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(Understanding the Positioning Matrix)
(Cube Trio by a Blender Developer)
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</table>
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====Example Implementation====
 +
 +
The COLLADA-formatted (.dae) file presented immediately below as ''Example #4'' is modified slightly from this original [https://www.blender.org Blender] example; on my Mac, the filename is: '''/Dropbox/3Dviewers/Cube/FirstCube/colladaOther20_HBook.dae'''
 +
 +
<table border="0" align="center" width="80%" cellpadding="5">
 +
<tr><th align="center" colspan="3">Example #4 &#8212; A [https://developer.blender.org/F18376 cube trio], slightly modified from a COLLADA file posted by [https://www.blender.org Blender]</th></tr>
 +
<tr><td align="left" colspan="2">
 +
<div style="height: 400px; width: 700px; overflow: scroll;">
 +
<pre>
 +
<?xml version="1.0" encoding="UTF-8" standalone="no" ?>
 +
<COLLADA xmlns="http://www.collada.org/2005/11/COLLADASchema" version="1.4.1">
 +
    <asset>
 +
        <contributor>
 +
            <authoring_tool>Google SketchUp 8.0.11752</authoring_tool>
 +
        </contributor>
 +
        <created>2012-04-27T21:07:03Z</created>
 +
        <modified>2012-04-27T21:07:03Z</modified>
 +
        <unit meter="0.0254" name="inch" />
 +
        <up_axis>Z_UP</up_axis>
 +
    </asset>
 +
    <library_visual_scenes>
 +
        <visual_scene id="ID1">
 +
            <node name="SketchUp">
 +
                <node id="ID2" name="instance_0">
 +
                    <matrix>1 0 0 0 0 1 0 25 0 0 1 0 0 0 0 1</matrix>
 +
                    <instance_node url="#ID3" />
 +
                </node>
 +
                <node id="ID28" name="instance_1">
 +
                    <matrix>1 0 0 15 0 1 0 120 0 0 1 0 0 0 0 1</matrix>
 +
                    <instance_node url="#ID3" />
 +
                </node>
 +
                <node id="ID29" name="instance_2">
 +
                    <matrix>1 0 0 120 0 1 0 0 0 0 1 0 0 0 0 1</matrix>
 +
                    <instance_node url="#ID3" />
 +
                </node>
 +
            </node>
 +
        </visual_scene>
 +
    </library_visual_scenes>
 +
    <library_nodes>
 +
        <node id="ID3" name="cube_component">
 +
            <instance_geometry url="#ID4">
 +
                <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="#ID12">
 +
                <bind_material>
 +
                    <technique_common>
 +
                        <instance_material symbol="Material2" target="#ID13">
 +
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
 +
                        </instance_material>
 +
                    </technique_common>
 +
                </bind_material>
 +
            </instance_geometry>
 +
            <instance_geometry url="#ID20">
 +
                <bind_material>
 +
                    <technique_common>
 +
                        <instance_material symbol="Material2" target="#ID21">
 +
                            <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 id="ID4">
 +
            <mesh>
 +
                <source id="ID7">
 +
                    <float_array id="ID10" count="48">39.37007874015748 39.37007874015748 0 0 0 0 0 39.37007874015748 0 39.37007874015748 0 0 0 39.37007874015748 39.37007874015748 39.37007874015748 39.37007874015748 0 0 39.37007874015748 0 39.37007874015748 39.37007874015748 39.37007874015748 39.37007874015748 39.37007874015748 0 39.37007874015748 0 39.37007874015748 39.37007874015748 0 0 39.37007874015748 39.37007874015748 39.37007874015748 39.37007874015748 0 39.37007874015748 0 39.37007874015748 39.37007874015748 0 0 39.37007874015748 39.37007874015748 39.37007874015748 39.37007874015748</float_array>
 +
                    <technique_common>
 +
                        <accessor count="16" source="#ID10" stride="3">
 +
                            <param name="X" type="float" />
 +
                            <param name="Y" type="float" />
 +
                            <param name="Z" type="float" />
 +
                        </accessor>
 +
                    </technique_common>
 +
                </source>
 +
                <source id="ID8">
 +
                    <float_array id="ID11" count="48">0 0 -1 0 0 -1 0 0 -1 0 0 -1 0 1 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1</float_array>
 +
                    <technique_common>
 +
                        <accessor count="16" source="#ID11" stride="3">
 +
                            <param name="X" type="float" />
 +
                            <param name="Y" type="float" />
 +
                            <param name="Z" type="float" />
 +
                        </accessor>
 +
                    </technique_common>
 +
                </source>
 +
                <vertices id="ID9">
 +
                    <input semantic="POSITION" source="#ID7" />
 +
                    <input semantic="NORMAL" source="#ID8" />
 +
                </vertices>
 +
                <triangles count="8" material="Material2">
 +
                    <input offset="0" semantic="VERTEX" source="#ID9" />
 +
                    <p>0 1 2 1 0 3 4 5 6 5 4 7 8 9 10 9 8 11 12 13 14 13 12 15</p>
 +
                </triangles>
 +
            </mesh>
 +
        </geometry>
 +
        <geometry id="ID12">
 +
            <mesh>
 +
                <source id="ID15">
 +
                    <float_array id="ID18" count="12">39.37007874015748 0 39.37007874015748 0 0 0 39.37007874015748 0 0 0 0 39.37007874015748</float_array>
 +
                    <technique_common>
 +
                        <accessor count="4" source="#ID18" stride="3">
 +
                            <param name="X" type="float" />
 +
                            <param name="Y" type="float" />
 +
                            <param name="Z" type="float" />
 +
                        </accessor>
 +
                    </technique_common>
 +
                </source>
 +
                <source id="ID16">
 +
                    <float_array id="ID19" count="12">-0 -1 -0 -0 -1 -0 -0 -1 -0 -0 -1 -0</float_array>
 +
                    <technique_common>
 +
                        <accessor count="4" source="#ID19" stride="3">
 +
                            <param name="X" type="float" />
 +
                            <param name="Y" type="float" />
 +
                            <param name="Z" type="float" />
 +
                        </accessor>
 +
                    </technique_common>
 +
                </source>
 +
                <vertices id="ID17">
 +
                    <input semantic="POSITION" source="#ID15" />
 +
                    <input semantic="NORMAL" source="#ID16" />
 +
                </vertices>
 +
                <triangles count="2" material="Material2">
 +
                    <input offset="0" semantic="VERTEX" source="#ID17" />
 +
                    <p>0 1 2 1 0 3</p>
 +
                </triangles>
 +
            </mesh>
 +
        </geometry>
 +
        <geometry id="ID20">
 +
            <mesh>
 +
                <source id="ID23">
 +
                    <float_array id="ID26" count="12">0 39.37007874015748 39.37007874015748 0 0 0 0 0 39.37007874015748 0 39.37007874015748 0</float_array>
 +
                    <technique_common>
 +
                        <accessor count="4" source="#ID26" stride="3">
 +
                            <param name="X" type="float" />
 +
                            <param name="Y" type="float" />
 +
                            <param name="Z" type="float" />
 +
                        </accessor>
 +
                    </technique_common>
 +
                </source>
 +
                <source id="ID24">
 +
                    <float_array id="ID27" count="12">-1 0 0 -1 0 0 -1 0 0 -1 0 0</float_array>
 +
                    <technique_common>
 +
                        <accessor count="4" source="#ID27" stride="3">
 +
                            <param name="X" type="float" />
 +
                            <param name="Y" type="float" />
 +
                            <param name="Z" type="float" />
 +
                        </accessor>
 +
                    </technique_common>
 +
                </source>
 +
                <vertices id="ID25">
 +
                    <input semantic="POSITION" source="#ID23" />
 +
                    <input semantic="NORMAL" source="#ID24" />
 +
                </vertices>
 +
                <triangles count="2" material="Material2">
 +
                    <input offset="0" semantic="VERTEX" source="#ID25" />
 +
                    <p>0 1 2 1 0 3</p>
 +
                </triangles>
 +
            </mesh>
 +
        </geometry>
 +
    </library_geometries>
 +
    <library_materials>
 +
        <material id="ID6" name="material">
 +
            <instance_effect url="#ID5" />
 +
        </material>
 +
        <material id="ID13" name="Color_005_">
 +
            <instance_effect url="#ID14" />
 +
        </material>
 +
        <material id="ID21" name="Color_A06_">
 +
            <instance_effect url="#ID22" />
 +
        </material>
 +
    </library_materials>
 +
    <library_effects>
 +
        <effect id="ID5">
 +
            <profile_COMMON>
 +
                <technique sid="COMMON">
 +
                    <lambert>
 +
                        <diffuse>
 +
                            <color>0 0 1 1</color>
 +
                        </diffuse>
 +
                    </lambert>
 +
                </technique>
 +
            </profile_COMMON>
 +
        </effect>
 +
        <effect id="ID14">
 +
            <profile_COMMON>
 +
                <technique sid="COMMON">
 +
                    <lambert>
 +
                        <diffuse>
 +
                            <color>0 1 0 1</color>
 +
                        </diffuse>
 +
                    </lambert>
 +
                </technique>
 +
            </profile_COMMON>
 +
        </effect>
 +
        <effect id="ID22">
 +
            <profile_COMMON>
 +
                <technique sid="COMMON">
 +
                    <lambert>
 +
                        <diffuse>
 +
                            <color>0.8 0 0 1</color>
 +
                        </diffuse>
 +
                    </lambert>
 +
                </technique>
 +
            </profile_COMMON>
 +
        </effect>
 +
    </library_effects>
 +
    <scene>
 +
        <instance_visual_scene url="#ID1" />
 +
    </scene>
 +
</COLLADA>
 +
</pre>
 +
</div>
 +
</td>
 +
<td align="center" rowspan="1" bgcolor="lightgrey">[[File:ColladaPlay06.png|250px|ColladaPlay06]]</td>
</tr>
</tr>
</table>
</table>

