ul>
 
===Khronos Group's COLLADA2GLTF Converter===
 
Among this group of potentially useful tools, we have had &#8212; by far &#8212; the most success/luck using the <font color="red">Khronos Group's COLLADA2GLTF</font> converter.  We downloaded and installed version 2 of this Khronos Group conversion tool on our Mac Pro. The executable, named <b>COLLADA2GLTF-bin</b>, was installed on our Mac at the end of a directory tree named &hellip;/Dropbox/Lenovo/COLLADA_to_gltf/COLLADA2GLTF-v2/.  In order to translate a specific COLLADA-formatted (''filename.dae) file:
<ul>
<li>From inside the Mac's "Terminal" application, we changed directories until we were sitting in the above-specified Mac (Dropbox) directory</li>
<li>We moved (or copied) the chosen COLLADA-formatted file (<b>''filename''.dae</b>) into the same directory
<li>At the terminal prompt, we typed the line command:  &nbsp; <b>./COLLADA2GLTF-bin -i ''filename''.dae -b</b></li>
<li>The .glb-formatted output file was stored as <b>&hellip;/Dropbox/Lenovo/COLLADA_to_gltf/COLLADA2GLTF-v2/output/''filename''.glb</b></li>
</ul>
 
 
<table border="1" cellpadding="8" align="center">
<tr>
  <td align="center">Example Mac-Pro Line Commands + Responses</td>
</tr>
<tr><td align="left">
<pre>
command:  pwd
response:  ../Dropbox/Lenovo/COLLADA_to_gltf/COLLADA2GLTF-v2
command:  ls *.dae
response:  Inertial17.dae
command:  ./COLLADA2GLTF-bin -i Inertial17.dae -b
response:  Converting Inertial17.dae -> output/Inertial17.glb
          Time: 48.166 ms
</pre>
</td></tr>
</table>
 
 
<font color="red">CAUTION!</font>  While we found this COLLADA2GLTF converter to be a very useful tool, we also discovered that porting a model from one visualization environment to another can be a challenging and frustrating endeavor.  It is difficult enough to build a (error-free) COLLADA-formatted model that will properly display a desired animated scene in the Mac's Preview app.  But it is naive to expect that that same COLLADA code will survive a translation to glTF and seamlessly construct the identical animated scene within the Oculus Rift S environment.  In a pair of accompanying chapters &#8212; [[User:Tohline/Appendix/Ramblings/OculusRift_S|this one]], followed by [[User:Tohline/Appendix/Ramblings/RiemannMeetsOculus#Rebuild_Riemann_S-Type_Ellipsoid_Inside_Oculus_Rift_S_Environment|another one]] &#8212; we have chronicled the steps that we have taken to generate our first few (error-free) COLLADA-based models that display properly in both environments.  Experience has taught us that &hellip; (1) When interpreting COLLADA's <xml>-formatted instructions, the Mac's Preview app is considerably more forgiving than is the Oculus system; (2) almost any code that display's properly in the Mac's Preview app will survive the translation to glTF, in the sense that the COLLADA2GLTF converter seldom complains; but, (3) nevertheless, frequently the Oculus system won't display the model because it detects an error(s), but it almost never suggests what the error(s) might be.  When embarking on the development of a new interactive and animated 3D visual scene, the best strategy is a time-consuming one:  Start with a COLLADA code that works in both environments &#8212; we provide two such codes herein; make only incremental changes and ensure that the model displays properly in the Mac's Preview app; convert the COLLADA-based code to glTF (.glb); don the Oculus Rift S headset & hand controllers, and attempt to import this new model into your "Oculus Home".
 
===Import to Oculus Rift S Environment===
 
We purchased a Lenovo PC (Windows 10) gaming laptop to drive the Oculus Rift S system; more specifically, it is Lenovo's Legion Y740 15" with NVIDIA GeForce GTX 1660Ti 6GB.  Two connections were required:  (1) Mini DisplayPort; and (2) USB.  We downloaded and installed the Oculus program files under the directory <b>C:\Program Files\Oculus</b>.  We also mounted Dropbox on the Lenovo, which gave us immediate access to the model files that were created using the Mac Pro.  As an example, we located the model file named <b>Inertial17.glb</b> and placed a copy of the file in the directory <b>&hellip; This PC\Documents\Oculus Home\_Import</b>.  Any (error free) ".glb"-formatted file that is located in this directory is available for import into the Oculus' 3D virtual-reality environment. 
 
 
When we want to view one of our models, we first start the Oculus application on the Lenovo then click on "Devices" to check whether the headset and two hand controllers are in proper communication with the PC (GREEN buttons) or not (RED buttons).  We don the headset & controllers, thereby entering the Oculus Rift S VR environment.  [Occasionally we forget to start the Oculus app before putting on the headset.  When this happens, the app seems to sense that we have donned the headset and it starts itself!]  The following sequence of steps allows us to place the example model, <b>Inertial17</b>, into our ''Oculus Home''.
 
 
<table border="1" align="left" width="100%" cellpadding="8">
<tr>
  <th align="center" colspan="2"><font size="+1">Inside the ''Oculus Rift S'' Home Environment</font></th>
</tr>
<tr>
  <td align="center">[[File:HomeImage01sm.png|200px|Oculus Home (view 1)]]</td>
  <td align="left">The image shown here, immediately to the left, is a snapshot of the first scene that is displayed in our ''Oculus Home'' shortly after we have donned the headset and the pair of hand controllers.  The shallow, curved desk immediately in front of us presents ten or so clickable panels (menu choices).  In the image, we have highlighted the "Home" button by pointing to it with the index finger of our right hand.
<ul>
  <li><font color="red">Click</font> on the "Home" button; the interactive panels in this scene will disappear.</li>
  <li>Wait (~ 10 seconds) and our stored "Home" environment will load.</li>
  <li>"Menu" button vs. "Oculus" button</li>
</ul>
</td>
</tr>
<tr>
  <td align="center">[[File:HomeImage02sm.mod.png|200px|Oculus Home (view 2)]]</td>
  <td align="left">
<ul>
  <li><font color="red">Click</font> the "Menu" button on the left-hand controller; it sits just below the "Y" and "X" buttons;</li>
</ul>
 
The image shown here, immediately to the left, is a snapshot of a portion of the scene that is displayed after we have clicked the "Menu" button on our left-hand controller.  As illustrated, we have pointed to &#8212; and thereby have highlighted in blue &#8212; the top menu item, "<font color="blue">Places</font>," and we are in the process of sliding our aim down to the next menu item, "Inventory."
<ul>
  <li><font color="red">Click</font> the "Inventory" menu item.</li>
</ul>
</td>
</tr>
<tr>
  <td align="center">[[File:HomeImage03sm.mod.png|200px|Oculus Home (view 3)]]</td>
  <td align="left">
As is shown here, immediately to the left, the menu panel is updated after the "Inventory" button has been clicked, as directed above.
<ul>
  <li><font color="red">Click</font> the "My Imports" menu item.</li>
</ul>
 
After highlighting then clicking "<font color="blue">My Imports</font>," a three-dimensional display case (a shadow box) containing up to 4 &times; 3 objects appears, as is illustrated here in the screenshot on the left.  Each object in this display case is generated from one of the (error free) ".glb"-formatted files that is located in the aforementioned Lenovo directory <b>&hellip; This PC\Documents\Oculus Home\_Import</b> &#8212; including files that reside in subdirectories of this parent _Import directory.
</td>
</tr>
<tr>
  <td align="left" colspan="2">
NOTE:
<ul>
<li>The display case can hold more than twelve objects, but it will only display twelve at a time.  In order to see more, you need to point to (any) one of the displayed objects then use the hand-controller's toggle button to scroll the shelves of the display case up or down.</li>
<li>If Oculus sees a (error free) ".glb" file that it has never seen before &#8212; for example, a new model file that you have just placed in the PC's <b>&hellip;\_Import</b> directory &#8212; it will display a panel asking you to "<font color="blue">Confirm</font>" that you have permission to load this material.</li>
<li>If the Oculus determines that one of your ".glb" files contains an error, it may try to display the faulty object in the display case and attach some sort of warning message.  More often than not, however, it will simply ignore the file and leave you wondering why the object does not appear in the display case.
</ul>
  </td>
</tr>
<tr>
  <td align="center">[[File:HomeImage04sm.mod.png|200px|Oculus Home (view 4)]]</td>
  <td align="left">
<ul>
  <li>Point at an object in the display case, then <font color="red">Grab</font> it (using the controller's middle-finger "grip" switch) and place it somewhere in your ''Home'' room.</li>
</ul>
In the image shown here, immediately on the left, we are pointing at, and are about to "grab", the model we have named, <b>MultiLagrange18</b>.  We could have, just as well, pointed at and grabbed the model sitting on the shelf next to it named, <b>Inertial17</b>.
 
<br />
It is worth mentioning that after you have ''grabbed'' an object &#8212; and before you have placed it in the room &#8212; you can do several things with it.
<ol><li>Using the hand controller's ''thumbstick'', you can move the object farther from (or closer to) you by pushing the thumbstick away from you (or by pulling it toward you).</li>
<li>Using the controller's index-finger ''trigger'', you can toggle between a mode that lets you spin the object and a mode that let's you resize it.  In either mode, the direction or amplitude of the spin/resizing is determined by pushing the ''thumbstick'' to the left or right varying amounts.</li>
</ol>
</td>
</tr>
<tr>
  <td align="center">[[File:HomeImage05sm.png|200px|Oculus Home (view 5)]]</td>
  <td align="left">
The image shown here, immediately on the left, is a snapshot of our Oculus ''Home'' shortly after our model named, <b>Inertial17</b>, has been resized (enlarged) then placed in the room.
</td>
</tr>
<tr>
  <td align="left" colspan="2">
NOTE:  The steps required to remove a model from the "<font color="blue">My Imports</font>" Inventory &#8212; that is, from the display case &#8212; are not easy to guess.  Here we identify what appears to be the required sequence of steps, using our model, <b>MultiLagrange18</b>, as an example.
<ul>
<li>Assuming the <b>MultiLagrange18</b> model is one of the objects that is on display in the ''Oculus Home'' room, grab it with the right-hand controller and use the index-finger "trigger" to toggle to the mode that lets you spin the object (the resize mode does not seem to work for this task).</li>
<li>Press the "B" button; this should return the object to the "My Imports" display case.</li>
<li>Point your index finger at the compartment on the "My Imports" display case that contains the (miniaturized) <b>MultiLagrange18</b> model, then use your thumb to press the "B" controller button.  [Be careful not to squeeze the "grip" button with your middle finger instead, as you will end up unintentionally grabbing the object again.]  A small panel containing bibliographical information about the <b>MultiLagrange18</b> file will appear immediately in front of your face; an even smaller accompanying panel will ask if you want to "Remove Upload", that is, do you want to remove the file from the inventory.</li>
<li>Point your index finger at the smaller of these two panels and click on it (using the middle finger's "grip" button) to indicate you want the file removed.  The panels will disappear but, confusingly, the inventory display box will not change in any way to signify that your request is being implemented.</li>
<li>Remove the headset; sit down in front of the Lenovo PC; locate the <b>MultiLagrange18.glb</b> that has been stored in the Oculus' _Import directory and trash it!
 
The next time you don the Oculus Rift S headset and look at the "My Imports" display case,  the <b>MultiLagrange18</b> will no lonber be among the group of displayed objects.
</ul>
  </td>
</tr>
</table>
 
<p>&nbsp;</p>
 
<table border="1" align="center" cellpadding="0" width="710px" cellpadding="5">
<tr>
  <th align="center" colspan="2"><font size="+1">Additional Photos from Inside the ''Oculus Rift S'' Home Environment</font></th>
</tr>
<tr>
  <td align="center">[[File:B41c385 Oculus03.jpg|350px|Third Oculus Rift Selfie]]</td>
  <td align="center">[[File:B41c385 Oculus02.jpg|350px|Second Oculus Rift Selfie]]</td>
</tr>
<tr>
  <td align="center" colspan="2">[[File:B41c385 Oculus01.jpg|700px|Third Oculus Rift Selfie]]</td>
</tr>
<tr>
  <td align="left" colspan="2">
Two of our COLLADA-driven animated models can be identified in each of the three frames of this image montage:  In all three cases, the one on the right is model <b>Inertial17</b> and the one on the left is model <b>MultiLagrange18</b>.  The bottom (selfie) visual scene illustrates that we can add to our Oculus home environment other items that are straightforwardly selected from a large Oculus objects inventory.
  </td>
</tr>
</table>
 
==Footnotes==
 
<sup>&Dagger;</sup>Adopting the characteristic mass <math>~(M_\mathrm{Ch} = \mu_e^{-2} \cdot 1.14205 \times 10^{34} ~\mathrm{g})</math> and characteristic length <math>~(\ell_1 = \mu_e^{-1} \cdot 7.71395 \times 10^{8} ~\mathrm{cm})</math> that are associated with a [[User:Tohline/SSC/Structure/WhiteDwarfs#White_Dwarfs|white dwarf]] equation of state, we can reasonably state that the characteristic mean density of a spherically symmetric white dwarf is,
<table border="0" cellpadding="5" align="center">
 
<tr>
  <td align="right">
<math>~{\bar\rho}_\mathrm{WD}</math>
  </td>
  <td align="center">
<math>~\equiv</math>
  </td>
  <td align="left">
<math>~
\frac{3 M_\mathrm{Ch}}{4\pi \ell_1^3} = \mu_e \cdot 5.93972 \times 10^{6}~\mathrm{g}~{\mathrm{cm}}^{-3} \, .
</math>
  </td>
</tr>
</table>
 
Drawing from our [[#Animation|above discussion of timescales that arise in the context of our COLLADA-driven animations]], we therefore appreciate that the characteristic oscillation period associated with a white dwarf whose molecular weight of electrons is <math>~\mu_e = 2</math>, proves to be,
<table border="0" cellpadding="5" align="center">
 
<tr>
  <td align="right">
<math>~[P_0]_\mathrm{WD}</math>
  </td>
  <td align="center">
<math>~=</math>
  </td>
  <td align="left">
<math>~
\biggl[ \frac{4\pi}{G{\bar\rho}_\mathrm{WD}} \biggr]^{1 / 2} = 3.98~\mathrm{s}\, .
</math>
  </td>
</tr>
</table>
 
By presenting animation scenes in which one wall-clock "hour" equates to approximately 4 seconds of real time, we can reasonably assert that our animated models fairly represent how a Riemann-ellipsoid-like white dwarf should behave in real time.
 
=See Also=


* Discussion of [[User:Tohline/ThreeDimensionalConfigurations/RiemannStype|Ou's Riemann-Like Ellipsoids]]
* Discussion of [[User:Tohline/ThreeDimensionalConfigurations/RiemannStype|Ou's Riemann-Like Ellipsoids]]
* [[User:Tohline/Appendix/Ramblings/VirtualReality|Virtual Reality and 3D Printing]]
 
* [[User:Tohline/Appendix/Ramblings/OculusRift_S|Success Importing Animated Scene into Oculus Rift S]]
* [[User:Tohline/ThreeDimensionalConfigurations/MeetsCOLLADAandOculusRiftS|Riemann Meets COLLADA &amp; Oculus Rift S]]: Example <b>(b/a, c/a) = (0.41, 0.385)</b>
* [[User:Tohline/Appendix/Ramblings/RiemannMeetsOculus|Carefully (Re)Build Riemann S-type Ellipsoids Inside Oculus Rift Environment]]
** [[User:Tohline/Appendix/Ramblings/VirtualReality#Virtual_Reality_and_3D_Printing|Virtual Reality and 3D Printing]]
** [[User:Tohline/Appendix/Ramblings/OculusRift_S|Success Importing Animated Scene into Oculus Rift S]]
** [[User:Tohline/Appendix/Ramblings/RiemannMeetsOculus|Carefully (Re)Build Riemann Type S Ellipsoids Inside Oculus Rift Environment]]
** Other Example S-type Riemann Ellipsoids:
*** <b>[[User:Tohline/Appendix/Ramblings/RiemannB90C333|(b/a, c/a) = (0.90, 0.333)]]</b>
*** <b>[[User:Tohline/Appendix/Ramblings/RiemannB74C692|(b/a, c/a) = (0.74, 0.692)]]</b>
*** <b>[[User:Tohline/Appendix/Ramblings/RiemannB28C256|(b/a, c/a) = (0.28, 0.256)]]</b>




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{{LSU_HBook_footer}}

Latest revision as of 03:56, 14 June 2020


Riemann Meets COLLADA & Oculus Rift S

If you want to jump straight to the fun part, copy the ASCII text file that is contained below within the scrollable box named, Inertial17.dae, and read the accompanying instructions regarding how to view this example model on a Mac. A second file — presenting the same example model, but as viewed from a rotating frame of reference — can be extracted from a separate scrollable box named, MultiLagrange18.dae.


Whitworth's (1981) Isothermal Free-Energy Surface
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Example Model

Key Physical Parameters

The model that we have chosen to use in our first successful construction of a COLLADA-based, 3D and interactive animation has the following properties; this model has been selected from Table 2 of our accompanying discussion of Riemann S-type ellipsoids:

Figure 1a
 
EFE Parameter Space

 

<math>~\frac{b}{a} = 0.41</math>

 

Figure 1b
EFE Model b41c385

<math>~\frac{c}{a} = 0.385</math>

Direct

 

Adjoint

<math>~\Omega_\mathrm{EFE} = 0.547874</math>

<math>~\Omega_\mathrm{EFE} = - 0.079886</math>

<math>~\lambda_\mathrm{EFE} = 0.079886</math>

<math>~\lambda_\mathrm{EFE} = - 0.547874</math>

<math>~f = - 0.415418</math>

<math>~f = - 19.53923</math>

The subscript "EFE" on Ω and λ means that the relevant frequency is given in units that have been adopted in [EFE], that is, in units of <math>~[\pi G\rho]^{1 / 2}</math>. In Figure 1a, the yellow circular marker, that has been placed where the pair of purple dashed lines cross, identifies the location of this model in the "c/a versus b/a" EFE Diagram that appears as Figure 2 on p. 902 of S. Chandrasekhar (1965); essentially the same diagram appears in §49 (p. 147) of [EFE].

In a separate chapter we have discussed various properties of uniformly rotating, Jacobi ellipsoids; they are equilibrium configurations that lie along the sequence that runs from "M2" (on the b/a = 1, Maclaurin sequence) to the origin of this diagram. Our chosen model lies off of — just above — the Jacobi-ellipsoid sequence, which means that it is not rotating as a solid body. Instead, as we focus first on the direct (as opposed to the adjoint) configuration, we appreciate that while the ellipsoid is spinning prograde (counter-clockwise) with a frequency given by |ΩEFE|, each Lagrangian fluid element inside as well as on the surface of the ellipsoid is traveling retrograde (clockwise) along an elliptical path with a frequency given by |λEFE|.

The COLLADA Code & Initial 3D Scene

The following scrollable box titled, Inertial17.dae, contains an <xml>-formatted COLLADA code that, when properly executed, uses the interactive, 3D animation capabilities of video game drivers to illustrate, in a quantitatively precise fashion, the dynamical flows that are associated with our chosen example model of an equilibrium S-type Riemann ellipsoid. On a Macintosh computer platform, all of the features of this animated and interactive model can be accessed by simply opening the file using Apple's in-house "Preview" application. Figure 1b provides a snapshot of the Preview app's window immediately (TIME = 0.0) after the COLLADA code has been read into the app. More elements of this 3D visual scene will be identified and discussed below, but for now we simply point out that the center of the opaque, purple ellipsoid coincides with the origin of the principal underlying "laboratory" coordinate frame — that is, at (X0, Y0, Z0) = (0, 0, 0) — and the ellipsoid has the desired axis ratios (b/a, c/a) = (0.41, 0.385).


