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(Import to Oculus Rift S Environment)
(Import to Oculus Rift S Environment)
Line 16,278: Line 16,278:
<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>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>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 instead.]  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 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>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!
<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!

Revision as of 18:57, 27 May 2020


Contents

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

 

~\frac{b}{a} = 0.41

 

Figure 1b
EFE Model b41c385

~\frac{c}{a} = 0.385

Direct

 

Adjoint

~\Omega_\mathrm{EFE} =  0.547874

~\Omega_\mathrm{EFE} = - 0.079886

~\lambda_\mathrm{EFE} = 0.079886

~\lambda_\mathrm{EFE} = - 0.547874

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 ~[\pi G\rho]^{1 / 2}. In Figure 1a, 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 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" />
                        </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">
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-1.0  0.0  0.0
 0.0  1.0  0.0
 0.0 -1.0  0.0
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 -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
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  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">
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 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
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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
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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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</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">
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</vertices>
<polylist count="  975" material="Material2">
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  <input semantic="NORMAL" source="#Reflect_Normals" offset="1" />
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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
</vcount>
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   49  970   24  970   50  970
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   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">
     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
   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
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   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
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    </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>
            <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 "8" ... has 8 + (4 x 22) = 96 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="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="IDe19" name="instance_e19">
                    <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="IDe21" name="instance_e21">
                    <matrix>0.25  0 0 0.0   0 0 -1 0.0  0 1 0 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </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="IDe19" 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="IDe20" 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="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>
<!-- covera_Digit3 is "5" -->
            <node name="covera_Digit3">
            <translate>0.0 37.1 -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 "5"  ... has 8 + (4 x 17) = 76 lines -->
                <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="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="IDf06" name="instance_f6">
                    <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 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 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDf11" name="instance_f11">
                    <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="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="IDf21" name="instance_f21">
                    <matrix>0.25  0 0 0.0   0 0 -1 0.0  0 1 0 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDz12" name="instance_z12">
                    <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="IDz13" name="instance_z13">
                    <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>
<!-- END LABELING HERE -->
            </node>
<!-- BEGIN CLOCK -->
          <node id="EntireClock" name="instance_Clock">
            <translate>7.0 0.0 5.0</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">1.00 1.00 1.00</scale>
            <node id="firstclock" name="instance_1">        <!-- TWO -->
              <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 -90.0</rotate>
              <rotate sid="rotationZ">0.0 0.0 1.0 0.0</rotate>
              <scale sid="scale">1.00 1.00 1.00</scale>
              <instance_node url="#ID3" />
            </node>                                         <!-- /TWO -->
            <node id="Jetman" name="instance_Arrow">        <!-- TWO -->
              <matrix sid="transformation"> 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</matrix>
              <instance_node url="#ArrowID3" />
            </node>                                         <!-- /TWO -->
            <node id="HourHand" name="instance_Hour">       <!-- TWO -->
              <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 -90.0</rotate>
              <rotate sid="rotationZ">0.0 0.0 1 270.0</rotate>
              <scale sid="scale">0.75 0.75 0.75</scale>
              <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, ~\Omega_0 \equiv [\pi G \rho]^{1 / 2}. More specifically, by declaration, one oscillation period of the red "minute" hand — that is to say, one wall-clock "hour" — is ~P_0 = 2\pi[\pi G \rho]^{-1 / 2} = [4\pi/(G \rho)]^{1 / 2}. 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 ~\Omega_\mathrm{EFE}, 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, ~P_\mathrm{spin} = |\Omega_\mathrm{EFE}|^{-1} = [0.5479]^{-1} = 1.825 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, ~P_\mathrm{Lagrange} = \lambda_\mathrm{EFE}^{-1} = [0.0799]^{-1} = 12.52 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 ~P_\mathrm{spin} \approx 1.827, 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 ~0.73 P_\mathrm{Lagrange}\approx~5 P_\mathrm{spin}, that is, ~P_\mathrm{Lagrange}\approx 6.849 P_\mathrm{spin}. 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, ~|\Omega_\mathrm{EFE}|/|\lambda_\mathrm{EFE}| = 6.8582. 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>
        <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
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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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</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" />
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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
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 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
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 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    9  505    9  504    9
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    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
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    0   24  520   24  519   24
  495   25  470   25  469   25
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  496   27  471   27  470   27
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  497   29  472   29  471   29
  497   30  498   30  472   30
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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
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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
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  103  874   78  874  104  874
   53  875   27  875   28  875
   53  876   28  876   54  876
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   55  879   29  879   30  879
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   59  888   34  888   60  888
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   76  922   51  922   77  922
   77  923   51  923   52  923
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   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
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 -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
   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
      </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" />
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            </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" />
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<!--  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" />
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                <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" -->
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            <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 -->
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                    <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" -->
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            <translate>0.0 31.8 -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 "8" ... has 8 + (4 x 22) = 96 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">
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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 not 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 ~(M_\mathrm{Ch} = \mu_e^{-2} \cdot 1.14205 \times 10^{34} ~\mathrm{g}) and characteristic length ~(\ell_1 = \mu_e^{-1} \cdot 7.71395 \times 10^{8} ~\mathrm{cm}) 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,

~{\bar\rho}_\mathrm{WD}

~\equiv

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

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 ~\mu_e = 2, proves to be,

~[P_0]_\mathrm{WD}

~=

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

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 - 2020 by Joel E. Tohline
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