Revision as of 14:48, 17 September 2019


Contents

Virtual Reality and 3D Printing

[Circa August 2019] I am once again considering whether steady improvements in certain digital technologies over the past half-a-dozen years can be straightforwardly called upon to display to a broad audience the three-dimensional characteristics of rapidly rotating fluid systems. Two specific technologies come to mind: (1) 3D printing; and (2) XR (virtual reality). A cursory online investigation suggests that we may be able to import OBJ-formatted files into the software algorithms that drive these two technologies. In addition, the popular Unity design tool may serve us well in our efforts to build/view/export such files.

Whitworth's (1981) Isothermal Free-Energy Surface
|   Tiled Menu   |   Tables of Content   |  Banner Video   |  Tohline Home Page   |

Initial Browsing of Online Resources

  • DAE files & XML COLLADA format   <--   the Preview application on my MacBook Air will open/display a .DAE file
    • A file with the DAE file extension is a Digital Asset Exchange file. DAE files are based on the COLLADA (COLLAborative Design Activity) XML schema, which is now owned and developed by Autodesk (e.g., Maya). DAE files allow users to transmit 3D graphics files across multiple graphics applications.
    • Examples:

      cube.dae  <--   NOTE: I have copied this "dae" file into a dropbox folder and have successfully modified it (changed color from red to purple) inside my txt editor.

      In March 2011, Khronos released the COLLADA Conformance Test Suite (CTS). The suite allows applications that import and export COLLADA to test against a large suite of examples, ensuring that they conform properly to the specification. In July 2012, the CTS software was released on GitHub — also see, an associated PDF document, and OpenCOLLADA hosted on Github — allowing for community contributions.

      Check out turbosquid.com; or Free3d

    • August 2013:  Autodesk has released Maya LT with COLLADA export capabilities.
  • Four most common 3D printer file formats in 2019.
    • STL:
      File Format Simply Explained.

      As of today, STL is the undisputed champion among 3D printer file formats. STL’s history goes back to the invention of 3D printing itself. The first 3D printer was invented by Chuck Hull in 1987 at 3D Systems. The same guy was behind the STL file format. If you are primarily printing with a single material and in a single color, STL will do the job. But the moment you move to multicolor printing, you have to ditch STL because it is simply not capable of storing colors.

      There are many repositories, marketplaces and search engines on the web containing literally millions of free STL files. Thingiverse is probably the largest STL file repository on the internet – so check it out. You can also refer to our regularly updated list: Best Sites for Free STL Files & 3D Printer Models.

      STL File Viewers

    • OBJ:

      File format explained.

      Format developed by Wavefront; note that a number of the above-referenced STL viewers will also view OBJ files.

    • AMF
    • 3MF
  • Try this online 3D converter; in principle, it can be used to convert a DAE (i.e., COLLADA) file to an STL or OBJ file, and visa versa.
  • Unity
    • See especially the Products page which briefly refers to …
      • Platforms: Build once, deploy anywhere to reach the largest possible audience on our industry-leading platform; 25+ platforms across mobile, desktop, console, TV, VR (virtual reality), AR (augmented reality) and the Web.
      • XR: Powering over two-thirds of VR and AR experiences; Unity is the preferred development tool for the majority of XR creators.
  • Unreal Engine 4 — competitor of Unity
  • Oculus Rift S driven by PC; or Oculus Quest, standalone 6DOF VR — looks like they both can be driven by either Unity or Unreal, or via the Native Platform provided by Oculus.
    • In principle, the Oculus Rift can import new, user-supplied 3D scenes — see the advanced help document — but, for now, it only accepts files in GLB format.
    • But see the import feature of Oculus Medium 2.0.
    • GLB format:  a binary form of glTF that includes textures instead of referencing them as external images.
    • glTF:   (derivative short form of GL Transmission Format) is a file format for 3D scenes and models using the JSON standard. It is an API-neutral runtime asset delivery format developed by the Khronos Group 3D Formats Working Group. It was announced at HTML5DevConf 2016. This format is intended to be an efficient, interoperable format with minimum file size and runtime processing by apps. As such, its creators have described it as the "JPEG of 3D."
  • Gear VR — Samsung's headset (powered by Oculus)

    GearVR Framework is the SDK for Samsung's Gear VR.
  • Also consider Oculus Go
  • vtk has vtkOBJExporter as well as vtkOBJReader
  • Kitware may also be relevant
  • Jinghua Ge's CCT-based visualization lab course
  • Look into the VR Model Viewer from MindRend Technologies, which "is a tool to import and view CAD models of various types in VR."