Inertial17.dae     …     a COLLADA code containing 7968 lines of <xml>-formatted ASCII text

<?xml version="1.0" encoding="UTF-8" standalone="no" ?>
<COLLADA xmlns="http://www.collada.org/2005/11/COLLADASchema" version="1.4.1">
    <asset>
        <contributor>
            <author>jet53man</author>
            <authoring_tool>Raw XML</authoring_tool>
        </contributor>
        <created>2020-04-28</created>
        <modified>2020-05-20</modified>
        <unit meter="0.0254" name="inch" />
        <up_axis>Z_UP</up_axis>
<!-- 
This file originally was named FullLast45X.dae ...
here its assigned name is Inertial17.dae (etc.)
we are inserting various objects, drawn from b41c385_DI.dae

                 <node>        <geometry>       <material>      <effect>
*** firstclock:    ID3     Clock_OuterEdge         ID6            ID5
***           :            Clock_InnerEdge       InnerID6       InnerID5
***   Jetman  :  ArrowID3  Clock_ArrowEdge       ArrowID6       ArrowID5
***  HourHand :  HourID3   Clock_HourEdge        HourID6        HourID5
-->
    </asset>
    <library_effects>
        <effect id="DiffusePurple_00">
            <profile_COMMON>
                <technique sid="COMMON">
                    <phong>
                        <diffuse>
                            <color>0.5 0.0 0.99  1.0</color>
                        </diffuse>
                        <transparency>
               <float sid="transparency">1.0</float>
                        </transparency>
                    </phong>
                </technique>
            </profile_COMMON>
        </effect>
        <effect id="DiffuseRed_EFE">
            <profile_COMMON>
                <technique sid="COMMON">
                    <lambert>
                        <diffuse>
                            <color>1.0 0.0 0.0  1.0</color>
                        </diffuse>
                    </lambert>
                </technique>
            </profile_COMMON>
        </effect>
<!-- effect:  MidPlane Frame -->
        <effect id="MidPlaneID5">
            <profile_COMMON>
                <technique sid="COMMON">
                    <lambert>
                        <diffuse>
                            <color>0.0 0.0 0.6 0.5</color>
                        </diffuse>
                    </lambert>
                </technique>
            </profile_COMMON>
        </effect>
<!-- effect:  Cylindrical Pointer -->
        <effect id="CylID5">
            <profile_COMMON>
                <technique sid="COMMON">
                    <lambert>
                        <diffuse>
                            <color>0.0 0.0 0.0 1.0</color>
                        </diffuse>
                    </lambert>
                </technique>
            </profile_COMMON>
        </effect>
        <effect id="MarkersID5">
          <profile_COMMON>
            <technique sid="COMMON">
              <lambert>
                <diffuse>
                  <color>1 1 0 1</color>
                </diffuse>
              </lambert>
            </technique>
          </profile_COMMON>
        </effect>
<!-- effect:  Letters -->
        <effect id="LettersID5">
            <profile_COMMON>
                <technique sid="COMMON">
                    <lambert>
                        <diffuse>
                            <color>0 0 0 1</color>
                        </diffuse>
                    </lambert>
                </technique>
            </profile_COMMON>
        </effect>
        <effect id="DiagonalID5">
            <profile_COMMON>
                <technique sid="COMMON">
                    <lambert>
                        <diffuse>
                            <color>0 0 1 1</color>
                        </diffuse>
                    </lambert>
                </technique>
            </profile_COMMON>
        </effect>
        <effect id="Black_DiagonalID5">
            <profile_COMMON>
                <technique sid="COMMON">
                    <lambert>
                        <diffuse>
                            <color>0 0 0 1</color>
                        </diffuse>
                    </lambert>
                </technique>
            </profile_COMMON>
        </effect>
<!-- effect:  Four Clock Components -->
        <effect id="ID5">
            <profile_COMMON>
                <technique sid="COMMON">
                    <lambert>
                        <diffuse>
                            <color>0 0 1 1</color>
                        </diffuse>
                    </lambert>
                </technique>
            </profile_COMMON>
        </effect>
        <effect id="InnerID5">
            <profile_COMMON>
                <technique sid="COMMON">
                    <lambert>
                        <diffuse>
                            <color>0.4 0.0 0.7 0.4</color>
                        </diffuse>
                    </lambert>
                </technique>
            </profile_COMMON>
        </effect>
        <effect id="ArrowID5">
            <profile_COMMON>
                <technique sid="COMMON">
                    <lambert>
                        <diffuse>
                            <color>1.0 0.0 0.0 1.0</color>
                        </diffuse>
                    </lambert>
                </technique>
            </profile_COMMON>
        </effect>
        <effect id="HourID5">
            <profile_COMMON>
                <technique sid="COMMON">
                    <lambert>
                        <diffuse>
                            <color>0.0 0.0 0.0 1.0</color>
                        </diffuse>
                    </lambert>
                </technique>
            </profile_COMMON>
        </effect>
    </library_effects>
    <library_materials>
<!-- material:  Four Clock Components -->
        <material id="ID6" name="material">
            <instance_effect url="#ID5" />
        </material>
        <material id="InnerID6" name="Inner_material">
            <instance_effect url="#InnerID5" />
        </material>
        <material id="ArrowID6" name="Arrow_material">
            <instance_effect url="#ArrowID5" />
        </material>
        <material id="HourID6" name="Hour_material">
            <instance_effect url="#HourID5" />
        </material>
        <material id="ID6_EFE" name="material">
            <instance_effect url="#DiffusePurple_00" />
        </material>
<!-- material:  MidPlane Frame -->
        <material id="MidPlaneID6" name="MidPlane_material">
            <instance_effect url="#MidPlaneID5" />
        </material>
<!-- material:  Cylindrical Pointer -->
        <material id="CylID6" name="Cyl_material">
            <instance_effect url="#CylID5" />
        </material>
        <material id="ZupID6" name="Zup_material">
            <instance_effect url="#MidPlaneID5" />
        </material>
        <material id="MarkersID6" name="markers_material">
            <instance_effect url="#MarkersID5" />
        </material>
        <material id="Primary_MarkerID6" name="primary_marker_material">
            <instance_effect url="#DiffuseRed_EFE" />
        </material>
<!-- material:  Letters -->
        <material id="LettersID6" name="material">
            <instance_effect url="#LettersID5" />
        </material>
        <material id="DiagonalID6" name="material">
            <instance_effect url="#DiagonalID5" />
        </material>
        <material id="Black_DiagonalID6" name="material">
            <instance_effect url="#Black_DiagonalID5" />
        </material>
    </library_materials>
    <library_nodes>
<!-- node:  Three clock components -->
        <node id="ID3" name="cube_component">
            <instance_geometry url="#Clock_OuterEdge">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#ID6">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
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                    </technique_common>
                </bind_material>
            </instance_geometry>
            <instance_geometry url="#Clock_InnerEdge">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#InnerID6">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
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                    </technique_common>
                </bind_material>
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            <instance_geometry url="#Clock_ArrowEdge">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#ArrowID6">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                        </instance_material>
                    </technique_common>
                </bind_material>
            </instance_geometry>
        </node>
        <node id="HourID3" name="hour_hand">
            <instance_geometry url="#Clock_HourEdge">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#HourID6">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                        </instance_material>
                    </technique_common>
                </bind_material>
            </instance_geometry>
        </node>
        <node id="ID3_EFE" name="cube_componentEFE">
            <instance_geometry url="#EllipsoidOctant">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#ID6_EFE">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                        </instance_material>
                    </technique_common>
                </bind_material>
            </instance_geometry>
            <instance_geometry url="#ReflectOctant">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#ID6_EFE">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                        </instance_material>
                    </technique_common>
                </bind_material>
            </instance_geometry>
        </node>
<!-- node:  MidPlane Frame -->
        <node id="EqPlane" name="equatorial_plane">
            <instance_geometry url="#EquatorialPlane">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#MidPlaneID6">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                        </instance_material>
                    </technique_common>
                </bind_material>
            </instance_geometry>
        </node>
<!-- node:  Cylindrical Pointer -->
        <node id="CylPointer" name="cylindrical_component">
            <instance_geometry url="#Cylinder">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#CylID6">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                        </instance_material>
                    </technique_common>
                </bind_material>
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        </node>
        <node id="ZupPointer" name="Zup_component">
            <instance_geometry url="#CubeID4">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#ZupID6">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
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                    </technique_common>
                </bind_material>
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        </node>
        <node id="MarkersID3" name="Lagrange_markers">
          <instance_geometry url="#CubeID4">
            <bind_material>
              <technique_common>
                <instance_material symbol="Material2" target="#MarkersID6">
                  <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                </instance_material>
              </technique_common>
            </bind_material>
          </instance_geometry>
        </node>
        <node id="Primary_MarkerID3" name="Primary_marker">
          <instance_geometry url="#CubeID4">
            <bind_material>
              <technique_common>
                <instance_material symbol="Material2" target="#Primary_MarkerID6">
                  <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                </instance_material>
              </technique_common>
            </bind_material>
          </instance_geometry>
        </node>
<!-- node:  Letters -->
        <node id="LettersID3" name="cube_component">
            <instance_geometry url="#CubeID4">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#LettersID6">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                        </instance_material>
                    </technique_common>
                </bind_material>
            </instance_geometry>
        </node>
        <node id="DiagonalID3" name="diagonal_component">
            <instance_geometry url="#DiagonalID4">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#DiagonalID6">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                        </instance_material>
                    </technique_common>
                </bind_material>
            </instance_geometry>
        </node>
        <node id="Black_DiagonalID3" name="Blackdiagonal_component">
            <instance_geometry url="#DiagonalID4">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#Black_DiagonalID6">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                        </instance_material>
                    </technique_common>
                </bind_material>
            </instance_geometry>
        </node>
    </library_nodes>
    <library_geometries>
<!-- geometry:  Four Clock Components -->
        <geometry id="Clock_OuterEdge">
            <mesh>
<!--
            **********************************************
            *
            *  Insert first portion of clock's structure
            *
            **********************************************
-->
                <source id="Clock_Positions">
                  <float_array id="Coordinates01" count="123"> 0.0  1.0  0.2 1.0  1.0  0.2 1.0  0.0  0.2 1.0 -1.0  0.2 0.0 -1.0  0.2 -1.0 -1.0  0.2 -1.0  0.0  0.2 -1.0  1.0  0.2 0.0  1.0 -0.2 1.0  1.0 -0.2 1.0  0.0 -0.2 1.0 -1.0 -0.2 0.0 -1.0 -0.2 -1.0 -1.0 -0.2 -1.0  0.0 -0.2 -1.0  1.0 -0.2 0.9  0.0  0.2 0.779423 0.45 0.2 0.45 0.779423 0.2 0.0  0.9  0.2 -0.45 0.779423 0.2 -0.779423 0.45 0.2 -0.9 0.0 0.2 -0.779423 -0.45 0.2 -0.45 -0.779423 0.2 0.0 -0.9 0.2 0.45 -0.779423 0.2 0.779423 -0.45 0.2 -0.9  0.0  -0.2 -0.779423 0.45 -0.2 -0.45 0.779423 -0.2 -0.0  0.9  -0.2 0.45 0.779423 -0.2 0.779423 0.45 -0.2 0.9 0.0 -0.2 0.779423 -0.45 -0.2 0.45 -0.779423 -0.2 -0.0 -0.9 -0.2 -0.45 -0.779423 -0.2 -0.779423 -0.45 -0.2  0.0 0.0 -0.2</float_array>
                  <technique_common>
                    <accessor source="#Coordinates01" count="41" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                    </accessor>
                  </technique_common>
                </source>
                <source id="Clock_Normals">
                  <float_array id="InnerNormals01" count="18">
 1.0  0.0  0.0
-1.0  0.0  0.0
 0.0  1.0  0.0
 0.0 -1.0  0.0
 0.0  0.0  1.0
 0.0  0.0 -1.0
                  </float_array>
                    <technique_common>
                        <accessor source="#InnerNormals01" count="6" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                        </accessor>
                    </technique_common>
                </source>
                <vertices id="Clock_Vertices">
                    <input semantic="POSITION" source="#Clock_Positions" />
                </vertices>
                <polylist count="56" material="Material2">
                    <input semantic="VERTEX" source="#Clock_Vertices" offset="0" />
                    <input semantic="NORMAL" source="#Clock_Normals" offset="1" />
<vcount> 3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3</vcount>
<p> 0 2 1 2 8 2  1 2 9 2 8 2  7 2 0 2 15 2  0 2 8 2 15 2 1 0 2 0 9 0  2 0 10 0 9 0  2 0 3 0 10 0  3 0 11 0 10 0 3 3 4 3 11 3  4 3 12 3 11 3  4 3 5 3 12 3  5 3 13 3 12 3 5 1 6 1 13 1  6 1 14 1 13 1  6 1 7 1 14 1  7 1 15 1 14 1 2 4 17 4 16 4  2 4 1 4 17 4  1 4 18 4 17 4  1 4 0 4 18 4  0 4 19 4 18 4 0 4 20 4 19 4  0 4 7 4 20 4  7 4 21 4 20 4  7 4 6 4 21 4  6 4 22 4 21 4 6 4 23 4 22 4  6 4 5 4 23 4  5 4 24 4 23 4  5 4 4 4 24 4  4 4 25 4 24 4 4 4 26 4 25 4  4 4 3 4 26 4  3 4 27 4 26 4  3 4 2 4 27 4  2 4 16 4 27 4 14 5 29 5 28 5  14 5 15 5 29 5  15 5 30 5 29 5  15 5 8 5 30 5  8 5 31 5 30 5 8 5 32 5 31 5  8 5 9 5 32 5  9 5 33 5 32 5  9 5 10 5 33 5  10 5 34 5 33 5 10 5 35 5 34 5  10 5 11 5 35 5  11 5 36 5 35 5  11 5 12 5 36 5  12 5 37 5 36 5 12 5 38 5 37 5  12 5 13 5 38 5  13 5 39 5 38 5  13 5 14 5 39 5  14 5 28 5 39 5 </p>
                </polylist>
            </mesh>
        </geometry>
        <geometry id="Clock_InnerEdge">
            <mesh>
<!--
            **********************************************
            *
            *  Insert second portion of clock's structure
            *
            **********************************************
-->
                <source id="Clock_InnerPositions">
                  <float_array id="InnerCoordinates01" count="123">
0.0  1.0  0.2 1.0  1.0  0.2 1.0  0.0  0.2 1.0 -1.0  0.2 0.0 -1.0  0.2 -1.0 -1.0  0.2 -1.0  0.0  0.2 -1.0  1.0  0.2 0.0  1.0 -0.2 1.0  1.0 -0.2 1.0  0.0 -0.2 1.0 -1.0 -0.2 0.0 -1.0 -0.2 -1.0 -1.0 -0.2 -1.0  0.0 -0.2 -1.0  1.0 -0.2 0.9  0.0  0.2 0.779423 0.45 0.2 0.45 0.779423 0.2 0.0  0.9  0.2 -0.45 0.779423 0.2 -0.779423 0.45 0.2 -0.9 0.0 0.2 -0.779423 -0.45 0.2 -0.45 -0.779423 0.2 0.0 -0.9 0.2 0.45 -0.779423 0.2 0.779423 -0.45 0.2 -0.9  0.0  -0.2 -0.779423 0.45 -0.2 -0.45 0.779423 -0.2 -0.0  0.9  -0.2 0.45 0.779423 -0.2 0.779423 0.45 -0.2 0.9 0.0 -0.2 0.779423 -0.45 -0.2 0.45 -0.779423 -0.2 -0.0 -0.9 -0.2 -0.45 -0.779423 -0.2 -0.779423 -0.45 -0.2  0.0 0.0 -0.2</float_array>
                  <technique_common>
                    <accessor source="#InnerCoordinates01" count="41" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                    </accessor>
                  </technique_common>
                </source>
                <source id="Clock_InnerNormals">
                  <float_array id="InnerNormals01" count="54">
 1.0  0.0  0.0
-1.0  0.0  0.0
 0.0  1.0  0.0
 0.0 -1.0  0.0
 0.0  0.0  1.0
 0.0  0.0 -1.0
 -0.965926 -0.258819 0.0
 -0.707107 -0.707107 0.0
 -0.258819 -0.965926 0.0
  0.258819 -0.965926 0.0
  0.707107 -0.707107 0.0
  0.965926 -0.258819 0.0
  0.965926  0.258819 0.0
  0.707107  0.707107 0.0
  0.258819  0.965926 0.0
 -0.258819  0.965926 0.0
 -0.707107  0.707107 0.0
 -0.965926  0.258819 0.0
                  </float_array>
                    <technique_common>
                        <accessor source="#InnerNormals01" count="18" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                        </accessor>
                    </technique_common>
                </source>
                <vertices id="Clock_InnerVertices">
                    <input semantic="POSITION" source="#Clock_InnerPositions" />
                </vertices>
                <polylist count="24" material="Material2">
                    <input semantic="VERTEX" source="#Clock_InnerVertices" offset="0" />
                    <input semantic="NORMAL" source="#Clock_InnerNormals" offset="1"/>
<vcount>4 4 4 4  4 4 4 4  4 4 4 4  3 3 3 3  3 3 3 3  3 3 3 3</vcount>
<p> 16 6 17 6 33 6 34 6 17 7 18 7 32 7 33 7 18 8 19 8 31 8 32 8 19 9 20 9 30 9 31 9 20 10 21 10 29 10 30 10 21 11 22 11 28 11 29 11 22 12 23 12 39 12 28 12 23 13 24 13 38 13 39 13 24 14 25 14 37 14 38 14 25 15 26 15 36 15 37 15 26 16 27 16 35 16 36 16 27 17 16 17 34 17 35 17 28 5 29 5 40 5 29 5 30 5 40 5 30 5 31 5 40 5 31 5 32 5 40 5 32 5 33 5 40 5 33 5 34 5 40 5 34 5 35 5 40 5 35 5 36 5 40 5 36 5 37 5 40 5 37 5 38 5 40 5 38 5 39 5 40 5 39 5 28 5 40 5 </p>
              </polylist>
            </mesh>
        </geometry>
        <geometry id="Clock_ArrowEdge">
            <mesh>
<!--
            **********************************************
            *
            *  Insert arrow portion of clock's structure
            *
            **********************************************
-->
                <source id="Clock_ArrowPositions">
                  <float_array id="ArrowCoordinates01" count="30"> 0.0  0.85 0.25 0.1  0.0 0.25 0.0 -0.2 0.25 -0.1  0.0 0.25 0.0  0.85 0.05 0.1  0.0 0.05 0.0 -0.2 0.05 -0.1  0.0 0.05 0.0  0.0 0.25 0.0  0.0 0.05 </float_array>
                  <technique_common>
                    <accessor source="#ArrowCoordinates01" count="10" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                    </accessor>
                  </technique_common>
                </source>
                <source id="Clock_ArrowNormals">
                  <float_array id="ArrowNormals01" count="18">
 0  0  1
 0  0 -1
 0.993151  0.116841 0.0
 0.447214 -0.894427 0.0
-0.447214 -0.894427 0.0
-0.993151  0.116841 0.0
                  </float_array>
                    <technique_common>
                        <accessor source="#ArrowNormals01" count="6" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                        </accessor>
                    </technique_common>
                </source>
                <vertices id="Clock_ArrowVertices">
                    <input semantic="POSITION" source="#Clock_ArrowPositions" />
                </vertices>
                <polylist count="12" material="Material2">
                    <input semantic="VERTEX" source="#Clock_ArrowVertices" offset="0" />
                    <input semantic="NORMAL" source="#Clock_ArrowNormals" offset="1"/>
<vcount>3 3 3 3 3 3 3 3 4 4 4 4</vcount>
<p> 0 0 8 0 1 0 1 0 8 0 2 0 2 0 8 0 3 0 3 0 8 0 0 0 4 1 5 1 9 1 5 1 6 1 9 1 6 1 7 1 9 1 7 1 4 1 9 1 0 2 1 2 5 2 4 2 1 3 2 3 6 3 5 3 2 4 3 4 7 4 6 4 3 5 0 5 4 5 7 5 </p>
              </polylist>
            </mesh>
        </geometry>
        <geometry id="Clock_HourEdge">
            <mesh>
<!--
            **********************************************
            *
            *  Insert hour_hand portion of clock's structure
            *
            **********************************************
-->
                <source id="Clock_HourPositions">
                  <float_array id="HourCoordinates01" count="30"> 0.0  0.85 0.25 0.1  0.0 0.25 0.0 -0.2 0.25 -0.1  0.0 0.25 0.0  0.85 0.05 0.1  0.0 0.05 0.0 -0.2 0.05 -0.1  0.0 0.05 0.0  0.0 0.25 0.0  0.0 0.05 </float_array>
                  <technique_common>
                    <accessor source="#HourCoordinates01" count="10" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                    </accessor>
                  </technique_common>
                </source>
                <source id="Clock_HourNormals">
                  <float_array id="HourNormals01" count="18">
 0  0  1
 0  0 -1
 0.993151  0.116841 0.0
 0.447214 -0.894427 0.0
-0.447214 -0.894427 0.0
-0.993151  0.116841 0.0
                  </float_array>
                    <technique_common>
                        <accessor source="#HourNormals01" count="6" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                        </accessor>
                    </technique_common>
                </source>
                <vertices id="Clock_HourVertices">
                    <input semantic="POSITION" source="#Clock_HourPositions" />
                </vertices>
                <polylist count="12" material="Material2">
                    <input semantic="VERTEX" source="#Clock_HourVertices" offset="0" />
                    <input semantic="NORMAL" source="#Clock_HourNormals" offset="1"/>
<vcount>3 3 3 3 3 3 3 3 4 4 4 4</vcount>
<p> 0 0 8 0 1 0 1 0 8 0 2 0 2 0 8 0 3 0 3 0 8 0 0 0 4 1 5 1 9 1 5 1 6 1 9 1 6 1 7 1 9 1 7 1 4 1 9 1 0 2 1 2 5 2 4 2 1 3 2 3 6 3 5 3 2 4 3 4 7 4 6 4 3 5 0 5 4 5 7 5 </p>
              </polylist>
            </mesh>
        </geometry>
<!-- geometry:  Letters -->
        <geometry id="CubeID4">
            <mesh>
                <source id="CubeID7_Positions">
                    <float_array id="CoordinatesID10" count="24">
   -0.5  -0.5  -0.5
   -0.5  -0.5   0.5
   -0.5   0.5  -0.5
   -0.5   0.5   0.5
    0.5  -0.5  -0.5
    0.5  -0.5   0.5
    0.5   0.5  -0.5
    0.5   0.5   0.5
                    </float_array>
                    <technique_common>
                        <accessor source="#CoordinatesID10" count="8" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                        </accessor>
                    </technique_common>
                </source>
                <source id="CubeID8_Normals">
                    <float_array id="NormalsID11" count="18">
    0  0 -1
    0  0  1
    0 -1  0
    0  1  0
   -1  0  0
    1  0  0
                    </float_array>
                    <technique_common>
                        <accessor source="#NormalsID11" count="6" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                        </accessor>
                    </technique_common>
                </source>
                <vertices id="CubeID9_Vertices">
                    <input semantic="POSITION" source="#CubeID7_Positions" />
                </vertices>
                <polylist count="12" material="Material2">
                    <input semantic="VERTEX" source="#CubeID9_Vertices" offset="0" />
                    <input semantic="NORMAL" source="#CubeID8_Normals" offset="1" />
<vcount>3 3 3 3  3 3 3 3  3 3 3 3</vcount>
<p>
0 0 2 0 6 0  0 0 6 0 4 0
1 1 7 1 3 1  1 1 5 1 7 1
0 2 4 2 5 2  0 2 5 2 1 2
2 3 3 3 7 3  2 3 7 3 6 3
0 4 1 4 3 4  0 4 3 4 2 4
4 5 6 5 7 5  4 5 7 5 5 5
</p>
                </polylist>
          </mesh>
        </geometry>
        <geometry id="DiagonalID4">
            <mesh>
                <source id="DiagonalID7_Positions">
                    <float_array id="Diag_CoordinatesID10" count="24">
   -0.5  -0.5  -0.5
   -0.5  -0.5   0.5
   -0.5   0.5  -0.5
   -0.5   0.5   0.5
    0.5  -0.5  -0.5
    0.5  -0.5   0.5
    0.5   0.5  -0.5
    0.5   0.5   0.5
                    </float_array>
                    <technique_common>
                        <accessor source="#Diag_CoordinatesID10" count="8" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                        </accessor>
                    </technique_common>
                </source>
                <source id="DiagonalID8_Normals">
                    <float_array id="Diagonal_NormalsID11" count="21">
    0  0 -1
    0  0  1
    0 -1  0
    0  1  0
   -1  0  0
    1  0  0
    0  -0.707 0.707
                    </float_array>
                    <technique_common>
                        <accessor source="#Diagonal_NormalsID11" count="7" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                        </accessor>
                    </technique_common>
                </source>
                <vertices id="DiagonalID9_Vertices">
                    <input semantic="POSITION" source="#DiagonalID7_Positions" />
                </vertices>
                <polylist count="8" material="Material2">
                    <input semantic="VERTEX" source="#DiagonalID9_Vertices" offset="0" />
                    <input semantic="NORMAL" source="#DiagonalID8_Normals" offset="1" />
<vcount>3 3 3 3  3 3 3 3</vcount>
<p>
0 0 2 0 6 0  0 0 6 0 4 0
2 3 3 3 7 3  2 3 7 3 6 3
0 4 3 4 2 4  4 5 6 5 7 5
0 6 7 6 3 6  0 6 4 6 7 6
</p>
                </polylist>
          </mesh>
        </geometry>
<!-- geometry:  Cubes for Lagrangian Markers -->
        <geometry id="CubeID4">
            <mesh>
                <source id="CubeID7_Positions">
                    <float_array id="CoordinatesID10" count="24">
   -0.5  -0.5  -0.5
   -0.5  -0.5   0.5
   -0.5   0.5  -0.5
   -0.5   0.5   0.5
    0.5  -0.5  -0.5
    0.5  -0.5   0.5
    0.5   0.5  -0.5
    0.5   0.5   0.5
                    </float_array>
                    <technique_common>
                        <accessor source="#CoordinatesID10" count="8" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                        </accessor>
                    </technique_common>
                </source>
                <source id="CubeID8_Normals">
                    <float_array id="NormalsID11" count="18">
    0  0 -1
    0  0  1
    0 -1  0
    0  1  0
   -1  0  0
    1  0  0
                    </float_array>
                    <technique_common>
                        <accessor source="#NormalsID11" count="6" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                        </accessor>