    It claims to provide support for three of the four formats identified above in connection with 3D printers, namely: STL, OBJ (with MTL file), and 3MF.

    It supports the following VR headsets: Oculus Rift and HTC Vive.

Best Info, to Date

  1. Check out the Khronos Group's Overview of glTF; note that GLB is the binary form of glTF.
  2. Evidently, a user's native 3D scene can be transferred (in GLB format) to the Oculus Medium 2.0, and then viewed with Oculus-supported headgear.

    An Oculus blog posted 14 February 2019 and titled, "Rift Platform Updates: Create Your Own Space," states the following … "Home is no longer limited to the stock cabin model. Now, we give you a couple templates, a cafe and theater, plus special themed decor and furniture items to play with — and you can upload any additional 3D models you’d like." See more details here.

  3. DAE (i.e., XML COLLADA-formatted) files …
    1. The Mac's Preview application can display DAE files — see, for example, cube.dae.
    2. Evidently I should expect most 3D printers to accept DAE-formatted files as well as the older and more familiar STL and OBJ files.
    3. Check out the Khronos Group's Overview of COLLADA.
    4. COLLADA Tutorials
    5. Animation Tutorial
    6. PowerPoint presentation with example of combining physics (kinematics) with visual scenes — see author Ender Yemenicioglu at tarakos.com
    7. astroBoy_walk.dae

I wonder if even very simple DAE files can be converted to glTF (and GLB) files; perhaps the tools, glTF API or COLLADA2GLTF will work. If so, then we can kill two birds with one stone; i.e., simply build DAE files, then they should be straightforwardly ported to Oculus headgear or a 3D printer.

Good Cube Examples

In the context of the following example discussions, I have relied upon just three available viewers to judge whether any/each <xml> file is properly formatted:

  • The Preview App on my desktop Mac;
  • The 3D Model Viewer App as installed on my Galaxy S8+ — the developer's name is Shyam Barange; and the relevant website appears to be GET INTO AR
  • The COLLADA Viewer App as installed on my Galaxy S8+ — the associated company is Googolplex Ltd

From COLLADA Release Notes

A useful Cube.dae example can be found in Appendix A of the PDF-formatted document titled, COLLADA — Digital Asset Schema Release 1.4.1 — Specification (2nd Edition), March 2008. I was able to execute/display this file using my Mac's Preview app after trimming it down a bit. (When I tried to "copy" then "paste" this text file into my Mac's vi editor, it did not initially execute properly in the Preview app, so I removed some lines of the xml code in an effort to debug my file. (I was guided in this effort by having access to a separately constructed example <xml> model file, named "cube001.dae", that was kindly sent to me by Shyam Barange, the developer of 3D model Viewer.) Much of this trimming may not have been necessary because, in the end, I realized that the essential spacings between integer vertex values and integer normal values in the polygons specification had disappeared during the copy-and-paste operation.) Here is my version of this executable COLLADA (.dae) file, created 2 September 2019; on my Mac, the filename is: /Dropbox/3Dviewers/Cube/ThirdCube/AppendA06Works.dae


Example #1 — Extracted from COLLADA release notes (modified here)
<?xml version="1.0" encoding="utf-8"?>
<COLLADA xmlns="http://www.collada.org/2005/11/COLLADASchema" version="1.4.1">
  <asset>
    <created>2005-11-14T02:16:38Z</created>
    <modified>2005-11-15T11:36:38Z</modified>
    <revision>1.0</revision>
  </asset>
  <library_effects>
    <effect id="whitePhong">
      <profile_COMMON>
        <technique sid="phong1">
          <phong>
            <diffuse>
              <color>0.8 0.0 0.8 1.0</color>
            </diffuse>
          </phong>
        </technique>
      </profile_COMMON>
    </effect>
  </library_effects>
<!--                 -->
  <library_materials>
    <material id="whiteMaterial">
      <instance_effect url="#whitePhong"/>
    </material>
  </library_materials>
  <library_geometries>
    <geometry id="box" name="box">
      <mesh>
        <source id="box-Pos">
          <float_array id="box-Pos-array" 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="#box-Pos-array" 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="box-0-Normal">
          <float_array id="box-0-Normal-array" 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="#box-0-Normal-array" 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="box-Vtx">
          <input semantic="POSITION" source="#box-Pos"/>
        </vertices>
<!--
The 6 separate polygons define the 6 sides of the "cube"; hence, each polygon will
have 4 vertices and 4 associated normals.
As identified in this xml file, the vertices + associated normal for each side/polygon
are listed between the <p></p> notation; the vertex number and associated normal
are interleaved such that the normal is offset by "1".  For example, the first of
the 6 sides/polygons is defined by connecting vertices:  0 -> 2 -> 3 -> 1 -> back to 0;
while all four normals are assigned the direction/number "4".
-->
        <polygons count="6" material="WHITE">
          <input semantic="VERTEX" source="#box-Vtx" offset="0"/>
          <input semantic="NORMAL" source="#box-0-Normal" offset="1"/>
          <p>0 4 2 4 3 4 1 4</p>
          <p>0 2 1 2 5 2 4 2</p>
          <p>6 3 7 3 3 3 2 3</p>
          <p>0 1 4 1 6 1 2 1</p>
          <p>3 0 7 0 5 0 1 0</p>
          <p>5 5 7 5 6 5 4 5</p>
        </polygons>
      </mesh>
    </geometry>
  </library_geometries>
  <library_visual_scenes>
    <visual_scene id="DefaultScene">
      <node id="Box" name="Box">
        <translate> 0  0  3</translate>
        <rotate> 0  0  1  0</rotate>
        <rotate> 0  1  0  0</rotate>
        <rotate> 1  0  0  0</rotate>
        <scale>  1  1  0.2</scale>
        <instance_geometry url="#box">
          <bind_material>
            <technique_common>
              <instance_material symbol="WHITE" target="#whiteMaterial"/>
            </technique_common>
          </bind_material>
        </instance_geometry>
      </node>
    </visual_scene>
  </library_visual_scenes>
  <scene>
    <instance_visual_scene url="#DefaultScene"/>
  </scene>
</COLLADA>


While I was able to view this file successfully within the Preview app on my Mac, it did not display at all on either of the above-identified 3D viewers that I had installed on my Galaxy S8+. As I discovered, the primary issue had to do with how the set of eight vertices were being connected in order to define the model's polygons. In the Example #1 <xml> code, the polygons instruction is used to define six 4-sided polygons. Evidently neither of the Galaxy S8+ viewers understands this polygons instruction. When I used, instead, the triangles instruction to define twelve 3-sided polygons, both of these viewers displayed a 3D object. Here is the relevant, modified executable COLLADA (.dae) file; on my Mac, the filename is: /Dropbox/3Dviewers/Cube/ThirdCube/AppendA08Works.dae


Example #2 — Basically the same as Example #1, but with <triangles> replacing <polygons>
<?xml version="1.0" encoding="utf-8"?>
<COLLADA xmlns="http://www.collada.org/2005/11/COLLADASchema" version="1.4.1">
  <asset>
    <created>2005-11-14T02:16:38Z</created>
    <modified>2005-11-15T11:36:38Z</modified>
    <revision>1.0</revision>
  </asset>
  <library_effects>
    <effect id="whitePhong">
      <profile_COMMON>
        <technique sid="phong1">
          <phong>
            <diffuse>
              <color>0.1 0.9 0.1 1.0</color>
            </diffuse>
          </phong>
        </technique>
      </profile_COMMON>
    </effect>
  </library_effects>
<!--                 -->
  <library_materials>
    <material id="whiteMaterial">
      <instance_effect url="#whitePhong"/>
    </material>
  </library_materials>
  <library_geometries>
    <geometry id="box" name="box">
      <mesh>
        <source id="box-Pos">
          <float_array id="box-Pos-array" 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="#box-Pos-array" 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="box-0-Normal">
          <float_array id="box-0-Normal-array" count="18">
           0.0  0.0 -1.0
           0.0  0.0  1.0
           1.0  0.0  0.0
           0.0 -1.0  0.0
          -1.0  0.0  0.0
           0.0  1.0  0.0
          </float_array>
          <technique_common>
            <accessor source="#box-0-Normal-array" 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="box-Vtx">
          <input semantic="POSITION" source="#box-Pos"/>
        </vertices>
        <triangles count="12" material="WHITE">
          <input semantic="VERTEX" source="#box-Vtx" offset="0"/>
          <input semantic="NORMAL" source="#box-0-Normal" offset="1"/>
          <p>0 0 2 0 3 0   7 1 5 1 4 1   4 2 1 2 0 2   5 3 2 3 1 3   2 4 7 4 3 4   0 5 7 5 4 5   0 0 1 0 2 0   7 1 6 1 5 1   4 2 5 2 1 2   5 3 6 3 2 3   2 4 6 4 7 4   0 5 3 5 7 5</p>
        </triangles>
      </mesh>
    </geometry>
  </library_geometries>
  <library_visual_scenes>
    <visual_scene id="DefaultScene">
      <node id="Box" name="Box">
        <translate> 0  0  3</translate>
        <rotate> 0  0  1  0</rotate>
        <rotate> 0  1  0  0</rotate>
        <rotate> 1  0  0  0</rotate>
        <scale>  1  1  0.2</scale>
        <instance_geometry url="#box">
          <bind_material>
            <technique_common>
              <instance_material symbol="WHITE" target="#whiteMaterial"/>
            </technique_common>
          </bind_material>
        </instance_geometry>
      </node>
    </visual_scene>
  </library_visual_scenes>
  <scene>
    <instance_visual_scene url="#DefaultScene"/>
  </scene>
</COLLADA>
AppendA08Works

Here are a few additional items of note regarding Example #2:

  • I set the <color> value to (R, G, B, alpha) = (0.1, 0.9, 0.1, 1), so the resulting "cube" is colored green.
  • I set the coordinate <scale> factors to (X, Y, Z) = (1, 1, 0.2), so the resulting "cube" is actually a solid rectangle that is substantially flatter in the Z-direction than in the other two directions.
  • While the Preview app on the Mac and the COLLADA Viewer on the Galaxy S8+ both displayed a flattened, green solid rectangle as depicted here to the right of the Example #2 <xml> model file, the 3D Model Viewer displayed a white cube instead.

We played with the <xml> code a bit more, changing individual instructions and/or changing various attribute values in an effort to better understand the consequences. The Example #3 <xml> code, shown immediately below, includes many of these alterations; on my Mac the filename is: /Dropbox/3Dviewers/Cube/FourthCube/AppendD13.dae. Both the Preview app on the Mac and the COLLADA Viewer on my Galaxy S8+ generated the red, solid rectangular model depicted here to the right of the Example #3 <xml> model file. The 3D Model Viewer displayed a red, rather than a white, object, which we count as a measure of success; but the displayed 3D object was still an equal-sided cube.

In evolving from the <xml> code displayed here as Example #2 to the <xml> code labeled Example #3, the following two changes appear to have been necessary in order for the 3D Model Viewer to display a red — rather than a white — cube:

  • In both Example #2 code locations where the attribute "WHITE" appears, we substituted the attribute "whiteMaterial".
  • In Example #3, the <visual_scene> includes what appears to be a key additional instruction, namely, <matrix sid="transform">.


Example #3 — Basically the same as Example #2, but after playing with various code modifications
<?xml version="1.0" encoding="utf-8"?>
<COLLADA xmlns="http://www.collada.org/2005/11/COLLADASchema" version="1.4.1">
  <asset>
    <created>2005-11-14T02:16:38Z</created>
    <modified>2005-11-15T11:36:38Z</modified>
    <revision>1.0</revision>
    <unit meter="0.0254" name="inch" />
    <up_axis>Z_UP</up_axis>
  </asset>
  <library_effects>
    <effect id="whitePhong">
      <profile_COMMON>
        <technique sid="phong1">
          <phong>
            <diffuse>
              <color>0.8 0.2 0.2 1.0</color>
            </diffuse>
          </phong>
        </technique>
      </profile_COMMON>
    </effect>
  </library_effects>
<!--                 -->
  <library_materials>
    <material id="whiteMaterial">
      <instance_effect url="#whitePhong"/>
    </material>
  </library_materials>
  <library_geometries>
    <geometry id="box" name="box">
      <mesh>
        <source id="box-Pos">
          <float_array id="box-Pos-array" count="24">
            0.0  1.0  1.0
            1.0  1.0  1.0
            0.0  0.0  1.0
            1.0  0.0  1.0
            0.0  1.0  0.0
            1.0  1.0  0.0
            0.0  0.0  0.0
            1.0  0.0  0.0
          </float_array>
          <technique_common>
            <accessor source="#box-Pos-array" 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="box-0-Normal">
          <float_array id="box-0-Normal-array" 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="#box-0-Normal-array" 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="box-Vtx">
          <input semantic="POSITION" source="#box-Pos"/>
        </vertices>
        <triangles count="12" material="whiteMaterial">
          <input semantic="VERTEX" source="#box-Vtx" offset="0"/>
          <input semantic="NORMAL" source="#box-0-Normal" offset="1"/>
          <p>0 4 2 4 3 4   0 4 3 4 1 4   4 5 5 5 7 5   4 5 7 5 6 5   0 3 4 3 6 3   0 3 6 3 2 3   3 2 7 2 5 2   3 2 5 2 1 2   2 1 6 1 7 1   2 1 7 1 3 1   0 0 1 0 5 0   0 0 5 0 4 0</p>
        </triangles>
<!--
        <polygons count="6" material="whiteMaterial">
          <input semantic="VERTEX" source="#box-Vtx" offset="0"/>
          <input semantic="NORMAL" source="#box-0-Normal" offset="1"/>
          <p>0 4 2 4 3 4 1 4</p>
          <p>0 2 1 2 5 2 4 2</p>
          <p>6 3 7 3 3 3 2 3</p>
          <p>0 1 4 1 6 1 2 1</p>
          <p>3 0 7 0 5 0 1 0</p>
          <p>5 5 7 5 6 5 4 5</p>
        </polygons>
-->
      </mesh>
    </geometry>
  </library_geometries>
  <library_visual_scenes>
    <visual_scene id="DefaultScene">
      <node id="Box" name="Box">
<!--
        <translate> 0  0.5  0.5</translate>
        <rotate> 0  0  0  0</rotate>
        <rotate> 0  0  0  0</rotate>
        <rotate> 0  0  0  0</rotate>
        <scale>  1  0.2  0.1</scale>
        <matrix sid="transform">1 0 0 0 0 0.292 0 0 0 0 1 1.026 0 0 0 1</matrix>
-->
        <rotate> 0  0  1  0</rotate>
        <rotate> 0  1  0  45</rotate>
        <rotate> 1  0  0  0</rotate>
        <scale>  0.05  0.2  0.1</scale>
        <matrix sid="transform">1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1</matrix>
        <instance_geometry url="#box">
          <bind_material>
            <technique_common>
              <instance_material symbol="whiteMaterial" target="#whiteMaterial"/>
            </technique_common>
          </bind_material>
        </instance_geometry>
      </node>
    </visual_scene>
  </library_visual_scenes>
  <scene>
    <instance_visual_scene url="#DefaultScene"/>
  </scene>
</COLLADA>
AppendD13