                    </technique_common>
                </source>
                <vertices id="CubeID9_Vertices">
                    <input semantic="POSITION" source="#CubeID7_Positions" />
                </vertices>
                <polylist count="12" material="Material2">
                    <input semantic="VERTEX" source="#CubeID9_Vertices" offset="0" />
                    <input semantic="NORMAL" source="#CubeID8_Normals" offset="1" />
<vcount>3 3 3 3  3 3 3 3  3 3 3 3</vcount>
<p>
0 0 2 0 6 0  0 0 6 0 4 0
1 1 7 1 3 1  1 1 5 1 7 1
0 2 4 2 5 2  0 2 5 2 1 2
2 3 3 3 7 3  2 3 7 3 6 3
0 4 1 4 3 4  0 4 3 4 2 4
4 5 6 5 7 5  4 5 7 5 5 5
</p>
                </polylist>
          </mesh>
        </geometry>
<!-- geometry:  Cylindrical Pointer -->
        <geometry id="Cylinder">
            <mesh>
                <source id="Cyl_Positions">
<float_array id="CylCoords01" count="54">
  -1.0  -0.9239   0.3827
  -1.0  -0.3827   0.9239
  -1.0   0.3827   0.9239
  -1.0   0.9239   0.3827
  -1.0   0.9239  -0.3827
  -1.0   0.3827  -0.9239
  -1.0  -0.3827  -0.9239
  -1.0  -0.9239  -0.3827
  -1.0   0.0000   0.0000
   1.0  -0.9239   0.3827
   1.0  -0.3827   0.9239
   1.0   0.3827   0.9239
   1.0   0.9239   0.3827
   1.0   0.9239  -0.3827
   1.0   0.3827  -0.9239
   1.0  -0.3827  -0.9239
   1.0  -0.9239  -0.3827
   1.5   0.0000   0.0000
</float_array>
                  <technique_common>
                    <accessor source="#CylCoords01" count="18" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                    </accessor>
                  </technique_common>
                </source>
                <source id="Cyl_Normals">
                  <float_array id="CylNormals01" count="54">
    1.0  0.0  0.0
   -1.0  0.0  0.0
    0.0  1.0  0.0
    0.0 -1.0  0.0
    0.0  0.0  1.0
    0.0  0.0 -1.0
    0.0  0.7071  0.7071
    0.0  0.7071 -0.7071
    0.0 -0.7071  0.7071
    0.0 -0.7071 -0.7071
    0.8795  -0.3365   0.3365
    0.8795   0.0000   0.4760
    0.8795   0.3365   0.3365
    0.8795   0.4760   0.0000
    0.8795   0.3365  -0.3365
    0.8795   0.0000  -0.4760
    0.8795  -0.3365  -0.3365
    0.8795  -0.4760   0.0000
                  </float_array>
                    <technique_common>
                        <accessor source="#CylNormals01" count="18" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                        </accessor>
                    </technique_common>
                </source>
                <vertices id="Cyl_Vertices">
                    <input semantic="POSITION" source="#Cyl_Positions" />
                </vertices>
                <polylist count="32" material="Material2">
                    <input semantic="VERTEX" source="#Cyl_Vertices" offset="0" />
                    <input semantic="NORMAL" source="#Cyl_Normals" offset="1" />
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<!--
            **********************************************
            *
            *  Insert Geometry of Ellipsoid Octant
            *
            **********************************************
-->
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</float_array>
<technique_common>
  <accessor source="#Ellipsoid_Coordinates" count="  521" stride="3">
        <param name="X" type="float" />
        <param name="Y" type="float" />
        <param name="Z" type="float" />
  </accessor>
</technique_common>
</source>
<source id="Ellipsoid_Normals">
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<technique_common>
  <accessor source="#Ellipsoid_Normals01" count="  975" stride="3">
        <param name="X" type="float" />
        <param name="Y" type="float" />
        <param name="Z" type="float" />
  </accessor>
</technique_common>
</source>
<vertices id="Ellipsoid_Vertices">
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</vertices>
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3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
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3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
</vcount>
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    0   18  514   18  513   18
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</float_array>
<technique_common>
  <accessor source="#Reflect_Coordinates" count="  521" stride="3">
        <param name="X" type="float" />
        <param name="Y" type="float" />
        <param name="Z" type="float" />
  </accessor>
</technique_common>
</source>
<source id="Reflect_Normals">
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3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
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3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
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   51  974   26  974   52  974
</p>
</polylist>
  </mesh>
</geometry>
<!-- EquatorialPlane (begin) -->
<geometry id="EquatorialPlane">
  <mesh>
<source id="EquatorialPlane_Positions">
<float_array id="EquatorialPlane_Coordinates" count="48">
   -5.5000    -5.5000    0.2000
    5.5000    -5.5000    0.2000
    5.5000     5.5000    0.2000
   -5.5000     5.5000    0.2000
   -5.7500    -5.7500    0.2000
    5.7500    -5.7500    0.2000
    5.7500     5.7500    0.2000
   -5.7500     5.7500    0.2000
   -5.5000    -5.5000   -0.2000
    5.5000    -5.5000   -0.2000
    5.5000     5.5000   -0.2000
   -5.5000     5.5000   -0.2000
   -5.7500    -5.7500   -0.2000
    5.7500    -5.7500   -0.2000
    5.7500     5.7500   -0.2000
   -5.7500     5.7500   -0.2000
</float_array>
<technique_common>
  <accessor source="#EquatorialPlane_Coordinates" count="  16" stride="3">
        <param name="X" type="float" />
        <param name="Y" type="float" />
        <param name="Z" type="float" />
  </accessor>
</technique_common>
</source>
<source id="EquatorialPlane_Normals">
<float_array id="EquatorialPlane_Normals01" count="18">
    0.0000    0.0000     1.0000
    0.0000    0.0000    -1.0000
    0.0000   -1.0000     0.0000
    0.0000    1.0000     0.0000
   -1.0000    0.0000     0.0000
    1.0000    0.0000     0.0000
</float_array>
<technique_common>
  <accessor source="#EquatorialPlane_Normals01" count="6" stride="3">
        <param name="X" type="float" />
        <param name="Y" type="float" />
        <param name="Z" type="float" />
  </accessor>
</technique_common>
</source>
<vertices id="EquatorialPlane_Vertices">
  <input semantic="POSITION" source="#EquatorialPlane_Positions" />
</vertices>
<polylist count="  12" material="Material2">
  <input semantic="VERTEX" source="#EquatorialPlane_Vertices" offset="0" />
  <input semantic="NORMAL" source="#EquatorialPlane_Normals" offset="1" />
<vcount>
4 4 4 4
4 4 4 4
4 4 4 4
</vcount>
<p>
 4 0  5 0  1 0  0 0
 5 0  6 0  2 0  1 0
 6 0  7 0  3 0  2 0
 7 0  4 0  0 0  3 0
 8 1   9 1  13 1  12 1
 9 1  10 1  14 1  13 1
10 1  11 1  15 1  14 1
11 1   8 1  12 1  15 1
12 2  13 2   5 2   4 2
14 3  15 3   7 3   6 3
15 4  12 4   4 4   7 4
13 5  14 5   6 5   5 5
</p>
</polylist>
  </mesh>
</geometry>
<!-- EquatorialPlane (end)   -->
    </library_geometries>
    <library_animations>
  <animation id="First_rotation_euler_Z">
<!-- for EFE/Ou model b41c385, clockstop = 36.5047 and anglestop = 1800.0 -->
<!-- this means that one 360 degree turn of the ellipsoid takes 7.3009 clock units -->
    <source id="First_rotation_euler_Z-input">
      <float_array id="First_rotation_euler_Z-input-array" count="31">
   0.00
   1.22
   2.43
   3.65
   4.87
   6.08
   7.30
   8.52
   9.73
  10.95
  12.17
  13.39
  14.60
  15.82
  17.04
  18.25
  19.47
  20.69
  21.90
  23.12
  24.34
  25.55
  26.77
  27.99
  29.20
  30.42
  31.64
  32.85
  34.07
  35.29
  36.50
      </float_array>
      <technique_common>
          <accessor source="#First_rotation_euler_Z-input-array" count="31" stride="1">
            <param name="TIME" type="float"/>
          </accessor>
      </technique_common>
    </source>
<!-- This sets the spin rate of the "Entire" ellipsoid -->
    <source id="First_rotation_euler_Z-output">
      <float_array id="First_rotation_euler_Z-output-array" count="31">
     3.0
    63.0
   123.0
   183.0
   243.0
   303.0
   363.0
   423.0
   483.0
   543.0
   603.0
   663.0
   723.0
   783.0
   843.0
   903.0
   963.0
  1023.0
  1083.0
  1143.0
  1203.0
  1263.0
  1323.0
  1383.0
  1443.0
  1503.0
  1563.0
  1623.0
  1683.0
  1743.0
  1803.0
      </float_array>
      <technique_common>
          <accessor source="#First_rotation_euler_Z-output-array" count="31" stride="1">
            <param name="ANGLE" type="float"/>
          </accessor>
      </technique_common>
    </source>
<!-- This sets the spin rate of the "MidPlane" Frame of reference -->
    <source id="Frame_rotation_euler_Z-output">
      <float_array id="Frame_rotation_euler_Z-output-array" count="31">
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
      </float_array>
      <technique_common>
          <accessor source="#Frame_rotation_euler_Z-output-array" count="31" stride="1">
            <param name="ANGLE" type="float"/>
          </accessor>
      </technique_common>
    </source>
    <sampler id="First_rotation_euler_Z-sampler">
      <input semantic="INPUT" source="#First_rotation_euler_Z-input"/>
      <input semantic="OUTPUT" source="#First_rotation_euler_Z-output"/>
    </sampler>
    <sampler id="Frame_rotation_euler_Z-sampler">
      <input semantic="INPUT" source="#First_rotation_euler_Z-input"/>
      <input semantic="OUTPUT" source="#Frame_rotation_euler_Z-output"/>
    </sampler>
    <channel source="#First_rotation_euler_Z-sampler" target="EntireEllipsoid/rotationZ.ANGLE"/>
    <channel source="#Frame_rotation_euler_Z-sampler" target="Inertial/rotationZ.ANGLE"/>
  </animation>
<!-- FLUID ELEMENT 1 -->
  <animation id="FluidElement1_location">
    <source id="Lagrange1_location_X-input">
      <float_array id="Lagrange1_location_X-input-array" count="   37">
  0.0000
  1.0014
  2.0029
  3.0043
  4.0057
  5.0071
  6.0086
  7.0100
  8.0114
  9.0129
 10.0143
 11.0157
 12.0171
 13.0186
 14.0200
 15.0214
 16.0229
 17.0243
 18.0257
 19.0271
 20.0286
 21.0300
 22.0314
 23.0329
 24.0343
 25.0357
 26.0371
 27.0386
 28.0400
 29.0414
 30.0429
 31.0443
 32.0457
 33.0472
 34.0486
 35.0500
 36.0514
      </float_array>
      <technique_common>
          <accessor source="#Lagrange1_location_X-input-array" count="   37" stride="1">
            <param name="TIME" type="float"/>
          </accessor>
      </technique_common>
    </source>
    <source id="Lagrange1_location_X-output">
      <float_array id="Lagrange1_location_X-output-array" count="   37">
  1.0000
  0.9921
  0.9686
  0.9298
  0.8763
  0.8090
  0.7290
  0.6374
  0.5358
  0.4258
  0.3090
  0.1874
  0.0628
 -0.0628
 -0.1874
 -0.3090
 -0.4258
 -0.5358
 -0.6374
 -0.7290
 -0.8090
 -0.8763
 -0.9298
 -0.9686
 -0.9921
 -1.0000
 -0.9921
 -0.9686
 -0.9298
 -0.8763
 -0.8090
 -0.7290
 -0.6374
 -0.5358
 -0.4258
 -0.3090
 -0.1874
      </float_array>
      <technique_common>
          <accessor source="#Lagrange1_location_X-output-array" count="   37" stride="1">
            <param name="X" type="float"/>
          </accessor>
      </technique_common>
    </source>
    <sampler id="Lagrange1_location_X-sampler">
      <input semantic="INPUT" source="#Lagrange1_location_X-input"/>
      <input semantic="OUTPUT" source="#Lagrange1_location_X-output"/>
    </sampler>
    <source id="Lagrange1_location_Y-output">
      <float_array id="Lagrange1_location_Y-output-array" count="   37">
 -0.0000
 -0.0514
 -0.1020
 -0.1509
 -0.1975
 -0.2410
 -0.2807
 -0.3159
 -0.3462
 -0.3710
 -0.3899
 -0.4027
 -0.4092
 -0.4092
 -0.4027
 -0.3899
 -0.3710
 -0.3462
 -0.3159
 -0.2807
 -0.2410
 -0.1975
 -0.1509
 -0.1020
 -0.0514
  0.0000
  0.0514
  0.1020
  0.1509
  0.1975
  0.2410
  0.2807
  0.3159
  0.3462
  0.3710
  0.3899
  0.4027
      </float_array>
      <technique_common>
          <accessor source="#Lagrange1_location_Y-output-array" count="   37" stride="1">
            <param name="Y" type="float"/>
          </accessor>
      </technique_common>
    </source>
    <sampler id="Lagrange1_location_Y-sampler">
      <input semantic="INPUT" source="#Lagrange1_location_X-input"/>
      <input semantic="OUTPUT" source="#Lagrange1_location_Y-output"/>
    </sampler>
    <channel source="#Lagrange1_location_X-sampler" target="Lagrange01/location.X"/>
    <channel source="#Lagrange1_location_Y-sampler" target="Lagrange01/location.Y"/>
</animation>
<!-- CLOCK (clockstop = 36.5047) 
     One spin of ellipsoid (or frame) is 1.8252 EFE sqrt(pi * G * rho) units;
     Want 1 EFE unit to take 4.0 seconds of TIME;
     Hence, one spin of ellipsoid (360 degrees) is 7.3009 seconds of TIME;
            and 5 ellipsoid spins is 36.5047 seconds of TIME.
     Divide one spin (360) into 12 pieces 
     ==> 30 degrees = 1 timestep = 4 x 0.1521 = 0.6084 seconds of TIME.
-->
  <animation id="Cube_quaternion_Z">
    <source id="Cube_quaternion_Z-input">
      <float_array id="Cube_quaternion_Z-input-array" count=" 147">
     0.00  0.25  0.50  0.75  1.00  1.25  1.50  1.75  2.00  2.25  2.50  2.75  3.00  3.25  3.50  3.75
     4.00  4.25  4.50  4.75  5.00  5.25  5.50  5.75  6.00  6.25  6.50  6.75  7.00  7.25  7.50  7.75
     8.00  8.25  8.50  8.75  9.00  9.25  9.50  9.75 10.00 10.25 10.50 10.75 11.00 11.25 11.50 11.75
    12.00 12.25 12.50 12.75 13.00 13.25 13.50 13.75 14.00 14.25 14.50 14.75 15.00 15.25 15.50 15.75
    16.00 16.25 16.50 16.75 17.00 17.25 17.50 17.75 18.00 18.25 18.50 18.75 19.00 19.25 19.50 19.75
    20.00 20.25 20.50 20.75 21.00 21.25 21.50 21.75 22.00 22.25 22.50 22.75 23.00 23.25 23.50 23.75
    24.00 24.25 24.50 24.75 25.00 25.25 25.50 25.75 26.00 26.25 26.50 26.75 27.00 27.25 27.50 27.75
    28.00 28.25 28.50 28.75 29.00 29.25 29.50 29.75 30.00 30.25 30.50 30.75 31.00 31.25 31.50 31.75
    32.00 32.25 32.50 32.75 33.00 33.25 33.50 33.75 34.00 34.25 34.50 34.75 35.00 35.25 35.50 35.75
    36.00 36.25 36.50 
      </float_array>
      <technique_common>
          <accessor source="#Cube_quaternion_Z-input-array" count="   147" stride="1">
            <param name="TIME" type="float"/>
          </accessor>
      </technique_common>
    </source>
    <source id="Cube_quaternion_Z-output">
      <float_array id="Cube_quaternion_Z-output-array" count="2352">
   0.000  0.000 -1.00  0.00  -1.0000  0.0000  0.000  0.000   0.0000  1.0000  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.9239 -0.3827  0.000  0.000  -0.3827  0.9239  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.7071 -0.7071  0.000  0.000  -0.7071  0.7071  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.3827 -0.9239  0.000  0.000  -0.9239  0.3827  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.0000 -1.0000  0.000  0.000  -1.0000  0.0000  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.3827 -0.9239  0.000  0.000  -0.9239 -0.3827  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.7071 -0.7071  0.000  0.000  -0.7071 -0.7071  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.9239 -0.3827  0.000  0.000  -0.3827 -0.9239  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   1.0000  0.0000  0.000  0.000   0.0000 -1.0000  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.9239  0.3827  0.000  0.000   0.3827 -0.9239  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.7071  0.7071  0.000  0.000   0.7071 -0.7071  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.3827  0.9239  0.000  0.000   0.9239 -0.3827  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.0000  1.0000  0.000  0.000   1.0000  0.0000  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.3827  0.9239  0.000  0.000   0.9239  0.3827  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.7071  0.7071  0.000  0.000   0.7071  0.7071  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.9239  0.3827  0.000  0.000   0.3827  0.9239  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -1.0000  0.0000  0.000  0.000   0.0000  1.0000  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.9239 -0.3827  0.000  0.000  -0.3827  0.9239  0.000  0.00   0.000  0.000  0.000  1.000
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   0.000  0.000 -1.00  0.00   0.9239 -0.3827  0.000  0.000  -0.3827 -0.9239  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   1.0000  0.0000  0.000  0.000   0.0000 -1.0000  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.9239  0.3827  0.000  0.000   0.3827 -0.9239  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.7071  0.7071  0.000  0.000   0.7071 -0.7071  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.3827  0.9239  0.000  0.000   0.9239 -0.3827  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.0000  1.0000  0.000  0.000   1.0000  0.0000  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.3827  0.9239  0.000  0.000   0.9239  0.3827  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.7071  0.7071  0.000  0.000   0.7071  0.7071  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.9239  0.3827  0.000  0.000   0.3827  0.9239  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -1.0000  0.0000  0.000  0.000   0.0000  1.0000  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.9239 -0.3827  0.000  0.000  -0.3827  0.9239  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.7071 -0.7071  0.000  0.000  -0.7071  0.7071  0.000  0.00   0.000  0.000  0.000  1.000
      </float_array>
      <technique_common>
          <accessor source="#Cube_quaternion_Z-output-array" count="  147" stride="16">
            <param name="TRANSFORM" type="float4x4"/>
          </accessor>
      </technique_common>
    </source>
    <sampler id="Cube_quaternion_Z-sampler">
      <input semantic="INPUT" source="#Cube_quaternion_Z-input"/>
      <input semantic="OUTPUT" source="#Cube_quaternion_Z-output"/>
    </sampler>
    <channel source="#Cube_quaternion_Z-sampler" target="Jetman/transformation"/>
  </animation>
<!-- HOURHAND (clockstop =    36.5047) -->
  <animation id="HourHand_euler_Z">
    <source id="HourHand_euler_Z-input">
      <float_array id="HourHand_euler_Z-input-array" count="  147">
     0.00  0.25  0.50  0.75  1.00  1.25  1.50  1.75  2.00  2.25  2.50  2.75  3.00  3.25  3.50  3.75
     4.00  4.25  4.50  4.75  5.00  5.25  5.50  5.75  6.00  6.25  6.50  6.75  7.00  7.25  7.50  7.75
     8.00  8.25  8.50  8.75  9.00  9.25  9.50  9.75 10.00 10.25 10.50 10.75 11.00 11.25 11.50 11.75
    12.00 12.25 12.50 12.75 13.00 13.25 13.50 13.75 14.00 14.25 14.50 14.75 15.00 15.25 15.50 15.75
    16.00 16.25 16.50 16.75 17.00 17.25 17.50 17.75 18.00 18.25 18.50 18.75 19.00 19.25 19.50 19.75
    20.00 20.25 20.50 20.75 21.00 21.25 21.50 21.75 22.00 22.25 22.50 22.75 23.00 23.25 23.50 23.75
    24.00 24.25 24.50 24.75 25.00 25.25 25.50 25.75 26.00 26.25 26.50 26.75 27.00 27.25 27.50 27.75
    28.00 28.25 28.50 28.75 29.00 29.25 29.50 29.75 30.00 30.25 30.50 30.75 31.00 31.25 31.50 31.75
    32.00 32.25 32.50 32.75 33.00 33.25 33.50 33.75 34.00 34.25 34.50 34.75 35.00 35.25 35.50 35.75
    36.00 36.25 36.50 
      </float_array>
      <technique_common>
          <accessor source="#HourHand_euler_Z-input-array" count="  147" stride="1">
            <param name="TIME" type="float"/>
          </accessor>
      </technique_common>
    </source>
    <source id="HourHand_euler_Z-output">
      <float_array id="HourHand_euler_Z-output-array" count="  147">
  270.0
  268.125
  266.25
  264.375
  262.5
  260.625
  258.75
  256.875
  255.0
  253.125
  251.25
  249.375
  247.5
  245.625
  243.75
  241.875
  240.0
  238.125
  236.25
  234.375
  232.5
  230.625
  228.75
  226.875
  225.0
  223.125
  221.25
  219.375
  217.5
  215.625
  213.75
  211.875
  210.0
  208.125
  206.25
  204.375
  202.5
  200.625
  198.75
  196.875
  195.0
  193.125
  191.25
  189.375
  187.5
  185.625
  183.75
  181.875
  180.0
  178.125
  176.25
  174.375
  172.5
  170.625
  168.75
  166.875
  165.0
  163.125
  161.25
  159.375
  157.5
  155.625
  153.75
  151.875
  150.0
  148.125
  146.25
  144.375
  142.5
  140.625
  138.75
  136.875
  135.0
  133.125
  131.25
  129.375
  127.5
  125.625
  123.75
  121.875
  120.0
  118.125
  116.25
  114.375
  112.5
  110.625
  108.75
  106.875
  105.0
  103.125
  101.25
   99.375
   97.5
   95.625
   93.75
   91.875
   90.0
   88.125
   86.25
   84.375
   82.5
   80.625
   78.75
   76.875
   75.0
   73.125
   71.25
   69.375
   67.5
   65.625
   63.75
   61.875
   60.0
   58.125
   56.25
   54.375
   52.5
   50.625
   48.75
   46.875
   45.0
   43.125
   41.25
   39.375
   37.5
   35.625
   33.75
   31.875
   30.0
   28.125
   26.25
   24.375
   22.5
   20.625
   18.75
   16.875
   15.0
   13.125
   11.25
    9.375
    7.5
    5.625
    3.75
    1.875
    0.0
   -1.875
   -3.75
      </float_array>
      <technique_common>
          <accessor source="#HourHand_euler_Z-output-array" count="   147" stride="1">
            <param name="ANGLE" type="float"/>
          </accessor>
      </technique_common>
    </source>
    <sampler id="HourHand_euler_Z-sampler">
      <input semantic="INPUT" source="#HourHand_euler_Z-input"/>
      <input semantic="OUTPUT" source="#HourHand_euler_Z-output"/>
    </sampler>
    <channel source="#HourHand_euler_Z-sampler" target="HourHand/rotationZ.ANGLE"/>
  </animation>
    </library_animations>
    <library_controllers/>
    <library_visual_scenes>
        <visual_scene id="ID1">
            <node id="EntireEllipsoid" name="OculusRift_EFE">
             <translate>0.0 0.0 0.0</translate>
             <rotate sid="rotationX">1.0 0.0 0.0  0.0</rotate>
             <rotate sid="rotationY">0.0 1.0 0.0  0.0</rotate>
             <rotate sid="rotationZ">0.0 0.0 1.0  3.0</rotate>
             <scale sid="scale">5.0 5.0 5.0</scale>
                <node id="First" name="First_instance_EFE">
                  <translate>0.0 0.0 0.0</translate>
                  <rotate sid="rotationX">1.0 0.0 0.0  0.0</rotate>
                  <rotate sid="rotationY">0.0 1.0 0.0  0.0</rotate>
                  <rotate sid="rotationZ">0.0 0.0 1.0  0.0</rotate>
                  <scale sid="scale">1.0 1.0 1.0</scale>
                  <instance_node url="#ID3_EFE" />
                </node>
                <node id="Second" name="Second_instance_EFE">
                  <translate>0.0 0.0 0.0</translate>
                  <rotate sid="rotationX">1.0 0.0 0.0  180.0</rotate>
                  <rotate sid="rotationY">0.0 1.0 0.0    0.0</rotate>
                  <rotate sid="rotationZ">0.0 0.0 1.0    0.0</rotate>
                  <scale sid="scale">1.0 1.0 1.0</scale>
                  <instance_node url="#ID3_EFE" />
                </node>
                <node id="Third" name="Third_instance_EFE">
                  <translate>0.0 0.0 0.0</translate>
                  <rotate sid="rotationX">1.0 0.0 0.0    0.0</rotate>
                  <rotate sid="rotationY">0.0 1.0 0.0  180.0</rotate>
                  <rotate sid="rotationZ">0.0 0.0 1.0    0.0</rotate>
                  <scale sid="scale">1.0 1.0 1.0</scale>
                  <instance_node url="#ID3_EFE" />
                </node>
                <node id="Fourth" name="Fourth_instance_EFE">
                  <translate>0.0 0.0 0.0</translate>
                  <rotate sid="rotationX">1.0 0.0 0.0  180.0</rotate>
                  <rotate sid="rotationY">0.0 1.0 0.0  180.0</rotate>
                  <rotate sid="rotationZ">0.0 0.0 1.0    0.0</rotate>
                  <scale sid="scale">1.0 1.0 1.0</scale>
                  <instance_node url="#ID3_EFE" />
                </node>
<!-- instance:  Cylindrical Pointer -->
                <node id="CylinderPointer" name="instance_cylinder">  
                  <translate sid="location">-1.0 0.0 0.0</translate>
                    <rotate sid="rotationX">1 0 0 0</rotate>
                    <rotate sid="rotationY">0 1 0 0</rotate>
                    <rotate sid="rotationZ">0 0 1 180</rotate>
                  <scale sid="scale">0.05 0.025 0.025</scale>
                  <instance_node url="#CylPointer" />
                </node>                                         
<!-- Begin LAGRANGE markers -->
              <node id="Lagrange01" name="instance_Lagrange01">
                  <translate sid="location">1.0000 0.0000 0.0</translate>
                  <rotate sid="rotationX">1.0 0.0 0.0  0.0</rotate>
                  <rotate sid="rotationY">0.0 1.0 0.0  0.0</rotate>
                  <rotate sid="rotationZ">0.0 0.0 1.0  0.0</rotate>
                  <scale sid="scale">0.075 0.075 0.075</scale>
                <instance_node url="#Primary_MarkerID3" />
              </node>
              <node id="Marker01" name="instance_marker01">
                <matrix>0.025 0.0 0.0 1.0000  0.0 0.025 0.0 -0.0000  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker02" name="instance_marker02">
                <matrix>0.025 0.0 0.0 0.9921  0.0 0.025 0.0 -0.0514  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker03" name="instance_marker03">
                <matrix>0.025 0.0 0.0 0.9686  0.0 0.025 0.0 -0.1020  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker04" name="instance_marker04">
                <matrix>0.025 0.0 0.0 0.9298  0.0 0.025 0.0 -0.1509  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker05" name="instance_marker05">
                <matrix>0.025 0.0 0.0 0.8763  0.0 0.025 0.0 -0.1975  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker06" name="instance_marker06">
                <matrix>0.025 0.0 0.0 0.8090  0.0 0.025 0.0 -0.2410  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker07" name="instance_marker07">
                <matrix>0.025 0.0 0.0 0.7290  0.0 0.025 0.0 -0.2807  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker08" name="instance_marker08">
                <matrix>0.025 0.0 0.0 0.6374  0.0 0.025 0.0 -0.3159  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker09" name="instance_marker09">
                <matrix>0.025 0.0 0.0 0.5358  0.0 0.025 0.0 -0.3462  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker10" name="instance_marker10">
                <matrix>0.025 0.0 0.0 0.4258  0.0 0.025 0.0 -0.3710  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker11" name="instance_marker11">
                <matrix>0.025 0.0 0.0 0.3090  0.0 0.025 0.0 -0.3899  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker12" name="instance_marker12">
                <matrix>0.025 0.0 0.0 0.1874  0.0 0.025 0.0 -0.4027  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker13" name="instance_marker13">
                <matrix>0.025 0.0 0.0 0.0628  0.0 0.025 0.0 -0.4092  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker14" name="instance_marker14">
                <matrix>0.025 0.0 0.0 -0.0628  0.0 0.025 0.0 -0.4092  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker15" name="instance_marker15">
                <matrix>0.025 0.0 0.0 -0.1874  0.0 0.025 0.0 -0.4027  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker16" name="instance_marker16">
                <matrix>0.025 0.0 0.0 -0.3090  0.0 0.025 0.0 -0.3899  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker17" name="instance_marker17">
                <matrix>0.025 0.0 0.0 -0.4258  0.0 0.025 0.0 -0.3710  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker18" name="instance_marker18">
                <matrix>0.025 0.0 0.0 -0.5358  0.0 0.025 0.0 -0.3462  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker19" name="instance_marker19">
                <matrix>0.025 0.0 0.0 -0.6374  0.0 0.025 0.0 -0.3159  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker20" name="instance_marker20">
                <matrix>0.025 0.0 0.0 -0.7290  0.0 0.025 0.0 -0.2807  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker21" name="instance_marker21">
                <matrix>0.025 0.0 0.0 -0.8090  0.0 0.025 0.0 -0.2410  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker22" name="instance_marker22">
                <matrix>0.025 0.0 0.0 -0.8763  0.0 0.025 0.0 -0.1975  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker23" name="instance_marker23">