Cube Trio by a Blender Developer

Implementing the Raw COLLADA Code

We have found another relatively simple COLLADA-formatted 3D model file on a web page titled, "cube.dae," that has been provided by Blender author, Martjn Berger. The interactive scene that is generated by this model file includes three separate — but identical — cubes; four of the cube faces are painted with one color (e.g., blue), another face is painted with a different color (e.g., green), and the sixth face is painted with yet a different color (e.g., red). The COLLADA-formatted (.dae) file presented immediately below as Example #4 is modified slightly from this original Blender example; on my Mac, the filename is: /Dropbox/3Dviewers/Cube/FirstCube/colladaPlay06.dae


Example #4 — A cube trio, slightly modified from a COLLADA file posted by Blender
<?xml version="1.0" encoding="UTF-8" standalone="no" ?>
<COLLADA xmlns="http://www.collada.org/2005/11/COLLADASchema" version="1.4.1">
    <asset>
        <contributor>
            <authoring_tool>Google SketchUp 8.0.11752</authoring_tool>
        </contributor>
        <created>2012-04-27T21:07:03Z</created>
        <modified>2012-04-27T21:07:03Z</modified>
        <unit meter="0.0254" name="inch" />
        <up_axis>Z_UP</up_axis>
    </asset>
    <library_visual_scenes>
        <visual_scene id="ID1">
            <node name="SketchUp">
                <node id="ID2" name="instance_0">
                    <matrix>1 0 0 0 0 1 0 25 0 0 1 0 0 0 0 1</matrix>
                    <instance_node url="#ID3" />
                </node>
                <node id="ID28" name="instance_1">
                    <matrix>1 0 0 15 0 1 0 120 0 0 1 0 0 0 0 1</matrix>
                    <instance_node url="#ID3" />
                </node>
                <node id="ID29" name="instance_2">
                    <matrix>1 0 0 120 0 1 0 0 0 0 1 0 0 0 0 1</matrix>
                    <instance_node url="#ID3" />
                </node>
            </node>
        </visual_scene>
    </library_visual_scenes>
    <library_nodes>
        <node id="ID3" name="cube_component">
            <instance_geometry url="#ID4">
                <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="#ID12">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#ID13">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                        </instance_material>
                    </technique_common>
                </bind_material>
            </instance_geometry>
            <instance_geometry url="#ID20">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#ID21">
                            <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 id="ID4">
            <mesh>
                <source id="ID7">
                    <float_array id="ID10" count="48">39.37007874015748 39.37007874015748 0 0 0 0 0 39.37007874015748 0 39.37007874015748 0 0 0 39.37007874015748 39.37007874015748 39.37007874015748 39.37007874015748 0 0 39.37007874015748 0 39.37007874015748 39.37007874015748 39.37007874015748 39.37007874015748 39.37007874015748 0 39.37007874015748 0 39.37007874015748 39.37007874015748 0 0 39.37007874015748 39.37007874015748 39.37007874015748 39.37007874015748 0 39.37007874015748 0 39.37007874015748 39.37007874015748 0 0 39.37007874015748 39.37007874015748 39.37007874015748 39.37007874015748</float_array>
                    <technique_common>
                        <accessor count="16" source="#ID10" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                        </accessor>
                    </technique_common>
                </source>
                <source id="ID8">
                    <float_array id="ID11" count="48">0 0 -1 0 0 -1 0 0 -1 0 0 -1 0 1 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1</float_array>
                    <technique_common>
                        <accessor count="16" source="#ID11" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                        </accessor>
                    </technique_common>
                </source>
                <vertices id="ID9">
                    <input semantic="POSITION" source="#ID7" />
                    <input semantic="NORMAL" source="#ID8" />
                </vertices>
                <triangles count="8" material="Material2">
                    <input offset="0" semantic="VERTEX" source="#ID9" />
                    <p>0 1 2 1 0 3 4 5 6 5 4 7 8 9 10 9 8 11 12 13 14 13 12 15</p>
                </triangles>
            </mesh>
        </geometry>
        <geometry id="ID12">
            <mesh>
                <source id="ID15">
                    <float_array id="ID18" count="12">39.37007874015748 0 39.37007874015748 0 0 0 39.37007874015748 0 0 0 0 39.37007874015748</float_array>
                    <technique_common>
                        <accessor count="4" source="#ID18" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                        </accessor>
                    </technique_common>
                </source>
                <source id="ID16">
                    <float_array id="ID19" count="12">-0 -1 -0 -0 -1 -0 -0 -1 -0 -0 -1 -0</float_array>
                    <technique_common>
                        <accessor count="4" source="#ID19" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                        </accessor>
                    </technique_common>
                </source>
                <vertices id="ID17">
                    <input semantic="POSITION" source="#ID15" />
                    <input semantic="NORMAL" source="#ID16" />
                </vertices>
                <triangles count="2" material="Material2">
                    <input offset="0" semantic="VERTEX" source="#ID17" />
                    <p>0 1 2 1 0 3</p>
                </triangles>
            </mesh>
        </geometry>
        <geometry id="ID20">
            <mesh>
                <source id="ID23">
                    <float_array id="ID26" count="12">0 39.37007874015748 39.37007874015748 0 0 0 0 0 39.37007874015748 0 39.37007874015748 0</float_array>
                    <technique_common>
                        <accessor count="4" source="#ID26" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                        </accessor>
                    </technique_common>
                </source>
                <source id="ID24">
                    <float_array id="ID27" count="12">-1 0 0 -1 0 0 -1 0 0 -1 0 0</float_array>
                    <technique_common>
                        <accessor count="4" source="#ID27" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                        </accessor>
                    </technique_common>
                </source>
                <vertices id="ID25">
                    <input semantic="POSITION" source="#ID23" />
                    <input semantic="NORMAL" source="#ID24" />
                </vertices>
                <triangles count="2" material="Material2">
                    <input offset="0" semantic="VERTEX" source="#ID25" />
                    <p>0 1 2 1 0 3</p>
                </triangles>
            </mesh>
        </geometry>
    </library_geometries>
    <library_materials>
        <material id="ID6" name="material">
            <instance_effect url="#ID5" />
        </material>
        <material id="ID13" name="Color_005_">
            <instance_effect url="#ID14" />
        </material>
        <material id="ID21" name="Color_A06_">
            <instance_effect url="#ID22" />
        </material>
    </library_materials>
    <library_effects>
        <effect id="ID5">
            <profile_COMMON>
                <technique sid="COMMON">
                    <lambert>
                        <diffuse>
                            <color>0 0 1 1</color>
                        </diffuse>
                    </lambert>
                </technique>
            </profile_COMMON>
        </effect>
        <effect id="ID14">
            <profile_COMMON>
                <technique sid="COMMON">
                    <lambert>
                        <diffuse>
                            <color>0 1 0 1</color>
                        </diffuse>
                    </lambert>
                </technique>
            </profile_COMMON>
        </effect>
        <effect id="ID22">
            <profile_COMMON>
                <technique sid="COMMON">
                    <lambert>
                        <diffuse>
                            <color>0.8 0 0 1</color>
                        </diffuse>
                    </lambert>
                </technique>
            </profile_COMMON>
        </effect>
    </library_effects>
    <scene>
        <instance_visual_scene url="#ID1" />
    </scene>
</COLLADA>
ColladaPlay06