                <matrix>0.025 0.0 0.0 -0.9298  0.0 0.025 0.0 -0.1509  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker24" name="instance_marker24">
                <matrix>0.025 0.0 0.0 -0.9686  0.0 0.025 0.0 -0.1020  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker25" name="instance_marker25">
                <matrix>0.025 0.0 0.0 -0.9921  0.0 0.025 0.0 -0.0514  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker26" name="instance_marker26">
                <matrix>0.025 0.0 0.0 -1.0000  0.0 0.025 0.0 -0.0000  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
<!-- Second Half -->
              <node id="Marker28" name="instance_marker28">
                <matrix>0.025 0.0 0.0 -0.9921  0.0 0.025 0.0 0.0514  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker29" name="instance_marker29">
                <matrix>0.025 0.0 0.0 -0.9686  0.0 0.025 0.0 0.1020  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker30" name="instance_marker30">
                <matrix>0.025 0.0 0.0 -0.9298  0.0 0.025 0.0 0.1509  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker31" name="instance_marker31">
                <matrix>0.025 0.0 0.0 -0.8763  0.0 0.025 0.0 0.1975  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker32" name="instance_marker32">
                <matrix>0.025 0.0 0.0 -0.8090  0.0 0.025 0.0 0.2410  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker33" name="instance_marker33">
                <matrix>0.025 0.0 0.0 -0.7290  0.0 0.025 0.0 0.2807  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker34" name="instance_marker34">
                <matrix>0.025 0.0 0.0 -0.6374  0.0 0.025 0.0 0.3159  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker35" name="instance_marker35">
                <matrix>0.025 0.0 0.0 -0.5358  0.0 0.025 0.0 0.3462  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker36" name="instance_marker36">
                <matrix>0.025 0.0 0.0 -0.4258  0.0 0.025 0.0 0.3710  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker37" name="instance_marker37">
                <matrix>0.025 0.0 0.0 -0.3090  0.0 0.025 0.0 0.3899  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker38" name="instance_marker38">
                <matrix>0.025 0.0 0.0 -0.1874  0.0 0.025 0.0 0.4027  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker39" name="instance_marker39">
                <matrix>0.025 0.0 0.0 -0.0628  0.0 0.025 0.0 0.4092  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker40" name="instance_marker40">
                <matrix>0.025 0.0 0.0 0.0628  0.0 0.025 0.0 0.4092  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker41" name="instance_marker41">
                <matrix>0.025 0.0 0.0 0.1874  0.0 0.025 0.0 0.4027  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker42" name="instance_marker42">
                <matrix>0.025 0.0 0.0 0.3090  0.0 0.025 0.0 0.3899  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker43" name="instance_marker43">
                <matrix>0.025 0.0 0.0 0.4258  0.0 0.025 0.0 0.3710  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker44" name="instance_marker44">
                <matrix>0.025 0.0 0.0 0.5358  0.0 0.025 0.0 0.3462  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker45" name="instance_marker45">
                <matrix>0.025 0.0 0.0 0.6374  0.0 0.025 0.0 0.3159  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker46" name="instance_marker46">
                <matrix>0.025 0.0 0.0 0.7290  0.0 0.025 0.0 0.2807  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker47" name="instance_marker47">
                <matrix>0.025 0.0 0.0 0.8090  0.0 0.025 0.0 0.2410  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker48" name="instance_marker48">
                <matrix>0.025 0.0 0.0 0.8763  0.0 0.025 0.0 0.1975  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker49" name="instance_marker49">
                <matrix>0.025 0.0 0.0 0.9298  0.0 0.025 0.0 0.1509  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker50" name="instance_marker50">
                <matrix>0.025 0.0 0.0 0.9686  0.0 0.025 0.0 0.1020  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker51" name="instance_marker51">
                <matrix>0.025 0.0 0.0 0.9921  0.0 0.025 0.0 0.0514  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
<!-- End LAGRANGE markers -->
            </node>                           <!-- END EntireEllipsoid -->
          <node id="Inertial" name="instance_inertial">  <!-- Start Inertial Grouping of Objects -->
            <translate>0.0 0.0 0.0</translate>
            <rotate sid="rotationX">1.0 0.0 0.0  0.0</rotate>
            <rotate sid="rotationY">0.0 1.0 0.0  0.0</rotate>
            <rotate sid="rotationZ">0.0 0.0 1.0  3.0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
            <node id="Zup_Pointer" name="instance_zupPointer">  
              <translate>0.0 0.0 5.0</translate>
                <rotate sid="rotationX">1 0 0  0.0</rotate>
                <rotate sid="rotationY">0 1 0  0.0</rotate>
                <rotate sid="rotationZ">0 0 1  0.0</rotate>
              <scale sid="scale">0.125 0.5 1.5</scale>
              <instance_node url="#ZupPointer" />
            </node>                                         
<!-- instance:  MidPlane Frame (MidPlane flips with rotationX = 180 for clockwise spin)-->
            <node id="MidPlane" name="instance_MidPlane">  
              <translate>0.0 0.0 0.0</translate>
                  <rotate sid="rotationX">1.0 0.0 0.0  0.0</rotate>
                  <rotate sid="rotationY">0.0 1.0 0.0  0.0</rotate>
                  <rotate sid="rotationZ">0.0 0.0 1.0  0.0</rotate>
              <scale sid="scale">1.25 1.25 1.25</scale>
              <instance_node url="#EqPlane" />
            </node> 
<!-- BEGIN LABELING HERE -->
          <node name="Labels">
          <translate>7.0 -2.0 5.0</translate>
          <rotate sid="rotationX">1 0 0 0.0</rotate>
          <rotate sid="rotationY">0 1 0 0</rotate>
          <rotate sid="rotationZ">0 0 1 180</rotate>
          <scale sid="scale">0.1 0.1 0.1</scale>
<!--  Equals sign #1  -->
            <node name="Equals1">
            <translate>0.0 15.0 1.0</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
                <node id="IDd51" name="instance_51">
                    <matrix>0.25  0 0 0.0   0 1  0 0.0  0 0 1 2.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDd52" name="instance_52">
                    <matrix>0.25  0 0 0.0   0 1  0 1.1  0 0 1 2.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDd53" name="instance_53">
                    <matrix>0.25  0 0 0.0   0 1  0 2.2  0 0 1 2.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDd55" name="instance_55">
                    <matrix>0.25  0 0 0.0   0 1  0 0.0  0 0 1 4.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDd56" name="instance_56">
                    <matrix>0.25  0 0 0.0   0 1  0 1.1  0 0 1 4.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDd57" name="instance_57">
                    <matrix>0.25  0 0 0.0   0 1  0 2.2  0 0 1 4.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
            </node>
<!--  Equals sign #2  -->
            <node name="Equals2">
            <translate>0.0 15.0 -8.5</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
                <node id="IDd51" name="instance_51">
                    <matrix>0.25  0 0 0.0   0 1  0 0.0  0 0 1 2.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDd52" name="instance_52">
                    <matrix>0.25  0 0 0.0   0 1  0 1.1  0 0 1 2.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDd53" name="instance_53">
                    <matrix>0.25  0 0 0.0   0 1  0 2.2  0 0 1 2.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDd55" name="instance_55">
                    <matrix>0.25  0 0 0.0   0 1  0 0.0  0 0 1 4.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDd56" name="instance_56">
                    <matrix>0.25  0 0 0.0   0 1  0 1.1  0 0 1 4.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDd57" name="instance_57">
                    <matrix>0.25  0 0 0.0   0 1  0 2.2  0 0 1 4.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
          </node>
<!--  Division sign #1  -->
            <node name="Divide1">
            <translate>0.0 4.4 1.0</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 0.75 1.0</scale>
                <node id="IDd21" name="instance_21">
                    <matrix>0.25  0 0 0.0   0 1  0 0.0  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
                <node id="IDd22" name="instance_22">
                    <matrix>0.25  0 0 0.0   0 -1  0 1.1  0 0 -1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
                <node id="IDd23" name="instance_23">
                    <matrix>0.25  0 0 0.0   0 1  0 1.1  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
                <node id="IDd24" name="instance_24">
                    <matrix>0.25  0 0 0.0   0 -1  0 2.2  0 0 -1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
                <node id="IDd25" name="instance_25">
                    <matrix>0.25  0 0 0.0   0 1  0 2.2  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
                <node id="IDd26" name="instance_26">
                    <matrix>0.25  0 0 0.0   0 -1  0 3.3  0 0 -1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
                <node id="IDd27" name="instance_27">
                    <matrix>0.25  0 0 0.0   0 1  0 3.3  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
            </node>
<!--  Division sign #2  -->
            <node name="Divide2">
            <translate>0.0 4.4 -8.5</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 0.75 1.0</scale>
                <node id="IDd21" name="instance_21">
                    <matrix>0.25  0 0 0.0   0 1  0 0.0  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
                <node id="IDd22" name="instance_22">
                    <matrix>0.25  0 0 0.0   0 -1  0 1.1  0 0 -1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
                <node id="IDd23" name="instance_23">
                    <matrix>0.25  0 0 0.0   0 1  0 1.1  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
                <node id="IDd24" name="instance_24">
                    <matrix>0.25  0 0 0.0   0 -1  0 2.2  0 0 -1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
                <node id="IDd25" name="instance_25">
                    <matrix>0.25  0 0 0.0   0 1  0 2.2  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
                <node id="IDd26" name="instance_26">
                    <matrix>0.25  0 0 0.0   0 -1  0 3.3  0 0 -1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
                <node id="IDd27" name="instance_27">
                    <matrix>0.25  0 0 0.0   0 1  0 3.3  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
            </node>
<!--  Letter "a" #1  -->
            <node name="Letter_a1">
            <translate>0.0 8.0 1.0</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
                <node id="IDa01" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa06" name="instance_6">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa07" name="instance_7">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa10" name="instance_10">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa11" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa18" name="instance_18">
                    <matrix>0.25  0 0 0.0  0 1 0 0.0  0 0  1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDa19" name="instance_19">
                    <matrix>0.25  0 0 0.0  0 0 1 4.4  0 -1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDa19" name="instance_19">
                    <matrix>0.25  0 0 0.0  0 0 -1 3.3  0 1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDa11" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa31" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa20" name="instance_20">
                    <matrix>0.25  0 0 0.0   0 0 1 3.3  0 -1 0 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDa21" name="instance_21">
                    <matrix>0.25  0 0 0.0   0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
            </node>
<!--  Letter "a" #2  -->
            <node name="Letter_a2">
            <translate>0.0 8.0 -8.5</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
                <node id="IDa01" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa06" name="instance_6">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa07" name="instance_7">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa10" name="instance_10">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa11" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa18" name="instance_18">
                    <matrix>0.25  0 0 0.0  0 1 0 0.0  0 0  1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDa19" name="instance_19">
                    <matrix>0.25  0 0 0.0  0 0 1 4.4  0 -1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDa19" name="instance_19">
                    <matrix>0.25  0 0 0.0  0 0 -1 3.3  0 1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDa11" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa31" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa20" name="instance_20">
                    <matrix>0.25  0 0 0.0   0 0 1 3.3  0 -1 0 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDa21" name="instance_21">
                    <matrix>0.25  0 0 0.0   0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
            </node>
<!--  Letter "a" #2  -->
            <node name="Letter_a2">
            <translate>0.0 8.0 -8.5</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
                <node id="IDa01" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa06" name="instance_6">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa07" name="instance_7">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa10" name="instance_10">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa11" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa18" name="instance_18">
                    <matrix>0.25  0 0 0.0  0 1 0 0.0  0 0  1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDa19" name="instance_19">
                    <matrix>0.25  0 0 0.0  0 0 1 4.4  0 -1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDa19" name="instance_19">
                    <matrix>0.25  0 0 0.0  0 0 -1 3.3  0 1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDa11" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa31" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa20" name="instance_20">
                    <matrix>0.25  0 0 0.0   0 0 1 3.3  0 -1 0 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDa21" name="instance_21">
                    <matrix>0.25  0 0 0.0   0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
            </node>
<!--  Letter "c"  -->
            <node name="Letter_c">
            <translate>0.0 0.0 -8.5</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
                <node id="ID001" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID002" name="instance_2">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID006" name="instance_6">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID007" name="instance_7">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID010" name="instance_10">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID011" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID018" name="instance_18">
                    <matrix>0.25  0 0 0.0  0 1 0 0.0  0 0  1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="ID019" name="instance_19">
                    <matrix>0.25  0 0 0.0  0 -1 0 3.3  0 0  -1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="ID020" name="instance_20">
                    <matrix>0.25  0 0 0.0   0 0 1 3.3  0 -1 0 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="ID021" name="instance_21">
                    <matrix>0.25  0 0 0.0   0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
            </node>
<!--  Letter "b"  ... has 8 + (4 x 15) = 68 lines -->
            <node name="Letter_b">
            <translate>0.0 0.0 1.0</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
                <node id="IDb01" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb02" name="instance_2">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb03" name="instance_3">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb04" name="instance_4">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 4.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb05" name="instance_5">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 5.5  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb12" name="instance_12">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb06" name="instance_6">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb07" name="instance_7">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb08" name="instance_8">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb09" name="instance_9">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb10" name="instance_10">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb11" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb19" name="instance_19">
                    <matrix>0.25  0 0 0.0  0 -1 0 3.3  0 0  -1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDb20" name="instance_20">
                    <matrix>0.25  0 0 0.0   0 0 1 3.3  0 -1 0 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDb21" name="instance_21">
                    <matrix>0.25  0 0 0.0   0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
            </node>
<!-- DECIMAL POINTS -->
                <node id="IDD01" name="Decimal_1">
                    <matrix>0.25 0 0 0.0  0 1 0 25.0  0 0 1 1.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDD02" name="Decimal_2">
                    <matrix>0.25 0 0 0.0  0 1 0 25.0  0 0 1 -8.5  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
<!--  Number "0" #1  ... has 8 + (4 x 18) = 80 lines -->
            <node name="Number_0">
            <translate>0.0 20.0 1.0</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
                <node id="IDb01" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb02" name="instance_2">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb03" name="instance_3">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb04" name="instance_4">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 4.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb05" name="instance_5">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 5.5  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDz19" name="instance_z19">
                    <matrix>0.25  0 0 0.0  0 1 0 0.0  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDb06" name="instance_6">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb07" name="instance_7">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb08" name="instance_8">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb09" name="instance_9">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb10" name="instance_10">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb11" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb19" name="instance_19">
                    <matrix>0.25  0 0 0.0  0 -1 0 3.3  0 0  -1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDb20" name="instance_20">
                    <matrix>0.25  0 0 0.0   0 0 1 3.3  0 -1 0 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDb21" name="instance_21">
                    <matrix>0.25  0 0 0.0   0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDz11" name="instance_z11">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDz12" name="instance_z12">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 4.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDz13" name="instance_z13">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 5.5  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
            </node>
<!--  Number "0" #2  ... has 8 + (4 x 18) = 80 lines -->
            <node name="Number_0b">
            <translate>0.0 20.0 -8.5</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
                <node id="IDb01" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb02" name="instance_2">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb03" name="instance_3">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb04" name="instance_4">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 4.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb05" name="instance_5">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 5.5  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDz19" name="instance_z19">
                    <matrix>0.25  0 0 0.0  0 1 0 0.0  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDb06" name="instance_6">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb07" name="instance_7">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb08" name="instance_8">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb09" name="instance_9">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb10" name="instance_10">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb11" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb19" name="instance_19">
                    <matrix>0.25  0 0 0.0  0 -1 0 3.3  0 0  -1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDb20" name="instance_20">
                    <matrix>0.25  0 0 0.0   0 0 1 3.3  0 -1 0 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDb21" name="instance_21">
                    <matrix>0.25  0 0 0.0   0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDz11" name="instance_z11">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDz12" name="instance_z12">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 4.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDz13" name="instance_z13">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 5.5  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
            </node>
<!--  Number "1" ... has 8 + (4 x 8) = 40 lines -->
<!--  Number "2" #1 ... has 8 + (4 x 17) = 76 lines -->
<!--  Number "2" #2 ... has 8 + (4 x 17) = 76 lines -->
<!--  Number "3"  ... has 8 + (4 x 18) = 80 lines -->
<!--  Number "4" ... has 8 + (4 x 13) = 60 lines -->
<!--  Number "5"  ... has 8 + (4 x 17) = 76 lines -->
<!--  Number "6" ... has 8 + (4 x 18) = 80 lines -->
<!--  Number "7" ... has 8 + (4 x 14) = 64 lines -->
<!--  Number "8" ... has 8 + (4 x 22) = 96 lines -->
<!--  Number "9"  ... has 8 + (4 x 15) = 68 lines -->
<!-- bovera_Digit1 is "4" -->
            <node name="bovera_Digit1">
            <translate>0.0 26.8 1.0</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
<!--  Number "4" ... has 8 + (4 x 13) = 60 lines -->
                <node id="IDe01" name="instance_e01">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDe02" name="instance_e02">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDe02" name="instance_e02">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb04" name="instance_4">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 4.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb05" name="instance_5">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 5.5  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb06" name="instance_6">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb08" name="instance_8">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb09" name="instance_9">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDn09" name="instance_9">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDf12" name="instance_n12">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDn12" name="instance_n12">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDz12" name="instance_z12">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 4.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDz13" name="instance_z13">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 5.5  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
            </node>
<!-- bovera_Digit2 is "1" -->
            <node name="bovera_Digit2">
            <translate>0.0 31.8 1.0</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
<!--  Number "1" ... has 8 + (4 x 8) = 40 lines -->
                <node id="ID101" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID102" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID103" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID104" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID105" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 4.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID106" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 5.5  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID107" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID109" name="instance_z19">
                    <matrix>0.25  0 0 0.0  0 1 0 1.1  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
            </node>
<!-- covera_Digit1 is "3" -->
            <node name="covera_Digit1">
            <translate>0.0 26.8 -8.5</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
<!--  Number "3"  ... has 8 + (4 x 18) = 80 lines -->
                <node id="ID301" name="instance_e01">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID302" name="instance_e02">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID303" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID304" name="instance_5">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 5.5  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID305" name="instance_z19">
                    <matrix>0.25  0 0 0.0  0 1 0 0.0  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="ID306" name="instance_6">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID307" name="instance_7">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID308" name="instance_8">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID309" name="instance_9">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID310" name="instance_10">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID311" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID312" name="instance_19">
                    <matrix>0.25  0 0 0.0  0 -1 0 3.3  0 0  -1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="ID313" name="instance_20">
                    <matrix>0.25  0 0 0.0   0 0 1 3.3  0 -1 0 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="ID314" name="instance_21">
                    <matrix>0.25  0 0 0.0   0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="ID315" name="instance_e19">
                    <matrix>0.25  0 0 0.0  0 -1 0 3.3  0 0  -1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="ID316" name="instance_e20">
                    <matrix>0.25  0 0 0.0   0 0 1 3.3  0 -1 0 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="ID317" name="instance_z12">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 4.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID318" name="instance_z13">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 5.5  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
            </node>
<!-- covera_Digit2 is "8" -->
            <node name="covera_Digit2">
            <translate>0.0 31.8 -8.5</translate>
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<!-- END LABELING HERE -->
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<!-- BEGIN CLOCK -->
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            </node>                                         <!-- /TWO -->
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              <instance_node url="#HourID3" />
            </node>                                         <!-- /TWO -->
          </node>
<!-- END CLOCK   -->
          </node> <!-- End Inertial Grouping of Objects -->
        </visual_scene>
    </library_visual_scenes>
    <scene>
        <instance_visual_scene url="#ID1" />
    </scene>
</COLLADA>


Instructions for Viewing the Example Model on a Mac:

  1. Click, then drag your cursor down through the scrollable box to highlight and select all 7968 lines of the COLLADA code.
  2. Make a copy (⌘-c) of the entire code.
  3. Paste (⌘-v) the code into an empty, plain text file (using, for example, Apple's TextEdit app) and save it with the name, Inertial17.dae. [NOTE: ".dae" is the file name suffix that is universally associated with an executable COLLADA file.]
  4. Open this file using Apple's Preview app; the static 3D model of our (opaque purple) ellipsoid should appear at TIME = 0.0 — see Figure 1b.
  5. To view the 3D (TIME = 0.0) model from different angles, place your mouse cursor anywhere near the center of the Preview app's image, then click and drag the cursor in different directions.
  6. The play/pause buttons — shown at the bottom of Figure 1b — become visible if the cursor is simply placed near the bottom of the image being displayed by the Preview app; the animation will start (on a continuous loop) when the play button is clicked.

Instructions for Viewing the Example Model on a Windows 10 PC:
We have not yet figured out how to similarly (at no cost) view COLLADA-based (.dae) 3D scenes on a PC. On my Lenovo system, the Windows 10 startup menu includes a "3D Viewer" app, but this app does not recognize .dae-formatted files. However, the app appears to read .glb-formatted files satisfactorily. As is discussed below, the Oculus Rift S system will import our COLLADA-based models only if each model file has been translated from a ".dae" format to a ".glb" format. Hence, after this translation has been made principally to facilitate the importation of our model into the Oculus Rift S virtual-reality environment — see our description, below, of the Khronos Group's COLLADA2GLTF Converter — we have also been able to straightforwardly view the 3D scene on our Lenovo PC using its "3D Viewer" app.


At TIME = 0.0 (see, again, Figure 1b), our purple ellipsoid is oriented such that its longest axis (of length, 2a) aligns with the X0-axis and such that the small red cubic "fluid marker" at the tip of the ellipsoid lies in the plus-X direction — initially at location (X0, Y0, Z0) = (+a, 0, 0). At the opposite end of the ellipsoid — initially at location (X0, Y0, Z0) = (-a, 0, 0) — we have attached a stubby black pointer; as the ellipsoid spins, this black pointer will remain affixed to the ellipsoid to aid in counting spin cycles, whereas the red fluid marker will not. The ellipsoid's shortest axis (length, 2c) aligns with the Z0-axis, with straight up being associated with the positive Z direction. The ellipsoid's intermediate axis (length, 2b) initially aligns with the lab's Y0-axis, with the positive direction being defined by the standard "righthand rule."

In addition to displaying an opaque purple Riemann ellipsoid, our COLLADA-defined 3D visual scene contains (see, again, Figure 1b):

  • A square gray "frame" that lies in the laboratory frame's equatorial, Z0 = 0.0, plane, just outside of and "framing" the ellipsoid; and a small gray solid rectangle that hovers above the ellipsoid and is affixed to the plus-Z0 axis, also intended to provide 3D orientation and registration queues.
  • A couple of lines of alpha-numeric characters that has been attached to an imaginary laboratory wall to label/quantify the geometric properties of this ellipsoid.
  • A clock that has been hung on the same imaginary laboratory wall.
  • A yellow-dotted ellipse (comprised of 50 individual small yellow markers) that lies in the equatorial plane and is attached to the ellipsoid, marking the trajectory that will be followed by the red cubic "fluid marker" during the animation sequence.

Animation

When the "play" button is clicked on the Preview app's control panel (again, reference Figure 1b), the COLLADA-directed scene-animation begins. Three different characteristic timescales are relevant:

Clock Image
  1. We use the motion of the hands on the wall-mounted clock to identify the natural oscillation frequency of the physical system, namely, <math>~\Omega_0 \equiv [\pi G \rho]^{1 / 2}</math>. More specifically, by declaration, one oscillation period of the red "minute" hand — that is to say, one wall-clock "hour" — is <math>~P_0 = 2\pi[\pi G \rho]^{-1 / 2} = [4\pi/(G \rho)]^{1 / 2}</math>. One full cycle of the wall-clock's black "hour" hand is therefore 12P0. For pedagogical purposes, in all of our COLLADA-driven animations we have equated P0 with a COLLADA TIME interval of 4.0, which means that during each animation, one wall-clock hour passes every (approximately) 4 seconds of real time.
  2. The purple ellipsoid spins in a prograde direction about its shortest axis — that is, about the Z0-axis — on a timescale set by the value of <math>~\Omega_\mathrm{EFE}</math>, which has already been normalized to Ω0. Specifically, as viewed from the inertial frame of reference, the ellipsoid will complete one full spin in a time, <math>~P_\mathrm{spin} = |\Omega_\mathrm{EFE}|^{-1} = [0.5479]^{-1} = 1.825</math> wall-clock hours, which is approximately 7.3 seconds of real time.
  3. As viewed from a frame of reference that is spinning with the ellipsoid, each Lagrangian fluid element inside as well as on the surface of the ellipsoid moves in a retro-grade direction along an elliptical trajectory that has the same ellipticity as does the equatorial surface of the 3D ellipsoid. Each and every Lagrangian fluid element completes one full elliptical orbit in a time, <math>~P_\mathrm{Lagrange} = \lambda_\mathrm{EFE}^{-1} = [0.0799]^{-1} = 12.52</math> wall-clock hours, which is about 50 seconds of real time.

In the COLLADA-based code (Inertial17.dae) that has been provided above in the scrollable box, we have instructed the animation sequence to follow the system's evolution through five complete spins of the purple ellipsoid. (Unless the pause button is clicked, the animation will actually loop repeatedly, but the time on the wall-mounted clock will reset to 0h0m after every fifth spin period.) In practice, this animation sequence lasts (5 × 1.825) × 4 = 36.5 seconds of real time.

Figure 2 displays a pair of still-frame images of our example (purple) ellipsoidal configuration after the ellipsoid has completed precisely five (counter-clockwise) spin cycles. (The snapshots have been taken at the same point in time, but from two different camera viewing angles.) In the left-hand image (Figure 2a), the time on the clock appears to be about 9h8m. This means that as the ellipsoid has completed five spin cycles, the "minute" hand of the clock has completed approximately [9 + 8/60] ≈ 9.13 cycles. Dividing this number by 5 gives a value of <math>~P_\mathrm{spin} \approx 1.827</math>, which is indeed the spin period we identified earlier. This illustrates that the proper physical timescales governing oscillations of the wall-mounted clock and of the spinning ellipsoid have been implemented in a quantitatively accurate manner within the COLLADA code.


Figure 2a Figure 2b

EFE Model b41c385

EFE Model b41c385


In Figure 1b, above, we have used a small red cube to mark the Lagrangian fluid element that is initially (TIME = 0.0) located at the end of the longest axis of the ellipsoid (in the +X direction). In Figure 2b we can see where this fluid element is located after the ellipsoid has completed five complete spins. After moving in a retrograde (clockwise) direction along its assigned elliptical trajectory while the ellipsoid completed five full spins, we see that the red-tagged Lagrangian fluid element has completed a little less than 3/4 of one full orbit; let's call it 73% of one orbit. We therefore infer from the COLLADA-driven animation that <math>~0.73 P_\mathrm{Lagrange}\approx~5 P_\mathrm{spin}</math>, that is, <math>~P_\mathrm{Lagrange}\approx 6.849 P_\mathrm{spin}</math>. This is indeed a proper reflection of the physical properties of our chosen example Riemann S-type ellipsoid, as its mathematically determined equilibrium frequency ratio is, <math>~|\Omega_\mathrm{EFE}|/|\lambda_\mathrm{EFE}| = 6.8582</math>. This, too, illustrates that the proper physical timescales governing oscillations of our chosen example Riemann ellipsoid have been implemented in a quantitatively accurate manner within the COLLADA code.

Rotating Reference Frame

 
Figure 3

Rotating Frame at TIME zero

The following scrollable box titled, MultiLagrange18.dae, contains another <xml>-formatted COLLADA code. It is identical in most respects to the COLLADA code named Inertial17.dae that has been discussed above in considerable detail. But there are two key differences:

  1. As Figure 3 illustrates, while the surface of the ellipsoid is still colored purple, it has been made partially transparent to reveal the location of three — rather than only one — Lagrangian fluid elements. All three are initially positioned along the plus-X0 axis, but two are located inside, rather than on the surface of, the ellipsoid.
  2. This new, "MultiLagrange" COLLADA animation presents the system's evolution as viewed from a frame of reference that is spinning with the frequency of the ellipsoid, ΩEFE. As before, the COLLADA-driven animation is carried through five full ellipsoid spins, but from the perspective of this new rotating frame, the ellipsoid remains stationary and it is the components of the "laboratory" that actually spin; and they spin clockwise rather than counter-clockwise.

From the point of view of this rotating reference frame, it is much easier to watch and diagnose the behavior of the fluid motion interior to the surface of the ellipsoid. Note, in particular, the relative speed and alignment of the three fluid elements at different points along their coordinated orbits. Because Riemann S-type ellipsoids are uniform-density configurations and they are composed of an incompressible fluid, at all points in time and in space (within the volume of the ellipsoid) the divergence of the velocity must be zero.


MultiLagrange18.dae     …     a COLLADA code containing 7994 lines of <xml>-formatted ASCII text

<?xml version="1.0" encoding="UTF-8" standalone="no" ?>
<COLLADA xmlns="http://www.collada.org/2005/11/COLLADASchema" version="1.4.1">
    <asset>
        <contributor>
            <author>jet53man</author>
            <authoring_tool>Raw XML</authoring_tool>
        </contributor>
        <created>2020-04-28</created>
        <modified>2020-05-10</modified>
        <unit meter="0.0254" name="inch" />
        <up_axis>Z_UP</up_axis>
<!-- 
This file originally was named FullLast45X.dae ...
here its assigned name is RiemannBuild05.dae (etc.)
we are inserting various objects, drawn from b41c385_DI.dae