Principal responsibilities of various subsections from the above, <xml>-formatted code:

A.
<library_visual_scenes>
  <visual_scene ID="ID1">
    <node name="SketcUp">

Generate 3 instances of #ID3, placing them at 3 separate 16-argument "matrix" positions, as explained below.

    </node>
  </visual_scene>
</library_visual_scenes>
B.
<library_nodes>
  <node id="ID3">

Define all components of a single node that describes a simple, 6-sided (8 vertices and 12 triangles) cube; this implementation builds the cube as being composed of three separate <instance_geometries>, as defined below:

  • url = "#ID4" should be colored/shaded as defined by material target = "#ID6", which in turn points to library effect = "#ID5".
  • url = "#ID12" should be colored/shaded as defined by material target = "#ID13", which in turn points to library effect = "#ID14".
  • url = "#ID20" should be colored/shaded as defined by material target = "#ID21", which in turn points to library effect = "#ID22".
  </node>
</library_nodes>
C.
<library_geometries>
  <geometry id="…">

Two co-planar and adjacent triangles are prescribed such that, together, they define a square, which serves as one of the six sides of the cube; four unique vertices are required, referenced as … 0, 1, 2, 3.
<mesh>
    <vertices id="ID17">

  • (X, Y, Z) coordinate locations are pulled from <source id="ID15"> , which contains a total of 4 × 3 = 12 floating-point numbers.
  • The (X, Y, Z)-normals assigned to the four vertices are pulled from <source id="ID16"> , which also contains a total of 4 × 3 = 12 floating-point numbers … the assigned values are usually 0 or ± 1.

    </vertices>
    <triangles source="#ID17" count="2">
    <p>0 1 2 1 0 3</p>

  • This sequence of six integers means that the 1st (of count="2") triangular polygon is formed by connecting three vertices in the order … 0, 1, 2, then back to 0; and the 2nd (of count="2") triangular polygon is formed by connecting three vertices in the order … 1, 0, 3, then back to 1.

    </triangles>
</mesh>

  </geometry>
</library_geometries>

Understanding the Positioning Matrix

Evidently, the COLLADA language allows you to reposition an object — for example, one of the cubes in this trio — (a) by explicitly specifying the separate instructions to <translate>, <rotate>, and <scale>; or (b) by specifying, in the form of a 4×4 <matrix>, a single instruction that combines all of the others via matrix multiplication.


For example, in COLLADA the instruction, <scale>Sx    Sy    Sz</scale>, is equivalent to,

Mscale =
Sx 0 0
0 Sy 0
0 0 Sz

And, drawing from the Wikipedia discussion of Basic Rotations in three dimensions, we recognize that rotations about the x, y, and z axes are quantitatively defined, respectively, by the following matrices:

Rx(α) =
1 0 0
0 cos(α) - sin(α)
0 sin(α) cos(α)
  ;   Ry(β) =
cos(β) 0 sin(β)
0 1 0
-sin(β) 0 cos(β)
    ;   Rz(γ) =
cos(γ) - sin(γ) 0
sin(γ) cos(γ) 0
0 0 1

The equivalent instructions in COLLADA are, respectively,

<rotate> 1    0    0    α </rotate>   ;  

<rotate> 0    1    0    β </rotate>   ;  

<rotate> 0    0    1    γ </rotate>   .

Drawing furthermore from the Wikipedia discussion of more General Rotations, we recognize that other rotation matrices can be obtained from these three using matrix multiplications. For example, the product

~R(\alpha,\beta,\gamma) = R_z(\alpha) \times R_y(\beta) \times R_x(\gamma) \, ,

— a 3×3 matrix — represents a rotation whose yaw, pitch, and roll angles are α, β, and γ, respectively. Finally, including possible translations Tx, Ty, and Tz in the x, y, and z directions, respectively, we can write

x'
y'
z'
=
T_x
T_y
T_z
+
 
R(α, β, γ) × Mscale
[3×3 matrix]
 
×
x
y
z

or, equivalently (I think this is correct!),

x'
y'
z'
1
=
R(α, β, γ) × Mscale Tx
Ty
Tz
0 0 0 1
×
x
y
z
1

Example Implementation

The COLLADA-formatted (.dae) file presented immediately below as Example #4 is modified slightly from this original Blender example; on my Mac, the filename is: /Dropbox/3Dviewers/Cube/FirstCube/colladaOther20_HBook.dae