                 <node>        <geometry>       <material>      <effect>
*** firstclock:    ID3     Clock_OuterEdge         ID6            ID5
***           :            Clock_InnerEdge       InnerID6       InnerID5
***   Jetman  :  ArrowID3  Clock_ArrowEdge       ArrowID6       ArrowID5
***  HourHand :  HourID3   Clock_HourEdge        HourID6        HourID5
-->
    </asset>
    <library_effects>
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            <profile_COMMON>
                <technique sid="COMMON">
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                        <diffuse>
                            <color>0.5 0.0 0.99  1.0</color>
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                    </lambert>
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            </profile_COMMON>
        </effect>
<!-- effect:  MidPlane Frame -->
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                <technique sid="COMMON">
                    <lambert>
                        <diffuse>
                            <color>0.0 0.0 0.6 0.5</color>
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        </effect>
<!-- effect:  Cylindrical Pointer -->
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                  <color>1 1 0 1</color>
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        </effect>
    </library_effects>
    <library_materials>
<!-- material:  Four Clock Components -->
        <material id="ID6" name="material">
            <instance_effect url="#ID5" />
        </material>
        <material id="InnerID6" name="Inner_material">
            <instance_effect url="#InnerID5" />
        </material>
        <material id="ArrowID6" name="Arrow_material">
            <instance_effect url="#ArrowID5" />
        </material>
        <material id="HourID6" name="Hour_material">
            <instance_effect url="#HourID5" />
        </material>
        <material id="ID6_EFE" name="material">
            <instance_effect url="#DiffusePurple_00" />
        </material>
<!-- material:  MidPlane Frame -->
        <material id="MidPlaneID6" name="MidPlane_material">
            <instance_effect url="#MidPlaneID5" />
        </material>
<!-- material:  Cylindrical Pointer -->
        <material id="CylID6" name="Cyl_material">
            <instance_effect url="#CylID5" />
        </material>
        <material id="ZupID6" name="Zup_material">
            <instance_effect url="#MidPlaneID5" />
        </material>
        <material id="MarkersID6" name="markers_material">
            <instance_effect url="#MarkersID5" />
        </material>
        <material id="Primary_MarkerID6" name="primary_marker_material">
            <instance_effect url="#DiffuseRed_EFE" />
        </material>
<!-- material:  Letters -->
        <material id="LettersID6" name="material">
            <instance_effect url="#LettersID5" />
        </material>
        <material id="DiagonalID6" name="material">
            <instance_effect url="#DiagonalID5" />
        </material>
        <material id="Black_DiagonalID6" name="material">
            <instance_effect url="#Black_DiagonalID5" />
        </material>
    </library_materials>
    <library_nodes>
<!-- node:  Three clock components -->
        <node id="ID3" name="cube_component">
            <instance_geometry url="#Clock_OuterEdge">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#ID6">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                        </instance_material>
                    </technique_common>
                </bind_material>
            </instance_geometry>
            <instance_geometry url="#Clock_InnerEdge">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#InnerID6">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                        </instance_material>
                    </technique_common>
                </bind_material>
            </instance_geometry>
        </node>
        <node id="ArrowID3" name="cube_component">
            <instance_geometry url="#Clock_ArrowEdge">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#ArrowID6">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                        </instance_material>
                    </technique_common>
                </bind_material>
            </instance_geometry>
        </node>
        <node id="HourID3" name="hour_hand">
            <instance_geometry url="#Clock_HourEdge">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#HourID6">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                        </instance_material>
                    </technique_common>
                </bind_material>
            </instance_geometry>
        </node>
        <node id="ID3_EFE" name="cube_componentEFE">
            <instance_geometry url="#EllipsoidOctant">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#ID6_EFE">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                        </instance_material>
                    </technique_common>
                </bind_material>
            </instance_geometry>
            <instance_geometry url="#ReflectOctant">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#ID6_EFE">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                        </instance_material>
                    </technique_common>
                </bind_material>
            </instance_geometry>
        </node>
<!-- node:  MidPlane Frame -->
        <node id="EqPlane" name="equatorial_plane">
            <instance_geometry url="#EquatorialPlane">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#MidPlaneID6">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                        </instance_material>
                    </technique_common>
                </bind_material>
            </instance_geometry>
        </node>
<!-- node:  Cylindrical Pointer -->
        <node id="CylPointer" name="cylindrical_component">
            <instance_geometry url="#Cylinder">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#CylID6">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                        </instance_material>
                    </technique_common>
                </bind_material>
            </instance_geometry>
        </node>
        <node id="ZupPointer" name="Zup_component">
            <instance_geometry url="#CubeID4">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#ZupID6">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                        </instance_material>
                    </technique_common>
                </bind_material>
            </instance_geometry>
        </node>
        <node id="MarkersID3" name="Lagrange_markers">
          <instance_geometry url="#CubeID4">
            <bind_material>
              <technique_common>
                <instance_material symbol="Material2" target="#MarkersID6">
                  <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                </instance_material>
              </technique_common>
            </bind_material>
          </instance_geometry>
        </node>
        <node id="Primary_MarkerID3" name="Primary_marker">
          <instance_geometry url="#CubeID4">
            <bind_material>
              <technique_common>
                <instance_material symbol="Material2" target="#Primary_MarkerID6">
                  <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                </instance_material>
              </technique_common>
            </bind_material>
          </instance_geometry>
        </node>
<!-- node:  Letters -->
        <node id="LettersID3" name="cube_component">
            <instance_geometry url="#CubeID4">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#LettersID6">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                        </instance_material>
                    </technique_common>
                </bind_material>
            </instance_geometry>
        </node>
        <node id="DiagonalID3" name="diagonal_component">
            <instance_geometry url="#DiagonalID4">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#DiagonalID6">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                        </instance_material>
                    </technique_common>
                </bind_material>
            </instance_geometry>
        </node>
        <node id="Black_DiagonalID3" name="Blackdiagonal_component">
            <instance_geometry url="#DiagonalID4">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#Black_DiagonalID6">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                        </instance_material>
                    </technique_common>
                </bind_material>
            </instance_geometry>
        </node>
    </library_nodes>
    <library_geometries>
<!-- geometry:  Four Clock Components -->
        <geometry id="Clock_OuterEdge">
            <mesh>
<!--
            **********************************************
            *
            *  Insert first portion of clock's structure
            *
            **********************************************
-->
                <source id="Clock_Positions">
                  <float_array id="Coordinates01" count="123"> 0.0  1.0  0.2 1.0  1.0  0.2 1.0  0.0  0.2 1.0 -1.0  0.2 0.0 -1.0  0.2 -1.0 -1.0  0.2 -1.0  0.0  0.2 -1.0  1.0  0.2 0.0  1.0 -0.2 1.0  1.0 -0.2 1.0  0.0 -0.2 1.0 -1.0 -0.2 0.0 -1.0 -0.2 -1.0 -1.0 -0.2 -1.0  0.0 -0.2 -1.0  1.0 -0.2 0.9  0.0  0.2 0.779423 0.45 0.2 0.45 0.779423 0.2 0.0  0.9  0.2 -0.45 0.779423 0.2 -0.779423 0.45 0.2 -0.9 0.0 0.2 -0.779423 -0.45 0.2 -0.45 -0.779423 0.2 0.0 -0.9 0.2 0.45 -0.779423 0.2 0.779423 -0.45 0.2 -0.9  0.0  -0.2 -0.779423 0.45 -0.2 -0.45 0.779423 -0.2 -0.0  0.9  -0.2 0.45 0.779423 -0.2 0.779423 0.45 -0.2 0.9 0.0 -0.2 0.779423 -0.45 -0.2 0.45 -0.779423 -0.2 -0.0 -0.9 -0.2 -0.45 -0.779423 -0.2 -0.779423 -0.45 -0.2  0.0 0.0 -0.2</float_array>
                  <technique_common>
                    <accessor source="#Coordinates01" count="41" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                    </accessor>
                  </technique_common>
                </source>
                <source id="Clock_Normals">
                  <float_array id="InnerNormals01" count="18">
 1.0  0.0  0.0
-1.0  0.0  0.0
 0.0  1.0  0.0
 0.0 -1.0  0.0
 0.0  0.0  1.0
 0.0  0.0 -1.0
                  </float_array>
                    <technique_common>
                        <accessor source="#InnerNormals01" count="6" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                        </accessor>
                    </technique_common>
                </source>
                <vertices id="Clock_Vertices">
                    <input semantic="POSITION" source="#Clock_Positions" />
                </vertices>
                <polylist count="56" material="Material2">
                    <input semantic="VERTEX" source="#Clock_Vertices" offset="0" />
                    <input semantic="NORMAL" source="#Clock_Normals" offset="1" />
<vcount> 3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3</vcount>
<p> 0 2 1 2 8 2  1 2 9 2 8 2  7 2 0 2 15 2  0 2 8 2 15 2 1 0 2 0 9 0  2 0 10 0 9 0  2 0 3 0 10 0  3 0 11 0 10 0 3 3 4 3 11 3  4 3 12 3 11 3  4 3 5 3 12 3  5 3 13 3 12 3 5 1 6 1 13 1  6 1 14 1 13 1  6 1 7 1 14 1  7 1 15 1 14 1 2 4 17 4 16 4  2 4 1 4 17 4  1 4 18 4 17 4  1 4 0 4 18 4  0 4 19 4 18 4 0 4 20 4 19 4  0 4 7 4 20 4  7 4 21 4 20 4  7 4 6 4 21 4  6 4 22 4 21 4 6 4 23 4 22 4  6 4 5 4 23 4  5 4 24 4 23 4  5 4 4 4 24 4  4 4 25 4 24 4 4 4 26 4 25 4  4 4 3 4 26 4  3 4 27 4 26 4  3 4 2 4 27 4  2 4 16 4 27 4 14 5 29 5 28 5  14 5 15 5 29 5  15 5 30 5 29 5  15 5 8 5 30 5  8 5 31 5 30 5 8 5 32 5 31 5  8 5 9 5 32 5  9 5 33 5 32 5  9 5 10 5 33 5  10 5 34 5 33 5 10 5 35 5 34 5  10 5 11 5 35 5  11 5 36 5 35 5  11 5 12 5 36 5  12 5 37 5 36 5 12 5 38 5 37 5  12 5 13 5 38 5  13 5 39 5 38 5  13 5 14 5 39 5  14 5 28 5 39 5 </p>
                </polylist>
            </mesh>
        </geometry>
        <geometry id="Clock_InnerEdge">
            <mesh>
<!--
            **********************************************
            *
            *  Insert second portion of clock's structure
            *
            **********************************************
-->
                <source id="Clock_InnerPositions">
                  <float_array id="InnerCoordinates01" count="123">
0.0  1.0  0.2 1.0  1.0  0.2 1.0  0.0  0.2 1.0 -1.0  0.2 0.0 -1.0  0.2 -1.0 -1.0  0.2 -1.0  0.0  0.2 -1.0  1.0  0.2 0.0  1.0 -0.2 1.0  1.0 -0.2 1.0  0.0 -0.2 1.0 -1.0 -0.2 0.0 -1.0 -0.2 -1.0 -1.0 -0.2 -1.0  0.0 -0.2 -1.0  1.0 -0.2 0.9  0.0  0.2 0.779423 0.45 0.2 0.45 0.779423 0.2 0.0  0.9  0.2 -0.45 0.779423 0.2 -0.779423 0.45 0.2 -0.9 0.0 0.2 -0.779423 -0.45 0.2 -0.45 -0.779423 0.2 0.0 -0.9 0.2 0.45 -0.779423 0.2 0.779423 -0.45 0.2 -0.9  0.0  -0.2 -0.779423 0.45 -0.2 -0.45 0.779423 -0.2 -0.0  0.9  -0.2 0.45 0.779423 -0.2 0.779423 0.45 -0.2 0.9 0.0 -0.2 0.779423 -0.45 -0.2 0.45 -0.779423 -0.2 -0.0 -0.9 -0.2 -0.45 -0.779423 -0.2 -0.779423 -0.45 -0.2  0.0 0.0 -0.2</float_array>
                  <technique_common>
                    <accessor source="#InnerCoordinates01" count="41" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                    </accessor>
                  </technique_common>
                </source>
                <source id="Clock_InnerNormals">
                  <float_array id="InnerNormals01" count="54">
 1.0  0.0  0.0
-1.0  0.0  0.0
 0.0  1.0  0.0
 0.0 -1.0  0.0
 0.0  0.0  1.0
 0.0  0.0 -1.0
 -0.965926 -0.258819 0.0
 -0.707107 -0.707107 0.0
 -0.258819 -0.965926 0.0
  0.258819 -0.965926 0.0
  0.707107 -0.707107 0.0
  0.965926 -0.258819 0.0
  0.965926  0.258819 0.0
  0.707107  0.707107 0.0
  0.258819  0.965926 0.0
 -0.258819  0.965926 0.0
 -0.707107  0.707107 0.0
 -0.965926  0.258819 0.0
                  </float_array>
                    <technique_common>
                        <accessor source="#InnerNormals01" count="18" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                        </accessor>
                    </technique_common>
                </source>
                <vertices id="Clock_InnerVertices">
                    <input semantic="POSITION" source="#Clock_InnerPositions" />
                </vertices>
                <polylist count="24" material="Material2">
                    <input semantic="VERTEX" source="#Clock_InnerVertices" offset="0" />
                    <input semantic="NORMAL" source="#Clock_InnerNormals" offset="1"/>
<vcount>4 4 4 4  4 4 4 4  4 4 4 4  3 3 3 3  3 3 3 3  3 3 3 3</vcount>
<p> 16 6 17 6 33 6 34 6 17 7 18 7 32 7 33 7 18 8 19 8 31 8 32 8 19 9 20 9 30 9 31 9 20 10 21 10 29 10 30 10 21 11 22 11 28 11 29 11 22 12 23 12 39 12 28 12 23 13 24 13 38 13 39 13 24 14 25 14 37 14 38 14 25 15 26 15 36 15 37 15 26 16 27 16 35 16 36 16 27 17 16 17 34 17 35 17 28 5 29 5 40 5 29 5 30 5 40 5 30 5 31 5 40 5 31 5 32 5 40 5 32 5 33 5 40 5 33 5 34 5 40 5 34 5 35 5 40 5 35 5 36 5 40 5 36 5 37 5 40 5 37 5 38 5 40 5 38 5 39 5 40 5 39 5 28 5 40 5 </p>
              </polylist>
            </mesh>
        </geometry>
        <geometry id="Clock_ArrowEdge">
            <mesh>
<!--
            **********************************************
            *
            *  Insert arrow portion of clock's structure
            *
            **********************************************
-->
                <source id="Clock_ArrowPositions">
                  <float_array id="ArrowCoordinates01" count="30"> 0.0  0.85 0.25 0.1  0.0 0.25 0.0 -0.2 0.25 -0.1  0.0 0.25 0.0  0.85 0.05 0.1  0.0 0.05 0.0 -0.2 0.05 -0.1  0.0 0.05 0.0  0.0 0.25 0.0  0.0 0.05 </float_array>
                  <technique_common>
                    <accessor source="#ArrowCoordinates01" count="10" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                    </accessor>
                  </technique_common>
                </source>
                <source id="Clock_ArrowNormals">
                  <float_array id="ArrowNormals01" count="18">
 0  0  1
 0  0 -1
 0.993151  0.116841 0.0
 0.447214 -0.894427 0.0
-0.447214 -0.894427 0.0
-0.993151  0.116841 0.0
                  </float_array>
                    <technique_common>
                        <accessor source="#ArrowNormals01" count="6" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                        </accessor>
                    </technique_common>
                </source>
                <vertices id="Clock_ArrowVertices">
                    <input semantic="POSITION" source="#Clock_ArrowPositions" />
                </vertices>
                <polylist count="12" material="Material2">
                    <input semantic="VERTEX" source="#Clock_ArrowVertices" offset="0" />
                    <input semantic="NORMAL" source="#Clock_ArrowNormals" offset="1"/>
<vcount>3 3 3 3 3 3 3 3 4 4 4 4</vcount>
<p> 0 0 8 0 1 0 1 0 8 0 2 0 2 0 8 0 3 0 3 0 8 0 0 0 4 1 5 1 9 1 5 1 6 1 9 1 6 1 7 1 9 1 7 1 4 1 9 1 0 2 1 2 5 2 4 2 1 3 2 3 6 3 5 3 2 4 3 4 7 4 6 4 3 5 0 5 4 5 7 5 </p>
              </polylist>
            </mesh>
        </geometry>
        <geometry id="Clock_HourEdge">
            <mesh>
<!--
            **********************************************
            *
            *  Insert hour_hand portion of clock's structure
            *
            **********************************************
-->
                <source id="Clock_HourPositions">
                  <float_array id="HourCoordinates01" count="30"> 0.0  0.85 0.25 0.1  0.0 0.25 0.0 -0.2 0.25 -0.1  0.0 0.25 0.0  0.85 0.05 0.1  0.0 0.05 0.0 -0.2 0.05 -0.1  0.0 0.05 0.0  0.0 0.25 0.0  0.0 0.05 </float_array>
                  <technique_common>
                    <accessor source="#HourCoordinates01" count="10" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                    </accessor>
                  </technique_common>
                </source>
                <source id="Clock_HourNormals">
                  <float_array id="HourNormals01" count="18">
 0  0  1
 0  0 -1
 0.993151  0.116841 0.0
 0.447214 -0.894427 0.0
-0.447214 -0.894427 0.0
-0.993151  0.116841 0.0
                  </float_array>
                    <technique_common>
                        <accessor source="#HourNormals01" count="6" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                        </accessor>
                    </technique_common>
                </source>
                <vertices id="Clock_HourVertices">
                    <input semantic="POSITION" source="#Clock_HourPositions" />
                </vertices>
                <polylist count="12" material="Material2">
                    <input semantic="VERTEX" source="#Clock_HourVertices" offset="0" />
                    <input semantic="NORMAL" source="#Clock_HourNormals" offset="1"/>
<vcount>3 3 3 3 3 3 3 3 4 4 4 4</vcount>
<p> 0 0 8 0 1 0 1 0 8 0 2 0 2 0 8 0 3 0 3 0 8 0 0 0 4 1 5 1 9 1 5 1 6 1 9 1 6 1 7 1 9 1 7 1 4 1 9 1 0 2 1 2 5 2 4 2 1 3 2 3 6 3 5 3 2 4 3 4 7 4 6 4 3 5 0 5 4 5 7 5 </p>
              </polylist>
            </mesh>
        </geometry>
<!-- geometry:  Letters -->
        <geometry id="CubeID4">
            <mesh>
                <source id="CubeID7_Positions">
                    <float_array id="CoordinatesID10" count="24">
   -0.5  -0.5  -0.5
   -0.5  -0.5   0.5
   -0.5   0.5  -0.5
   -0.5   0.5   0.5
    0.5  -0.5  -0.5
    0.5  -0.5   0.5
    0.5   0.5  -0.5
    0.5   0.5   0.5
                    </float_array>
                    <technique_common>
                        <accessor source="#CoordinatesID10" count="8" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                        </accessor>
                    </technique_common>
                </source>
                <source id="CubeID8_Normals">
                    <float_array id="NormalsID11" count="18">
    0  0 -1
    0  0  1
    0 -1  0
    0  1  0
   -1  0  0
    1  0  0
                    </float_array>
                    <technique_common>
                        <accessor source="#NormalsID11" count="6" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                        </accessor>
                    </technique_common>
                </source>
                <vertices id="CubeID9_Vertices">
                    <input semantic="POSITION" source="#CubeID7_Positions" />
                </vertices>
                <polylist count="12" material="Material2">
                    <input semantic="VERTEX" source="#CubeID9_Vertices" offset="0" />
                    <input semantic="NORMAL" source="#CubeID8_Normals" offset="1" />
<vcount>3 3 3 3  3 3 3 3  3 3 3 3</vcount>
<p>
0 0 2 0 6 0  0 0 6 0 4 0
1 1 7 1 3 1  1 1 5 1 7 1
0 2 4 2 5 2  0 2 5 2 1 2
2 3 3 3 7 3  2 3 7 3 6 3
0 4 1 4 3 4  0 4 3 4 2 4
4 5 6 5 7 5  4 5 7 5 5 5
</p>
                </polylist>
          </mesh>
        </geometry>
        <geometry id="DiagonalID4">
            <mesh>
                <source id="DiagonalID7_Positions">
                    <float_array id="Diag_CoordinatesID10" count="24">
   -0.5  -0.5  -0.5
   -0.5  -0.5   0.5
   -0.5   0.5  -0.5
   -0.5   0.5   0.5
    0.5  -0.5  -0.5
    0.5  -0.5   0.5
    0.5   0.5  -0.5
    0.5   0.5   0.5
                    </float_array>
                    <technique_common>
                        <accessor source="#Diag_CoordinatesID10" count="8" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                        </accessor>
                    </technique_common>
                </source>
                <source id="DiagonalID8_Normals">
                    <float_array id="Diagonal_NormalsID11" count="21">
    0  0 -1
    0  0  1
    0 -1  0
    0  1  0
   -1  0  0
    1  0  0
    0  -0.707 0.707
                    </float_array>
                    <technique_common>
                        <accessor source="#Diagonal_NormalsID11" count="7" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                        </accessor>
                    </technique_common>
                </source>
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<!-- geometry:  Cylindrical Pointer -->
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  16 16  15 16  17 16
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<!--
            **********************************************
            *
            *  Insert Geometry of Ellipsoid Octant
            *
            **********************************************
-->
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<technique_common>
  <accessor source="#Ellipsoid_Coordinates" count="  521" stride="3">
        <param name="X" type="float" />
        <param name="Y" type="float" />
        <param name="Z" type="float" />
  </accessor>
</technique_common>
</source>
<source id="Ellipsoid_Normals">
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3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
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3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
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</float_array>
<technique_common>
  <accessor source="#Reflect_Coordinates" count="  521" stride="3">
        <param name="X" type="float" />
        <param name="Y" type="float" />
        <param name="Z" type="float" />
  </accessor>
</technique_common>
</source>
<source id="Reflect_Normals">
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</p>
</polylist>
  </mesh>
</geometry>
<!-- EquatorialPlane (begin) -->
<geometry id="EquatorialPlane">
  <mesh>
<source id="EquatorialPlane_Positions">
<float_array id="EquatorialPlane_Coordinates" count="48">
   -5.5000    -5.5000    0.2000
    5.5000    -5.5000    0.2000
    5.5000     5.5000    0.2000
   -5.5000     5.5000    0.2000
   -5.7500    -5.7500    0.2000
    5.7500    -5.7500    0.2000
    5.7500     5.7500    0.2000
   -5.7500     5.7500    0.2000
   -5.5000    -5.5000   -0.2000
    5.5000    -5.5000   -0.2000
    5.5000     5.5000   -0.2000
   -5.5000     5.5000   -0.2000
   -5.7500    -5.7500   -0.2000
    5.7500    -5.7500   -0.2000
    5.7500     5.7500   -0.2000
   -5.7500     5.7500   -0.2000
</float_array>
<technique_common>
  <accessor source="#EquatorialPlane_Coordinates" count="  16" stride="3">
        <param name="X" type="float" />
        <param name="Y" type="float" />
        <param name="Z" type="float" />
  </accessor>
</technique_common>
</source>
<source id="EquatorialPlane_Normals">
<float_array id="EquatorialPlane_Normals01" count="18">
    0.0000    0.0000     1.0000
    0.0000    0.0000    -1.0000
    0.0000   -1.0000     0.0000
    0.0000    1.0000     0.0000
   -1.0000    0.0000     0.0000
    1.0000    0.0000     0.0000
</float_array>
<technique_common>
  <accessor source="#EquatorialPlane_Normals01" count="6" stride="3">
        <param name="X" type="float" />
        <param name="Y" type="float" />
        <param name="Z" type="float" />
  </accessor>
</technique_common>
</source>
<vertices id="EquatorialPlane_Vertices">
  <input semantic="POSITION" source="#EquatorialPlane_Positions" />
</vertices>
<polylist count="  12" material="Material2">
  <input semantic="VERTEX" source="#EquatorialPlane_Vertices" offset="0" />
  <input semantic="NORMAL" source="#EquatorialPlane_Normals" offset="1" />
<vcount>
4 4 4 4
4 4 4 4
4 4 4 4
</vcount>
<p>
 4 0  5 0  1 0  0 0
 5 0  6 0  2 0  1 0
 6 0  7 0  3 0  2 0
 7 0  4 0  0 0  3 0
 8 1   9 1  13 1  12 1
 9 1  10 1  14 1  13 1
10 1  11 1  15 1  14 1
11 1   8 1  12 1  15 1
12 2  13 2   5 2   4 2
14 3  15 3   7 3   6 3
15 4  12 4   4 4   7 4
13 5  14 5   6 5   5 5
</p>
</polylist>
  </mesh>
</geometry>
<!-- EquatorialPlane (end)   -->
    </library_geometries>
    <library_animations>
  <animation id="First_rotation_euler_Z">
<!-- for EFE/Ou model b41c385, clockstop = 36.5047 and anglestop = 1800.0 -->
<!-- this means that one 360 degree turn of the ellipsoid takes 7.3009 clock units -->
    <source id="First_rotation_euler_Z-input">
      <float_array id="First_rotation_euler_Z-input-array" count="31">
   0.00
   1.22
   2.43
   3.65
   4.87
   6.08
   7.30
   8.52
   9.73
  10.95
  12.17
  13.39
  14.60
  15.82
  17.04
  18.25
  19.47
  20.69
  21.90
  23.12
  24.34
  25.55
  26.77
  27.99
  29.20
  30.42
  31.64
  32.85
  34.07
  35.29
  36.50
      </float_array>
      <technique_common>
          <accessor source="#First_rotation_euler_Z-input-array" count="31" stride="1">
            <param name="TIME" type="float"/>
          </accessor>
      </technique_common>
    </source>
<!-- This sets the spin rate of the "Entire" ellipsoid -->
    <source id="First_rotation_euler_Z-output">
      <float_array id="First_rotation_euler_Z-output-array" count="31">
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
      </float_array>
      <technique_common>
          <accessor source="#First_rotation_euler_Z-output-array" count="31" stride="1">
            <param name="ANGLE" type="float"/>
          </accessor>
      </technique_common>
    </source>
<!-- This sets the spin rate of the "MidPlane" Frame of reference -->
    <source id="Frame_rotation_euler_Z-output">
      <float_array id="Frame_rotation_euler_Z-output-array" count="31">
  1803.0
  1743.0
  1683.0
  1623.0
  1563.0
  1503.0
  1443.0
  1383.0
  1323.0
  1263.0
  1203.0
  1143.0
  1083.0
  1023.0
   963.0
   903.0
   843.0
   783.0
   723.0
   663.0
   603.0
   543.0
   483.0
   423.0
   363.0
   303.0
   243.0
   183.0
   123.0
    63.0
     3.0
      </float_array>
      <technique_common>
          <accessor source="#Frame_rotation_euler_Z-output-array" count="31" stride="1">
            <param name="ANGLE" type="float"/>
          </accessor>
      </technique_common>
    </source>
    <sampler id="First_rotation_euler_Z-sampler">
      <input semantic="INPUT" source="#First_rotation_euler_Z-input"/>
      <input semantic="OUTPUT" source="#First_rotation_euler_Z-output"/>
    </sampler>
    <sampler id="Frame_rotation_euler_Z-sampler">
      <input semantic="INPUT" source="#First_rotation_euler_Z-input"/>
      <input semantic="OUTPUT" source="#Frame_rotation_euler_Z-output"/>
    </sampler>
    <channel source="#First_rotation_euler_Z-sampler" target="EntireEllipsoid/rotationZ.ANGLE"/>
    <channel source="#Frame_rotation_euler_Z-sampler" target="Inertial/rotationZ.ANGLE"/>
  </animation>
<!-- FLUID ELEMENT 1 -->
  <animation id="FluidElement1_location">
    <source id="Lagrange1_location_X-input">
      <float_array id="Lagrange1_location_X-input-array" count="   37">
  0.0000
  1.0014
  2.0029
  3.0043
  4.0057
  5.0071
  6.0086
  7.0100
  8.0114
  9.0129
 10.0143
 11.0157
 12.0171
 13.0186
 14.0200
 15.0214
 16.0229
 17.0243
 18.0257
 19.0271
 20.0286
 21.0300
 22.0314
 23.0329
 24.0343
 25.0357
 26.0371
 27.0386
 28.0400
 29.0414
 30.0429
 31.0443
 32.0457
 33.0472
 34.0486
 35.0500
 36.0514
      </float_array>
      <technique_common>
          <accessor source="#Lagrange1_location_X-input-array" count="   37" stride="1">
            <param name="TIME" type="float"/>
          </accessor>
      </technique_common>
    </source>
    <source id="Lagrange1_location_X-output">
      <float_array id="Lagrange1_location_X-output-array" count="   37">
  1.0000
  0.9921
  0.9686
  0.9298
  0.8763
  0.8090
  0.7290
  0.6374
  0.5358
  0.4258
  0.3090
  0.1874
  0.0628
 -0.0628
 -0.1874
 -0.3090
 -0.4258
 -0.5358
 -0.6374
 -0.7290
 -0.8090
 -0.8763
 -0.9298
 -0.9686
 -0.9921
 -1.0000
 -0.9921
 -0.9686
 -0.9298
 -0.8763
 -0.8090
 -0.7290
 -0.6374
 -0.5358
 -0.4258
 -0.3090
 -0.1874
      </float_array>
      <technique_common>
          <accessor source="#Lagrange1_location_X-output-array" count="   37" stride="1">
            <param name="X" type="float"/>
          </accessor>
      </technique_common>
    </source>
    <sampler id="Lagrange1_location_X-sampler">
      <input semantic="INPUT" source="#Lagrange1_location_X-input"/>
      <input semantic="OUTPUT" source="#Lagrange1_location_X-output"/>
    </sampler>
    <source id="Lagrange1_location_Y-output">
      <float_array id="Lagrange1_location_Y-output-array" count="   37">
 -0.0000
 -0.0514
 -0.1020
 -0.1509
 -0.1975
 -0.2410
 -0.2807
 -0.3159
 -0.3462
 -0.3710
 -0.3899
 -0.4027
 -0.4092
 -0.4092
 -0.4027
 -0.3899
 -0.3710
 -0.3462
 -0.3159
 -0.2807
 -0.2410
 -0.1975
 -0.1509
 -0.1020
 -0.0514
  0.0000
  0.0514
  0.1020
  0.1509
  0.1975
  0.2410
  0.2807
  0.3159
  0.3462
  0.3710
  0.3899
  0.4027
      </float_array>
      <technique_common>
          <accessor source="#Lagrange1_location_Y-output-array" count="   37" stride="1">
            <param name="Y" type="float"/>
          </accessor>
      </technique_common>
    </source>
    <sampler id="Lagrange1_location_Y-sampler">
      <input semantic="INPUT" source="#Lagrange1_location_X-input"/>
      <input semantic="OUTPUT" source="#Lagrange1_location_Y-output"/>
    </sampler>
    <channel source="#Lagrange1_location_X-sampler" target="Lagrange01/location.X"/>
    <channel source="#Lagrange1_location_Y-sampler" target="Lagrange01/location.Y"/>
    <channel source="#Lagrange1_location_X-sampler" target="Lagrange02/location.X"/>
    <channel source="#Lagrange1_location_Y-sampler" target="Lagrange02/location.Y"/>
    <channel source="#Lagrange1_location_X-sampler" target="Lagrange03/location.X"/>
    <channel source="#Lagrange1_location_Y-sampler" target="Lagrange03/location.Y"/>
</animation>
<!-- CLOCK (clockstop = 36.5047) 
     One spin of ellipsoid (or frame) is 1.8252 EFE sqrt(pi * G * rho) units;
     Want 1 EFE unit to take 4.0 seconds of TIME;
     Hence, one spin of ellipsoid (360 degrees) is 7.3009 seconds of TIME;
            and 5 ellipsoid spins is 36.5047 seconds of TIME.
     Divide one spin (360) into 12 pieces 
     ==> 30 degrees = 1 timestep = 4 x 0.1521 = 0.6084 seconds of TIME.
-->
  <animation id="Cube_quaternion_Z">
    <source id="Cube_quaternion_Z-input">
      <float_array id="Cube_quaternion_Z-input-array" count=" 147">
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    36.00 36.25 36.50 
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   0.000  0.000 -1.00  0.00   0.3827  0.9239  0.000  0.000   0.9239 -0.3827  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.0000  1.0000  0.000  0.000   1.0000  0.0000  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.3827  0.9239  0.000  0.000   0.9239  0.3827  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.7071  0.7071  0.000  0.000   0.7071  0.7071  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.9239  0.3827  0.000  0.000   0.3827  0.9239  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -1.0000  0.0000  0.000  0.000   0.0000  1.0000  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.9239 -0.3827  0.000  0.000  -0.3827  0.9239  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.7071 -0.7071  0.000  0.000  -0.7071  0.7071  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.3827 -0.9239  0.000  0.000  -0.9239  0.3827  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.0000 -1.0000  0.000  0.000  -1.0000  0.0000  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.3827 -0.9239  0.000  0.000  -0.9239 -0.3827  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.7071 -0.7071  0.000  0.000  -0.7071 -0.7071  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.9239 -0.3827  0.000  0.000  -0.3827 -0.9239  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   1.0000  0.0000  0.000  0.000   0.0000 -1.0000  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.9239  0.3827  0.000  0.000   0.3827 -0.9239  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.7071  0.7071  0.000  0.000   0.7071 -0.7071  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.3827  0.9239  0.000  0.000   0.9239 -0.3827  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.0000  1.0000  0.000  0.000   1.0000  0.0000  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.3827  0.9239  0.000  0.000   0.9239  0.3827  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.7071  0.7071  0.000  0.000   0.7071  0.7071  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.9239  0.3827  0.000  0.000   0.3827  0.9239  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -1.0000  0.0000  0.000  0.000   0.0000  1.0000  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.9239 -0.3827  0.000  0.000  -0.3827  0.9239  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.7071 -0.7071  0.000  0.000  -0.7071  0.7071  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.3827 -0.9239  0.000  0.000  -0.9239  0.3827  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.0000 -1.0000  0.000  0.000  -1.0000  0.0000  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.3827 -0.9239  0.000  0.000  -0.9239 -0.3827  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.7071 -0.7071  0.000  0.000  -0.7071 -0.7071  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.9239 -0.3827  0.000  0.000  -0.3827 -0.9239  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   1.0000  0.0000  0.000  0.000   0.0000 -1.0000  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.9239  0.3827  0.000  0.000   0.3827 -0.9239  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.7071  0.7071  0.000  0.000   0.7071 -0.7071  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.3827  0.9239  0.000  0.000   0.9239 -0.3827  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.0000  1.0000  0.000  0.000   1.0000  0.0000  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.3827  0.9239  0.000  0.000   0.9239  0.3827  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.7071  0.7071  0.000  0.000   0.7071  0.7071  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.9239  0.3827  0.000  0.000   0.3827  0.9239  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -1.0000  0.0000  0.000  0.000   0.0000  1.0000  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.9239 -0.3827  0.000  0.000  -0.3827  0.9239  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.7071 -0.7071  0.000  0.000  -0.7071  0.7071  0.000  0.00   0.000  0.000  0.000  1.000
      </float_array>