Example #4 — A cube trio, slightly modified from a COLLADA file posted by Blender
<?xml version="1.0" encoding="UTF-8" standalone="no" ?>
<COLLADA xmlns="http://www.collada.org/2005/11/COLLADASchema" version="1.4.1">
    <asset>
        <contributor>
            <authoring_tool>Google SketchUp 8.0.11752</authoring_tool>
        </contributor>
        <created>2012-04-27T21:07:03Z</created>
        <modified>2012-04-27T21:07:03Z</modified>
        <unit meter="0.0254" name="inch" />
        <up_axis>Z_UP</up_axis>
    </asset>
    <library_visual_scenes>
        <visual_scene id="ID1">
            <node name="SketchUp">
                <node id="ID2" name="instance_0">
                    <matrix>1 0 0 0 0 1 0 25 0 0 1 0 0 0 0 1</matrix>
                    <instance_node url="#ID3" />
                </node>
                <node id="ID28" name="instance_1">
                    <matrix>1 0 0 15 0 1 0 120 0 0 1 0 0 0 0 1</matrix>
                    <instance_node url="#ID3" />
                </node>
                <node id="ID29" name="instance_2">
                    <matrix>1 0 0 120 0 1 0 0 0 0 1 0 0 0 0 1</matrix>
                    <instance_node url="#ID3" />
                </node>
            </node>
        </visual_scene>
    </library_visual_scenes>
    <library_nodes>
        <node id="ID3" name="cube_component">
            <instance_geometry url="#ID4">
                <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="#ID12">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#ID13">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                        </instance_material>
                    </technique_common>
                </bind_material>
            </instance_geometry>
            <instance_geometry url="#ID20">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#ID21">
                            <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 id="ID4">
            <mesh>
                <source id="ID7">
                    <float_array id="ID10" count="48">39.37007874015748 39.37007874015748 0 0 0 0 0 39.37007874015748 0 39.37007874015748 0 0 0 39.37007874015748 39.37007874015748 39.37007874015748 39.37007874015748 0 0 39.37007874015748 0 39.37007874015748 39.37007874015748 39.37007874015748 39.37007874015748 39.37007874015748 0 39.37007874015748 0 39.37007874015748 39.37007874015748 0 0 39.37007874015748 39.37007874015748 39.37007874015748 39.37007874015748 0 39.37007874015748 0 39.37007874015748 39.37007874015748 0 0 39.37007874015748 39.37007874015748 39.37007874015748 39.37007874015748</float_array>
                    <technique_common>
                        <accessor count="16" source="#ID10" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                        </accessor>
                    </technique_common>
                </source>
                <source id="ID8">
                    <float_array id="ID11" count="48">0 0 -1 0 0 -1 0 0 -1 0 0 -1 0 1 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1</float_array>
                    <technique_common>
                        <accessor count="16" source="#ID11" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                        </accessor>
                    </technique_common>
                </source>
                <vertices id="ID9">
                    <input semantic="POSITION" source="#ID7" />
                    <input semantic="NORMAL" source="#ID8" />
                </vertices>
                <triangles count="8" material="Material2">
                    <input offset="0" semantic="VERTEX" source="#ID9" />
                    <p>0 1 2 1 0 3 4 5 6 5 4 7 8 9 10 9 8 11 12 13 14 13 12 15</p>
                </triangles>
            </mesh>
        </geometry>
        <geometry id="ID12">
            <mesh>
                <source id="ID15">
                    <float_array id="ID18" count="12">39.37007874015748 0 39.37007874015748 0 0 0 39.37007874015748 0 0 0 0 39.37007874015748</float_array>
                    <technique_common>
                        <accessor count="4" source="#ID18" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                        </accessor>
                    </technique_common>
                </source>
                <source id="ID16">
                    <float_array id="ID19" count="12">-0 -1 -0 -0 -1 -0 -0 -1 -0 -0 -1 -0</float_array>
                    <technique_common>
                        <accessor count="4" source="#ID19" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                        </accessor>
                    </technique_common>
                </source>
                <vertices id="ID17">
                    <input semantic="POSITION" source="#ID15" />
                    <input semantic="NORMAL" source="#ID16" />
                </vertices>
                <triangles count="2" material="Material2">
                    <input offset="0" semantic="VERTEX" source="#ID17" />
                    <p>0 1 2 1 0 3</p>
                </triangles>
            </mesh>
        </geometry>
        <geometry id="ID20">
            <mesh>
                <source id="ID23">
                    <float_array id="ID26" count="12">0 39.37007874015748 39.37007874015748 0 0 0 0 0 39.37007874015748 0 39.37007874015748 0</float_array>
                    <technique_common>
                        <accessor count="4" source="#ID26" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                        </accessor>
                    </technique_common>
                </source>
                <source id="ID24">
                    <float_array id="ID27" count="12">-1 0 0 -1 0 0 -1 0 0 -1 0 0</float_array>
                    <technique_common>
                        <accessor count="4" source="#ID27" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                        </accessor>
                    </technique_common>
                </source>
                <vertices id="ID25">
                    <input semantic="POSITION" source="#ID23" />
                    <input semantic="NORMAL" source="#ID24" />
                </vertices>
                <triangles count="2" material="Material2">
                    <input offset="0" semantic="VERTEX" source="#ID25" />
                    <p>0 1 2 1 0 3</p>
                </triangles>
            </mesh>
        </geometry>
    </library_geometries>
    <library_materials>
        <material id="ID6" name="material">
            <instance_effect url="#ID5" />
        </material>
        <material id="ID13" name="Color_005_">
            <instance_effect url="#ID14" />
        </material>
        <material id="ID21" name="Color_A06_">
            <instance_effect url="#ID22" />
        </material>
    </library_materials>
    <library_effects>
        <effect id="ID5">
            <profile_COMMON>
                <technique sid="COMMON">
                    <lambert>
                        <diffuse>
                            <color>0 0 1 1</color>
                        </diffuse>
                    </lambert>
                </technique>
            </profile_COMMON>
        </effect>
        <effect id="ID14">
            <profile_COMMON>
                <technique sid="COMMON">
                    <lambert>
                        <diffuse>
                            <color>0 1 0 1</color>
                        </diffuse>
                    </lambert>
                </technique>
            </profile_COMMON>
        </effect>
        <effect id="ID22">
            <profile_COMMON>
                <technique sid="COMMON">
                    <lambert>
                        <diffuse>
                            <color>0.8 0 0 1</color>
                        </diffuse>
                    </lambert>
                </technique>
            </profile_COMMON>
        </effect>
    </library_effects>
    <scene>
        <instance_visual_scene url="#ID1" />
    </scene>
</COLLADA>
ColladaPlay06

AstroBoyWalk

While searching for an executable COLLADA (.dae) file that illustrates most of the 3D-animation features that I am most interested in and at the same time is relatively simple/short, I came to appreciate that astroBoy_walk is a model that has served as a reasonably good teaching example for the visualization/gaming community over the past ∼decade. I first found the relevant (approximately 5000-line) COLLADA file — named, astroBoy_walk.dae— in a github repository hosted by @jtasn001. Using a repetitive sequence of copy-and-paste strokes — transferring about 60 lines of code at a time — I generated a duplicate of this COLLADA file on my Mac. (Initially, I made one copy/paste mistake; but, thankfully, a second careful perusal through my Mac file identified the error and it was easy to fix.) On my Mac, the filename is: /Dropbox/3Dviewers/astroBoy/JoelBoyWalk02.dae.

Amazingly, when I opened this .dae file inside the Mac's Preview app, a properly constructed 3D astroBoy appeared — absent its associated, colorful texture map. By clicking on/dragging across the Preview window, I was immediately able to view the 3D model from all sides. When I moved the mouse across the lowest segment of the Preview window, a set of stop/play buttons appeared; when I clicked the play button, astroBoy started walking! This was quite exciting, as it meant that in principle I had in-hand a readable & executable COLLADA file that would serve to teach me many essential — and sometimes, subtle — aspects of modern 3D animation/gaming techniques!

NOTE: After joining github on 12 September 2019, I was able to directly download the astroBoy_walk.dae COLLADA file from the @jtasn001 github repository — bypassing the tedious, time-consuming, and error-susceptible copy-and-paste steps. I was also able to directly download from this same repository the boy_10.tga image file that is used by the animation/gaming community as a default, purple & gold texture map for astroBoy. (See Wikipedia's history of .tga file format.)

Immediately below, in the scrolling text window of Example #5, I have highlighted the <xml>-based instructional statements that appear throughout the astroBoy_walk.dae COLLADA file. The results of this initial analysis of the model file should aid my efforts to focus on the visualization tasks that are accomplished in separate, individual subsections of the code.