      <technique_common>
          <accessor source="#Cube_quaternion_Z-output-array" count="  147" stride="16">
            <param name="TRANSFORM" type="float4x4"/>
          </accessor>
      </technique_common>
    </source>
    <sampler id="Cube_quaternion_Z-sampler">
      <input semantic="INPUT" source="#Cube_quaternion_Z-input"/>
      <input semantic="OUTPUT" source="#Cube_quaternion_Z-output"/>
    </sampler>
    <channel source="#Cube_quaternion_Z-sampler" target="Jetman/transformation"/>
  </animation>
<!-- HOURHAND (clockstop =    36.5047) -->
  <animation id="HourHand_euler_Z">
    <source id="HourHand_euler_Z-input">
      <float_array id="HourHand_euler_Z-input-array" count="  147">
     0.00  0.25  0.50  0.75  1.00  1.25  1.50  1.75  2.00  2.25  2.50  2.75  3.00  3.25  3.50  3.75
     4.00  4.25  4.50  4.75  5.00  5.25  5.50  5.75  6.00  6.25  6.50  6.75  7.00  7.25  7.50  7.75
     8.00  8.25  8.50  8.75  9.00  9.25  9.50  9.75 10.00 10.25 10.50 10.75 11.00 11.25 11.50 11.75
    12.00 12.25 12.50 12.75 13.00 13.25 13.50 13.75 14.00 14.25 14.50 14.75 15.00 15.25 15.50 15.75
    16.00 16.25 16.50 16.75 17.00 17.25 17.50 17.75 18.00 18.25 18.50 18.75 19.00 19.25 19.50 19.75
    20.00 20.25 20.50 20.75 21.00 21.25 21.50 21.75 22.00 22.25 22.50 22.75 23.00 23.25 23.50 23.75
    24.00 24.25 24.50 24.75 25.00 25.25 25.50 25.75 26.00 26.25 26.50 26.75 27.00 27.25 27.50 27.75
    28.00 28.25 28.50 28.75 29.00 29.25 29.50 29.75 30.00 30.25 30.50 30.75 31.00 31.25 31.50 31.75
    32.00 32.25 32.50 32.75 33.00 33.25 33.50 33.75 34.00 34.25 34.50 34.75 35.00 35.25 35.50 35.75
    36.00 36.25 36.50 
      </float_array>
      <technique_common>
          <accessor source="#HourHand_euler_Z-input-array" count="  147" stride="1">
            <param name="TIME" type="float"/>
          </accessor>
      </technique_common>
    </source>
    <source id="HourHand_euler_Z-output">
      <float_array id="HourHand_euler_Z-output-array" count="  147">
  270.0
  268.125
  266.25
  264.375
  262.5
  260.625
  258.75
  256.875
  255.0
  253.125
  251.25
  249.375
  247.5
  245.625
  243.75
  241.875
  240.0
  238.125
  236.25
  234.375
  232.5
  230.625
  228.75
  226.875
  225.0
  223.125
  221.25
  219.375
  217.5
  215.625
  213.75
  211.875
  210.0
  208.125
  206.25
  204.375
  202.5
  200.625
  198.75
  196.875
  195.0
  193.125
  191.25
  189.375
  187.5
  185.625
  183.75
  181.875
  180.0
  178.125
  176.25
  174.375
  172.5
  170.625
  168.75
  166.875
  165.0
  163.125
  161.25
  159.375
  157.5
  155.625
  153.75
  151.875
  150.0
  148.125
  146.25
  144.375
  142.5
  140.625
  138.75
  136.875
  135.0
  133.125
  131.25
  129.375
  127.5
  125.625
  123.75
  121.875
  120.0
  118.125
  116.25
  114.375
  112.5
  110.625
  108.75
  106.875
  105.0
  103.125
  101.25
   99.375
   97.5
   95.625
   93.75
   91.875
   90.0
   88.125
   86.25
   84.375
   82.5
   80.625
   78.75
   76.875
   75.0
   73.125
   71.25
   69.375
   67.5
   65.625
   63.75
   61.875
   60.0
   58.125
   56.25
   54.375
   52.5
   50.625
   48.75
   46.875
   45.0
   43.125
   41.25
   39.375
   37.5
   35.625
   33.75
   31.875
   30.0
   28.125
   26.25
   24.375
   22.5
   20.625
   18.75
   16.875
   15.0
   13.125
   11.25
    9.375
    7.5
    5.625
    3.75
    1.875
    0.0
   -1.875
   -3.75
      </float_array>
      <technique_common>
          <accessor source="#HourHand_euler_Z-output-array" count="   147" stride="1">
            <param name="ANGLE" type="float"/>
          </accessor>
      </technique_common>
    </source>
    <sampler id="HourHand_euler_Z-sampler">
      <input semantic="INPUT" source="#HourHand_euler_Z-input"/>
      <input semantic="OUTPUT" source="#HourHand_euler_Z-output"/>
    </sampler>
    <channel source="#HourHand_euler_Z-sampler" target="HourHand/rotationZ.ANGLE"/>
  </animation>
    </library_animations>
    <library_controllers/>
    <library_visual_scenes>
        <visual_scene id="ID1">
            <node id="EntireEllipsoid" name="OculusRift_EFE">
             <translate>0.0 0.0 0.0</translate>
             <rotate sid="rotationX">1.0 0.0 0.0  0.0</rotate>
             <rotate sid="rotationY">0.0 1.0 0.0  0.0</rotate>
             <rotate sid="rotationZ">0.0 0.0 1.0  5.0</rotate>
             <scale sid="scale">5.0 5.0 5.0</scale>
                <node id="First" name="First_instance_EFE">
                  <translate>0.0 0.0 0.0</translate>
                  <rotate sid="rotationX">1.0 0.0 0.0  0.0</rotate>
                  <rotate sid="rotationY">0.0 1.0 0.0  0.0</rotate>
                  <rotate sid="rotationZ">0.0 0.0 1.0  0.0</rotate>
                  <scale sid="scale">1.0 1.0 1.0</scale>
                  <instance_node url="#ID3_EFE" />
                </node>
                <node id="Second" name="Second_instance_EFE">
                  <translate>0.0 0.0 0.0</translate>
                  <rotate sid="rotationX">1.0 0.0 0.0  180.0</rotate>
                  <rotate sid="rotationY">0.0 1.0 0.0    0.0</rotate>
                  <rotate sid="rotationZ">0.0 0.0 1.0    0.0</rotate>
                  <scale sid="scale">1.0 1.0 1.0</scale>
                  <instance_node url="#ID3_EFE" />
                </node>
                <node id="Third" name="Third_instance_EFE">
                  <translate>0.0 0.0 0.0</translate>
                  <rotate sid="rotationX">1.0 0.0 0.0    0.0</rotate>
                  <rotate sid="rotationY">0.0 1.0 0.0  180.0</rotate>
                  <rotate sid="rotationZ">0.0 0.0 1.0    0.0</rotate>
                  <scale sid="scale">1.0 1.0 1.0</scale>
                  <instance_node url="#ID3_EFE" />
                </node>
                <node id="Fourth" name="Fourth_instance_EFE">
                  <translate>0.0 0.0 0.0</translate>
                  <rotate sid="rotationX">1.0 0.0 0.0  180.0</rotate>
                  <rotate sid="rotationY">0.0 1.0 0.0  180.0</rotate>
                  <rotate sid="rotationZ">0.0 0.0 1.0    0.0</rotate>
                  <scale sid="scale">1.0 1.0 1.0</scale>
                  <instance_node url="#ID3_EFE" />
                </node>
<!-- instance:  Cylindrical Pointer -->
                <node id="CylinderPointer" name="instance_cylinder">  
                  <translate sid="location">-1.0 0.0 0.0</translate>
                    <rotate sid="rotationX">1 0 0 0</rotate>
                    <rotate sid="rotationY">0 1 0 0</rotate>
                    <rotate sid="rotationZ">0 0 1 180</rotate>
                  <scale sid="scale">0.05 0.025 0.025</scale>
                  <instance_node url="#CylPointer" />
                </node>                                         
<!-- Begin LAGRANGE markers -->
              <node id="Lagrange01" name="instance_Lagrange01">
                  <translate sid="location">1.0000 0.0000 0.0</translate>
                  <rotate sid="rotationX">1.0 0.0 0.0  0.0</rotate>
                  <rotate sid="rotationY">0.0 1.0 0.0  0.0</rotate>
                  <rotate sid="rotationZ">0.0 0.0 1.0  0.0</rotate>
                  <scale sid="scale">0.06 0.06 0.06</scale>
                <instance_node url="#Primary_MarkerID3" />
              </node>
            <node id="Shrink02" name="instance_Shrink02">
              <scale sid="scale">0.8 0.8 0.8</scale>
              <node id="Lagrange02" name="instance_Lagrange02">
                  <translate sid="location">1.0000 0.0000 0.0</translate>
                  <rotate sid="rotationX">1.0 0.0 0.0  0.0</rotate>
                  <rotate sid="rotationY">0.0 1.0 0.0  0.0</rotate>
                  <rotate sid="rotationZ">0.0 0.0 1.0  0.0</rotate>
                  <scale sid="scale">0.075 0.075 0.075</scale>
                <instance_node url="#Primary_MarkerID3" />
              </node>
            </node>
            <node id="Shrink03" name="instance_Shrink03">
              <scale sid="scale">0.6 0.6 0.6</scale>
              <node id="Lagrange03" name="instance_Lagrange03">
                  <translate sid="location">1.0000 0.0000 0.0</translate>
                  <rotate sid="rotationX">1.0 0.0 0.0  0.0</rotate>
                  <rotate sid="rotationY">0.0 1.0 0.0  0.0</rotate>
                  <rotate sid="rotationZ">0.0 0.0 1.0  0.0</rotate>
                  <scale sid="scale">0.1 0.1 0.1</scale>
                <instance_node url="#Primary_MarkerID3" />
              </node>
            </node>
              <node id="Marker01" name="instance_marker01">
                <matrix>0.025 0.0 0.0 1.0000  0.0 0.025 0.0 -0.0000  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker02" name="instance_marker02">
                <matrix>0.025 0.0 0.0 0.9921  0.0 0.025 0.0 -0.0514  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker03" name="instance_marker03">
                <matrix>0.025 0.0 0.0 0.9686  0.0 0.025 0.0 -0.1020  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker04" name="instance_marker04">
                <matrix>0.025 0.0 0.0 0.9298  0.0 0.025 0.0 -0.1509  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker05" name="instance_marker05">
                <matrix>0.025 0.0 0.0 0.8763  0.0 0.025 0.0 -0.1975  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker06" name="instance_marker06">
                <matrix>0.025 0.0 0.0 0.8090  0.0 0.025 0.0 -0.2410  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker07" name="instance_marker07">
                <matrix>0.025 0.0 0.0 0.7290  0.0 0.025 0.0 -0.2807  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker08" name="instance_marker08">
                <matrix>0.025 0.0 0.0 0.6374  0.0 0.025 0.0 -0.3159  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker09" name="instance_marker09">
                <matrix>0.025 0.0 0.0 0.5358  0.0 0.025 0.0 -0.3462  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker10" name="instance_marker10">
                <matrix>0.025 0.0 0.0 0.4258  0.0 0.025 0.0 -0.3710  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker11" name="instance_marker11">
                <matrix>0.025 0.0 0.0 0.3090  0.0 0.025 0.0 -0.3899  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker12" name="instance_marker12">
                <matrix>0.025 0.0 0.0 0.1874  0.0 0.025 0.0 -0.4027  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker13" name="instance_marker13">
                <matrix>0.025 0.0 0.0 0.0628  0.0 0.025 0.0 -0.4092  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker14" name="instance_marker14">
                <matrix>0.025 0.0 0.0 -0.0628  0.0 0.025 0.0 -0.4092  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker15" name="instance_marker15">
                <matrix>0.025 0.0 0.0 -0.1874  0.0 0.025 0.0 -0.4027  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker16" name="instance_marker16">
                <matrix>0.025 0.0 0.0 -0.3090  0.0 0.025 0.0 -0.3899  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker17" name="instance_marker17">
                <matrix>0.025 0.0 0.0 -0.4258  0.0 0.025 0.0 -0.3710  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker18" name="instance_marker18">
                <matrix>0.025 0.0 0.0 -0.5358  0.0 0.025 0.0 -0.3462  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker19" name="instance_marker19">
                <matrix>0.025 0.0 0.0 -0.6374  0.0 0.025 0.0 -0.3159  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker20" name="instance_marker20">
                <matrix>0.025 0.0 0.0 -0.7290  0.0 0.025 0.0 -0.2807  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker21" name="instance_marker21">
                <matrix>0.025 0.0 0.0 -0.8090  0.0 0.025 0.0 -0.2410  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker22" name="instance_marker22">
                <matrix>0.025 0.0 0.0 -0.8763  0.0 0.025 0.0 -0.1975  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker23" name="instance_marker23">
                <matrix>0.025 0.0 0.0 -0.9298  0.0 0.025 0.0 -0.1509  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker24" name="instance_marker24">
                <matrix>0.025 0.0 0.0 -0.9686  0.0 0.025 0.0 -0.1020  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker25" name="instance_marker25">
                <matrix>0.025 0.0 0.0 -0.9921  0.0 0.025 0.0 -0.0514  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker26" name="instance_marker26">
                <matrix>0.025 0.0 0.0 -1.0000  0.0 0.025 0.0 -0.0000  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
<!-- Second Half -->
              <node id="Marker28" name="instance_marker28">
                <matrix>0.025 0.0 0.0 -0.9921  0.0 0.025 0.0 0.0514  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker29" name="instance_marker29">
                <matrix>0.025 0.0 0.0 -0.9686  0.0 0.025 0.0 0.1020  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker30" name="instance_marker30">
                <matrix>0.025 0.0 0.0 -0.9298  0.0 0.025 0.0 0.1509  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker31" name="instance_marker31">
                <matrix>0.025 0.0 0.0 -0.8763  0.0 0.025 0.0 0.1975  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker32" name="instance_marker32">
                <matrix>0.025 0.0 0.0 -0.8090  0.0 0.025 0.0 0.2410  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker33" name="instance_marker33">
                <matrix>0.025 0.0 0.0 -0.7290  0.0 0.025 0.0 0.2807  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker34" name="instance_marker34">
                <matrix>0.025 0.0 0.0 -0.6374  0.0 0.025 0.0 0.3159  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker35" name="instance_marker35">
                <matrix>0.025 0.0 0.0 -0.5358  0.0 0.025 0.0 0.3462  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker36" name="instance_marker36">
                <matrix>0.025 0.0 0.0 -0.4258  0.0 0.025 0.0 0.3710  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker37" name="instance_marker37">
                <matrix>0.025 0.0 0.0 -0.3090  0.0 0.025 0.0 0.3899  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker38" name="instance_marker38">
                <matrix>0.025 0.0 0.0 -0.1874  0.0 0.025 0.0 0.4027  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker39" name="instance_marker39">
                <matrix>0.025 0.0 0.0 -0.0628  0.0 0.025 0.0 0.4092  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker40" name="instance_marker40">
                <matrix>0.025 0.0 0.0 0.0628  0.0 0.025 0.0 0.4092  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker41" name="instance_marker41">
                <matrix>0.025 0.0 0.0 0.1874  0.0 0.025 0.0 0.4027  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker42" name="instance_marker42">
                <matrix>0.025 0.0 0.0 0.3090  0.0 0.025 0.0 0.3899  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker43" name="instance_marker43">
                <matrix>0.025 0.0 0.0 0.4258  0.0 0.025 0.0 0.3710  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker44" name="instance_marker44">
                <matrix>0.025 0.0 0.0 0.5358  0.0 0.025 0.0 0.3462  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker45" name="instance_marker45">
                <matrix>0.025 0.0 0.0 0.6374  0.0 0.025 0.0 0.3159  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker46" name="instance_marker46">
                <matrix>0.025 0.0 0.0 0.7290  0.0 0.025 0.0 0.2807  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker47" name="instance_marker47">
                <matrix>0.025 0.0 0.0 0.8090  0.0 0.025 0.0 0.2410  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker48" name="instance_marker48">
                <matrix>0.025 0.0 0.0 0.8763  0.0 0.025 0.0 0.1975  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker49" name="instance_marker49">
                <matrix>0.025 0.0 0.0 0.9298  0.0 0.025 0.0 0.1509  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker50" name="instance_marker50">
                <matrix>0.025 0.0 0.0 0.9686  0.0 0.025 0.0 0.1020  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker51" name="instance_marker51">
                <matrix>0.025 0.0 0.0 0.9921  0.0 0.025 0.0 0.0514  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
<!-- End LAGRANGE markers -->
            </node>                           <!-- END EntireEllipsoid -->
          <node id="Inertial" name="instance_inertial">  <!-- Start Inertial Grouping of Objects -->
            <translate>0.0 0.0 0.0</translate>
            <rotate sid="rotationX">1.0 0.0 0.0  0.0</rotate>
            <rotate sid="rotationY">0.0 1.0 0.0  0.0</rotate>
            <rotate sid="rotationZ">0.0 0.0 1.0  1803.0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
            <node id="Zup_Pointer" name="instance_zupPointer">  
              <translate>0.0 0.0 5.0</translate>
                <rotate sid="rotationX">1 0 0  0.0</rotate>
                <rotate sid="rotationY">0 1 0  0.0</rotate>
                <rotate sid="rotationZ">0 0 1  0.0</rotate>
              <scale sid="scale">0.125 0.5 1.5</scale>
              <instance_node url="#ZupPointer" />
            </node>                                         
<!-- instance:  MidPlane Frame (MidPlane flips with rotationX = 180 for clockwise spin)-->
            <node id="MidPlane" name="instance_MidPlane">  
              <translate>0.0 0.0 0.0</translate>
                  <rotate sid="rotationX">1.0 0.0 0.0  0.0</rotate>
                  <rotate sid="rotationY">0.0 1.0 0.0  0.0</rotate>
                  <rotate sid="rotationZ">0.0 0.0 1.0  0.0</rotate>
              <scale sid="scale">1.25 1.25 1.25</scale>
              <instance_node url="#EqPlane" />
            </node> 
<!-- BEGIN LABELING HERE -->
          <node name="Labels">
          <translate>7.0 -2.0 5.0</translate>
          <rotate sid="rotationX">1 0 0 0.0</rotate>
          <rotate sid="rotationY">0 1 0 0</rotate>
          <rotate sid="rotationZ">0 0 1 180</rotate>
          <scale sid="scale">0.1 0.1 0.1</scale>
<!--  Equals sign #1  -->
            <node name="Equals1">
            <translate>0.0 15.0 1.0</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
                <node id="IDd51" name="instance_51">
                    <matrix>0.25  0 0 0.0   0 1  0 0.0  0 0 1 2.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDd52" name="instance_52">
                    <matrix>0.25  0 0 0.0   0 1  0 1.1  0 0 1 2.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDd53" name="instance_53">
                    <matrix>0.25  0 0 0.0   0 1  0 2.2  0 0 1 2.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDd55" name="instance_55">
                    <matrix>0.25  0 0 0.0   0 1  0 0.0  0 0 1 4.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDd56" name="instance_56">
                    <matrix>0.25  0 0 0.0   0 1  0 1.1  0 0 1 4.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDd57" name="instance_57">
                    <matrix>0.25  0 0 0.0   0 1  0 2.2  0 0 1 4.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
            </node>
<!--  Equals sign #2  -->
            <node name="Equals2">
            <translate>0.0 15.0 -8.5</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
                <node id="IDd51" name="instance_51">
                    <matrix>0.25  0 0 0.0   0 1  0 0.0  0 0 1 2.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDd52" name="instance_52">
                    <matrix>0.25  0 0 0.0   0 1  0 1.1  0 0 1 2.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDd53" name="instance_53">
                    <matrix>0.25  0 0 0.0   0 1  0 2.2  0 0 1 2.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDd55" name="instance_55">
                    <matrix>0.25  0 0 0.0   0 1  0 0.0  0 0 1 4.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDd56" name="instance_56">
                    <matrix>0.25  0 0 0.0   0 1  0 1.1  0 0 1 4.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDd57" name="instance_57">
                    <matrix>0.25  0 0 0.0   0 1  0 2.2  0 0 1 4.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
          </node>
<!--  Division sign #1  -->
            <node name="Divide1">
            <translate>0.0 4.4 1.0</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 0.75 1.0</scale>
                <node id="IDd21" name="instance_21">
                    <matrix>0.25  0 0 0.0   0 1  0 0.0  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
                <node id="IDd22" name="instance_22">
                    <matrix>0.25  0 0 0.0   0 -1  0 1.1  0 0 -1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
                <node id="IDd23" name="instance_23">
                    <matrix>0.25  0 0 0.0   0 1  0 1.1  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
                <node id="IDd24" name="instance_24">
                    <matrix>0.25  0 0 0.0   0 -1  0 2.2  0 0 -1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
                <node id="IDd25" name="instance_25">
                    <matrix>0.25  0 0 0.0   0 1  0 2.2  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
                <node id="IDd26" name="instance_26">
                    <matrix>0.25  0 0 0.0   0 -1  0 3.3  0 0 -1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
                <node id="IDd27" name="instance_27">
                    <matrix>0.25  0 0 0.0   0 1  0 3.3  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
            </node>
<!--  Division sign #2  -->
            <node name="Divide2">
            <translate>0.0 4.4 -8.5</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 0.75 1.0</scale>
                <node id="IDd21" name="instance_21">
                    <matrix>0.25  0 0 0.0   0 1  0 0.0  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
                <node id="IDd22" name="instance_22">
                    <matrix>0.25  0 0 0.0   0 -1  0 1.1  0 0 -1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
                <node id="IDd23" name="instance_23">
                    <matrix>0.25  0 0 0.0   0 1  0 1.1  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
                <node id="IDd24" name="instance_24">
                    <matrix>0.25  0 0 0.0   0 -1  0 2.2  0 0 -1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
                <node id="IDd25" name="instance_25">
                    <matrix>0.25  0 0 0.0   0 1  0 2.2  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
                <node id="IDd26" name="instance_26">
                    <matrix>0.25  0 0 0.0   0 -1  0 3.3  0 0 -1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
                <node id="IDd27" name="instance_27">
                    <matrix>0.25  0 0 0.0   0 1  0 3.3  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
            </node>
<!--  Letter "a" #1  -->
            <node name="Letter_a1">
            <translate>0.0 8.0 1.0</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
                <node id="IDa01" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa06" name="instance_6">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa07" name="instance_7">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa10" name="instance_10">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa11" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa18" name="instance_18">
                    <matrix>0.25  0 0 0.0  0 1 0 0.0  0 0  1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDa19" name="instance_19">
                    <matrix>0.25  0 0 0.0  0 0 1 4.4  0 -1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDa19" name="instance_19">
                    <matrix>0.25  0 0 0.0  0 0 -1 3.3  0 1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDa11" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa31" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa20" name="instance_20">
                    <matrix>0.25  0 0 0.0   0 0 1 3.3  0 -1 0 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDa21" name="instance_21">
                    <matrix>0.25  0 0 0.0   0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
            </node>
<!--  Letter "a" #2  -->
            <node name="Letter_a2">
            <translate>0.0 8.0 -8.5</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
                <node id="IDa01" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa06" name="instance_6">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa07" name="instance_7">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa10" name="instance_10">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa11" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa18" name="instance_18">
                    <matrix>0.25  0 0 0.0  0 1 0 0.0  0 0  1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDa19" name="instance_19">
                    <matrix>0.25  0 0 0.0  0 0 1 4.4  0 -1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDa19" name="instance_19">
                    <matrix>0.25  0 0 0.0  0 0 -1 3.3  0 1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDa11" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa31" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa20" name="instance_20">
                    <matrix>0.25  0 0 0.0   0 0 1 3.3  0 -1 0 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDa21" name="instance_21">
                    <matrix>0.25  0 0 0.0   0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
            </node>
<!--  Letter "a" #2  -->
            <node name="Letter_a2">
            <translate>0.0 8.0 -8.5</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
                <node id="IDa01" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa06" name="instance_6">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa07" name="instance_7">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa10" name="instance_10">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa11" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa18" name="instance_18">
                    <matrix>0.25  0 0 0.0  0 1 0 0.0  0 0  1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDa19" name="instance_19">
                    <matrix>0.25  0 0 0.0  0 0 1 4.4  0 -1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDa19" name="instance_19">
                    <matrix>0.25  0 0 0.0  0 0 -1 3.3  0 1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDa11" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa31" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa20" name="instance_20">
                    <matrix>0.25  0 0 0.0   0 0 1 3.3  0 -1 0 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDa21" name="instance_21">
                    <matrix>0.25  0 0 0.0   0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
            </node>
<!--  Letter "c"  -->
            <node name="Letter_c">
            <translate>0.0 0.0 -8.5</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
                <node id="ID001" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID002" name="instance_2">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID006" name="instance_6">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID007" name="instance_7">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID010" name="instance_10">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID011" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID018" name="instance_18">
                    <matrix>0.25  0 0 0.0  0 1 0 0.0  0 0  1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="ID019" name="instance_19">
                    <matrix>0.25  0 0 0.0  0 -1 0 3.3  0 0  -1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="ID020" name="instance_20">
                    <matrix>0.25  0 0 0.0   0 0 1 3.3  0 -1 0 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="ID021" name="instance_21">
                    <matrix>0.25  0 0 0.0   0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
            </node>
<!--  Letter "b"  ... has 8 + (4 x 15) = 68 lines -->
            <node name="Letter_b">
            <translate>0.0 0.0 1.0</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
                <node id="IDb01" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb02" name="instance_2">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb03" name="instance_3">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb04" name="instance_4">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 4.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb05" name="instance_5">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 5.5  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb12" name="instance_12">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb06" name="instance_6">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb07" name="instance_7">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb08" name="instance_8">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb09" name="instance_9">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb10" name="instance_10">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb11" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb19" name="instance_19">
                    <matrix>0.25  0 0 0.0  0 -1 0 3.3  0 0  -1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDb20" name="instance_20">
                    <matrix>0.25  0 0 0.0   0 0 1 3.3  0 -1 0 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDb21" name="instance_21">
                    <matrix>0.25  0 0 0.0   0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
            </node>
<!-- DECIMAL POINTS -->
                <node id="IDD01" name="Decimal_1">
                    <matrix>0.25 0 0 0.0  0 1 0 25.0  0 0 1 1.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDD02" name="Decimal_2">
                    <matrix>0.25 0 0 0.0  0 1 0 25.0  0 0 1 -8.5  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
<!--  Number "0" #1  ... has 8 + (4 x 18) = 80 lines -->
            <node name="Number_0">
            <translate>0.0 20.0 1.0</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
                <node id="IDb01" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb02" name="instance_2">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb03" name="instance_3">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb04" name="instance_4">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 4.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb05" name="instance_5">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 5.5  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDz19" name="instance_z19">
                    <matrix>0.25  0 0 0.0  0 1 0 0.0  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDb06" name="instance_6">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb07" name="instance_7">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb08" name="instance_8">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb09" name="instance_9">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb10" name="instance_10">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb11" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb19" name="instance_19">
                    <matrix>0.25  0 0 0.0  0 -1 0 3.3  0 0  -1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDb20" name="instance_20">
                    <matrix>0.25  0 0 0.0   0 0 1 3.3  0 -1 0 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDb21" name="instance_21">
                    <matrix>0.25  0 0 0.0   0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDz11" name="instance_z11">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDz12" name="instance_z12">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 4.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDz13" name="instance_z13">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 5.5  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
            </node>
<!--  Number "0" #2  ... has 8 + (4 x 18) = 80 lines -->
            <node name="Number_0b">
            <translate>0.0 20.0 -8.5</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
                <node id="IDb01" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb02" name="instance_2">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb03" name="instance_3">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb04" name="instance_4">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 4.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb05" name="instance_5">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 5.5  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDz19" name="instance_z19">
                    <matrix>0.25  0 0 0.0  0 1 0 0.0  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDb06" name="instance_6">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb07" name="instance_7">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb08" name="instance_8">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb09" name="instance_9">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb10" name="instance_10">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb11" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb19" name="instance_19">
                    <matrix>0.25  0 0 0.0  0 -1 0 3.3  0 0  -1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDb20" name="instance_20">
                    <matrix>0.25  0 0 0.0   0 0 1 3.3  0 -1 0 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDb21" name="instance_21">
                    <matrix>0.25  0 0 0.0   0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDz11" name="instance_z11">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDz12" name="instance_z12">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 4.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDz13" name="instance_z13">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 5.5  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
            </node>
<!--  Number "1" ... has 8 + (4 x 8) = 40 lines -->
<!--  Number "2" #1 ... has 8 + (4 x 17) = 76 lines -->
<!--  Number "2" #2 ... has 8 + (4 x 17) = 76 lines -->
<!--  Number "3"  ... has 8 + (4 x 18) = 80 lines -->
<!--  Number "4" ... has 8 + (4 x 13) = 60 lines -->
<!--  Number "5"  ... has 8 + (4 x 17) = 76 lines -->
<!--  Number "6" ... has 8 + (4 x 18) = 80 lines -->
<!--  Number "7" ... has 8 + (4 x 14) = 64 lines -->
<!--  Number "8" ... has 8 + (4 x 22) = 96 lines -->
<!--  Number "9"  ... has 8 + (4 x 15) = 68 lines -->
<!-- bovera_Digit1 is "4" -->
            <node name="bovera_Digit1">
            <translate>0.0 26.8 1.0</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
<!--  Number "4" ... has 8 + (4 x 13) = 60 lines -->
                <node id="IDe01" name="instance_e01">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDe02" name="instance_e02">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDe02" name="instance_e02">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb04" name="instance_4">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 4.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb05" name="instance_5">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 5.5  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb06" name="instance_6">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb08" name="instance_8">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb09" name="instance_9">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDn09" name="instance_9">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDf12" name="instance_n12">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDn12" name="instance_n12">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDz12" name="instance_z12">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 4.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDz13" name="instance_z13">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 5.5  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
            </node>
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Inside the Oculus Rift S Environment

Introduction

The Oculus Rift S will import user-constructed 3D objects and allow you to place those objects in a high-quality, interactive virtual reality (VR) environment. But the Oculus system does not accept COLLADA-formatted files directly. Instead, it is set up to import files that are in a ".glb" format, which is the binary version of a "GL Transmission Format" (glTF) file. My original expectation was that, after I learned how to construct some intricate and astrophysically interesting 3D visual scenes using COLLADA — successfully accomplished (!) as illustrated above — all I would need to do is find a community tool that could translate a COLLADA (.dae) file into glTF (.glb).

Here are a few discoveries I made along the way:

  • The Windows 10 startup menu includes a "3D Viewer" app but, at least on my Lenova PC, it does not recognize .dae-formatted files.
  • The Windows 10 startup menu includes a "Paint 3D" application. Using this app, it was very easy to "draw" some simple 3D geometric objects — such as a cube or a torus — and it was straightforward to export each object to a .glb-formatted file.
  • Adobe Photoshop can read in a COLLADA (.dae) file and it is capable of exporting a 3D scene in .glb format.
  • BlackThread.io offers a browser-based tool, named "glTF Converter", that can ostensibly translate .dae-formatted files into .glb-formatted files.
  • The Khronos Group's "COLLADA to glTF" conversion tool can be located under the group's name on GitHub.

Khronos Group's COLLADA2GLTF Converter

Among this group of potentially useful tools, we have had — by far — the most success/luck using the Khronos Group's COLLADA2GLTF converter. We downloaded and installed version 2 of this Khronos Group conversion tool on our Mac Pro. The executable, named COLLADA2GLTF-bin, was installed on our Mac at the end of a directory tree named …/Dropbox/Lenovo/COLLADA_to_gltf/COLLADA2GLTF-v2/. In order to translate a specific COLLADA-formatted (filename.dae) file:

  • From inside the Mac's "Terminal" application, we changed directories until we were sitting in the above-specified Mac (Dropbox) directory
  • We moved (or copied) the chosen COLLADA-formatted file (filename.dae) into the same directory
  • At the terminal prompt, we typed the line command:   ./COLLADA2GLTF-bin -i filename.dae -b
  • The .glb-formatted output file was stored as …/Dropbox/Lenovo/COLLADA_to_gltf/COLLADA2GLTF-v2/output/filename.glb


Example Mac-Pro Line Commands + Responses
command:   pwd
response:  ../Dropbox/Lenovo/COLLADA_to_gltf/COLLADA2GLTF-v2
command:   ls *.dae
response:  Inertial17.dae
command:   ./COLLADA2GLTF-bin -i Inertial17.dae -b
response:  Converting Inertial17.dae -> output/Inertial17.glb
           Time: 48.166 ms


CAUTION! While we found this COLLADA2GLTF converter to be a very useful tool, we also discovered that porting a model from one visualization environment to another can be a challenging and frustrating endeavor. It is difficult enough to build a (error-free) COLLADA-formatted model that will properly display a desired animated scene in the Mac's Preview app. But it is naive to expect that that same COLLADA code will survive a translation to glTF and seamlessly construct the identical animated scene within the Oculus Rift S environment. In a pair of accompanying chapters — this one, followed by another one — we have chronicled the steps that we have taken to generate our first few (error-free) COLLADA-based models that display properly in both environments. Experience has taught us that … (1) When interpreting COLLADA's <xml>-formatted instructions, the Mac's Preview app is considerably more forgiving than is the Oculus system; (2) almost any code that display's properly in the Mac's Preview app will survive the translation to glTF, in the sense that the COLLADA2GLTF converter seldom complains; but, (3) nevertheless, frequently the Oculus system won't display the model because it detects an error(s), but it almost never suggests what the error(s) might be. When embarking on the development of a new interactive and animated 3D visual scene, the best strategy is a time-consuming one: Start with a COLLADA code that works in both environments — we provide two such codes herein; make only incremental changes and ensure that the model displays properly in the Mac's Preview app; convert the COLLADA-based code to glTF (.glb); don the Oculus Rift S headset & hand controllers, and attempt to import this new model into your "Oculus Home".

Import to Oculus Rift S Environment

We purchased a Lenovo PC (Windows 10) gaming laptop to drive the Oculus Rift S system; more specifically, it is Lenovo's Legion Y740 15" with NVIDIA GeForce GTX 1660Ti 6GB. Two connections were required: (1) Mini DisplayPort; and (2) USB. We downloaded and installed the Oculus program files under the directory C:\Program Files\Oculus. We also mounted Dropbox on the Lenovo, which gave us immediate access to the model files that were created using the Mac Pro. As an example, we located the model file named Inertial17.glb and placed a copy of the file in the directory … This PC\Documents\Oculus Home\_Import. Any (error free) ".glb"-formatted file that is located in this directory is available for import into the Oculus' 3D virtual-reality environment.


When we want to view one of our models, we first start the Oculus application on the Lenovo then click on "Devices" to check whether the headset and two hand controllers are in proper communication with the PC (GREEN buttons) or not (RED buttons). We don the headset & controllers, thereby entering the Oculus Rift S VR environment. [Occasionally we forget to start the Oculus app before putting on the headset. When this happens, the app seems to sense that we have donned the headset and it starts itself!] The following sequence of steps allows us to place the example model, Inertial17, into our Oculus Home.


Inside the Oculus Rift S Home Environment
Oculus Home (view 1) The image shown here, immediately to the left, is a snapshot of the first scene that is displayed in our Oculus Home shortly after we have donned the headset and the pair of hand controllers. The shallow, curved desk immediately in front of us presents ten or so clickable panels (menu choices). In the image, we have highlighted the "Home" button by pointing to it with the index finger of our right hand.
  • Click on the "Home" button; the interactive panels in this scene will disappear.
  • Wait (~ 10 seconds) and our stored "Home" environment will load.
  • "Menu" button vs. "Oculus" button
Oculus Home (view 2)
  • Click the "Menu" button on the left-hand controller; it sits just below the "Y" and "X" buttons;

The image shown here, immediately to the left, is a snapshot of a portion of the scene that is displayed after we have clicked the "Menu" button on our left-hand controller. As illustrated, we have pointed to — and thereby have highlighted in blue — the top menu item, "Places," and we are in the process of sliding our aim down to the next menu item, "Inventory."

  • Click the "Inventory" menu item.
Oculus Home (view 3)

As is shown here, immediately to the left, the menu panel is updated after the "Inventory" button has been clicked, as directed above.

  • Click the "My Imports" menu item.

After highlighting then clicking "My Imports," a three-dimensional display case (a shadow box) containing up to 4 × 3 objects appears, as is illustrated here in the screenshot on the left. Each object in this display case is generated from one of the (error free) ".glb"-formatted files that is located in the aforementioned Lenovo directory … This PC\Documents\Oculus Home\_Import — including files that reside in subdirectories of this parent _Import directory.

NOTE:

  • The display case can hold more than twelve objects, but it will only display twelve at a time. In order to see more, you need to point to (any) one of the displayed objects then use the hand-controller's toggle button to scroll the shelves of the display case up or down.
  • If Oculus sees a (error free) ".glb" file that it has never seen before — for example, a new model file that you have just placed in the PC's …\_Import directory — it will display a panel asking you to "Confirm" that you have permission to load this material.
  • If the Oculus determines that one of your ".glb" files contains an error, it may try to display the faulty object in the display case and attach some sort of warning message. More often than not, however, it will simply ignore the file and leave you wondering why the object does not appear in the display case.
Oculus Home (view 4)
  • Point at an object in the display case, then Grab it (using the controller's middle-finger "grip" switch) and place it somewhere in your Home room.

In the image shown here, immediately on the left, we are pointing at, and are about to "grab", the model we have named, MultiLagrange18. We could have, just as well, pointed at and grabbed the model sitting on the shelf next to it named, Inertial17.


It is worth mentioning that after you have grabbed an object — and before you have placed it in the room — you can do several things with it.

  1. Using the hand controller's thumbstick, you can move the object farther from (or closer to) you by pushing the thumbstick away from you (or by pulling it toward you).
  2. Using the controller's index-finger trigger, you can toggle between a mode that lets you spin the object and a mode that let's you resize it. In either mode, the direction or amplitude of the spin/resizing is determined by pushing the thumbstick to the left or right varying amounts.
Oculus Home (view 5)

The image shown here, immediately on the left, is a snapshot of our Oculus Home shortly after our model named, Inertial17, has been resized (enlarged) then placed in the room.

NOTE: The steps required to remove a model from the "My Imports" Inventory — that is, from the display case — are not easy to guess. Here we identify what appears to be the required sequence of steps, using our model, MultiLagrange18, as an example.

  • Assuming the MultiLagrange18 model is one of the objects that is on display in the Oculus Home room, grab it with the right-hand controller and use the index-finger "trigger" to toggle to the mode that lets you spin the object (the resize mode does not seem to work for this task).
  • Press the "B" button; this should return the object to the "My Imports" display case.
  • Point your index finger at the compartment on the "My Imports" display case that contains the (miniaturized) MultiLagrange18 model, then use your thumb to press the "B" controller button. [Be careful not to squeeze the "grip" button with your middle finger instead, as you will end up unintentionally grabbing the object again.] A small panel containing bibliographical information about the MultiLagrange18 file will appear immediately in front of your face; an even smaller accompanying panel will ask if you want to "Remove Upload", that is, do you want to remove the file from the inventory.
  • Point your index finger at the smaller of these two panels and click on it (using the middle finger's "grip" button) to indicate you want the file removed. The panels will disappear but, confusingly, the inventory display box will not change in any way to signify that your request is being implemented.
  • Remove the headset; sit down in front of the Lenovo PC; locate the MultiLagrange18.glb that has been stored in the Oculus' _Import directory and trash it! The next time you don the Oculus Rift S headset and look at the "My Imports" display case, the MultiLagrange18 will no lonber be among the group of displayed objects.

 

Additional Photos from Inside the Oculus Rift S Home Environment
Third Oculus Rift Selfie Second Oculus Rift Selfie
Third Oculus Rift Selfie

Two of our COLLADA-driven animated models can be identified in each of the three frames of this image montage: In all three cases, the one on the right is model Inertial17 and the one on the left is model MultiLagrange18. The bottom (selfie) visual scene illustrates that we can add to our Oculus home environment other items that are straightforwardly selected from a large Oculus objects inventory.

Footnotes

Adopting the characteristic mass <math>~(M_\mathrm{Ch} = \mu_e^{-2} \cdot 1.14205 \times 10^{34} ~\mathrm{g})</math> and characteristic length <math>~(\ell_1 = \mu_e^{-1} \cdot 7.71395 \times 10^{8} ~\mathrm{cm})</math> that are associated with a white dwarf equation of state, we can reasonably state that the characteristic mean density of a spherically symmetric white dwarf is,

<math>~{\bar\rho}_\mathrm{WD}</math>

<math>~\equiv</math>

<math>~ \frac{3 M_\mathrm{Ch}}{4\pi \ell_1^3} = \mu_e \cdot 5.93972 \times 10^{6}~\mathrm{g}~{\mathrm{cm}}^{-3} \, . </math>

Drawing from our above discussion of timescales that arise in the context of our COLLADA-driven animations, we therefore appreciate that the characteristic oscillation period associated with a white dwarf whose molecular weight of electrons is <math>~\mu_e = 2</math>, proves to be,

<math>~[P_0]_\mathrm{WD}</math>

<math>~=</math>

<math>~ \biggl[ \frac{4\pi}{G{\bar\rho}_\mathrm{WD}} \biggr]^{1 / 2} = 3.98~\mathrm{s}\, . </math>

By presenting animation scenes in which one wall-clock "hour" equates to approximately 4 seconds of real time, we can reasonably assert that our animated models fairly represent how a Riemann-ellipsoid-like white dwarf should behave in real time.

See Also


Whitworth's (1981) Isothermal Free-Energy Surface

© 2014 - 2021 by Joel E. Tohline
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Recommended citation:   Tohline, Joel E. (2021), The Structure, Stability, & Dynamics of Self-Gravitating Fluids, a (MediaWiki-based) Vistrails.org publication, https://www.vistrails.org/index.php/User:Tohline/citation