Example #5 — Initial Analysis of astroBoy_walk.dae
<?xml version="1.0" encoding="utf-8"?>
<COLLADA xmlns="http://www.collada.org/2005/11/COLLADASchema" version="1.4.1">
  <asset>
    <contributor>
      <author>lwong</author>
      <authoring_tool>Maya2008 | ColladaMaya v3.04E</authoring_tool>
      <copyright>
Copyright 2008 Sony Computer Entertainment Inc.
Licensed under the Creative Commons Attribution Noncommercial Share Alike license.
See license file or www.creativecommons.org for details.
      </copyright>
    </contributor>
    <created>2008-06-18T18:16:41Z</created>
    <modified>2008-06-18T18:16:41Z</modified>
    <unit meter="0.01" name="centimeter"/>
    <up_axis>Y_UP</up_axis>
  </asset>
  <library_animations>
    <animation id="spine01.blendParent1"> <!-- Line 21 of 4968 -->
      <source id="spine01.blendParent1_astroBoy_newSkeleton_spine01_blendParent1-input">
        <float_array id="spine01.blendParent1_astroBoy_newSkeleton_spine01_blendParent1-input-array" count="26">
...
      </source>
      <source id="spine01.blendParent1_astroBoy_newSkeleton_spine01_blendParent1-output">
        <float_array id="spine01.blendParent1_astroBoy_newSkeleton_spine01_blendParent1-input-array" count="26">
...
      </source>
      <source id="spine01.blendParent1_astroBoy_newSkeleton_spine01_blendParent1-interpolations">
        <Name_array id="spine01.blendParent1_astroBoy_newSkeleton_spine01_blendParent1-interpolations-array" count="26">
...
      </source>
      <source id="spine01.blendParent1_astroBoy_newSkeleton_spine01_blendParent1-intangents">
        <float_array id="spine01.blendParent1_astroBoy_newSkeleton_spine01_blendParent1-intangents-array" count="52">
...
      </source>
      <source id="spine01.blendParent1_astroBoy_newSkeleton_spine01_blendParent1-outtangents">
        <float_array id="spine01.blendParent1_astroBoy_newSkeleton_spine01_blendParent1-outtangents-array" count="52">
...
      </source>
      <sampler id="spine01.blendParent1_astroBoy_newSkeleton_spine01_blendParent1-sampler">
...
      </sampler>
      <channel source="#spine01.blendParent1_astroBoy_newSkeleton_spine01_blendParent1-sampler" target="astroBoy_newSkeleton_spine01/blendParent1"/>
    </animation> <!-- Line 76 of 4968 -->
...
<!-- Multiple <animation> subsections THRU line #3557 
<animation id="spine01.blendParent1">count = 26, Lines 21 - 76.
<animation id="root.translate">count = 26, Lines 77 - 142
<animation id="root.rotateX">count = 26, Lines 143 - 199
<animation id="root.rotateY">count = 26, Lines 200 - 256
<animation id="root.rotateZ">count = 26, Lines 257 - 314
<animation id="spine01.rotateX">count = 26, Lines 315 - 371
<animation id="spine01.rotateY">count = 26, Lines 372 - 429
<animation id="spine01.rotateZ">count = 26, LInes 430 - 486
<animation id="spine02.rotateX">count = 26, Lines 487 - 543
<animation id="spine02.rotateY">count = 26, Lines 544 - 600
<animation id="spine02.rotateZ">count = 26, Lines 601 - 658
<animation id="neck01.rotateX">count = 26, Lines 659 - 715
<animation id="neck01.rotateY">count = 26, Lines 716 - 772
<animation id="neck01.rotateZ">count = 26, Lines 773 - 829
<animation id="head.rotateX">count = 26, Lines 830 - 886
<animation id="head.rotateY">count = 26, Lines 887 - 944
<animation id="head.rotateZ">count = 26, Lines 945 - 1001
<animation id="L_clavicle.rotateX">count = 26, Lines 1002 - 1058
<animation id="L_clavicle.rotateY">count = 26, Lines 1059 - 1115
<animation id="L_clavicle.rotateZ">count = 26, Lines 1116 - 1173
<animation id="L_shoulder.rotateX">count = 26, Lines 1174 - 1230
<animation id="L_shoulder.rotateY">count = 26, Lines 1231 - 1287
<animation id="L_shoulder.rotateZ">count = 26, Lines 1288 - 1344
<animation id="L_elbow.rotateX">count = 26, Lines 1345 - 1401
<animation id="L_elbow.rotateY">count = 26, Lines 1402 - 1459
<animation id="L_elbow.rotateZ">count = 26, Lines 1460 - 1516
<animation id="L_wrist.rotateZ">count = 26, Lines 1517 - 1573
<animation id="R_clavicle.rotateX">count = 26, Lines 1574 - 1630
<animation id="R_clavicle.rotateY">count = 26, Lines 1631 - 1688
<animation id="R_clavicle.rotateZ">count = 26, Lines 1689 - 1745
<animation id="R_shoulder.rotateX">count = 26, Lines 1746 - 1802
<animation id="R_shoulder.rotateY">count = 26, Lines 1803 - 1859
<animation id="R_shoulder.rotateZ">count = 26, Lines 1860 - 1917
<animation id="R_elbow.rotateX">count = 26, Lines 1918 - 1974
<animation id="R_elbow.rotateY">count = 26, Lines 1975 - 2031
<animation id="R_elbow.rotateZ">count = 26, Lines 2032 - 2088
<animation id="R_wrist.rotateX">count = 26, Lines 2089 - 2146
<animation id="R_wrist.rotateZ">count = 26, Lines 2147 - 2203
<animation id="hips.rotateX"> THRU <animation id="hips.rotateZ">count = 26, Lines 2204 - 2375
<animation id="L_hip.rotateX"> THRU <animation id="L_hip.rotateZ">count = 26, Lines 2376 - 2546
<animation id="L_knee_01.rotateZ">count = 26, Lines 2547 - 2603
<animation id="L_knee_02.rotateZ">count = 26, Lines 2604 - 2661
<animation id="L_ankle.rotateX">  THRU <animation id="L_ankle.rotateZ">count = 26, Lines 2662 - 2832
<animation id="L_toeBall.rotateX"> THRU <animation id="L_toeBall.rotateZ">count = 26, Lines 2833 - 3004
<animation id="R_hip.rotateX"> THRU <animation id="R_hip.rotateZ">count = 26, Lines 3005 - 3176
<animation id="R_knee_01.rotateZ">count = 26, LInes 3177 - 3233
<animation id="R_knee_02.rotateZ">count = 26, Lines 3234 - 3290
<animation id="R_ankle.rotateX"> THRU <animation id="R_ankle.rotateZ">count = 26, Lines 3291 - 3462
<animation id="R_toeBall.rotateX"> THRU <animation id="R_toeBall.rotateZ">count = 26, Lines 3463 - 3634
-->
...
    </animation>
  </library_animations>
  <library_physics_scenes> <!-- Line 3637 of 4968 -->
    <physics_scene id="MayaNativePhysicsScene">
      <technique_common>
        <gravity>0 -980 0</gravity>
        <time_step>0.083</time_step>
      </technique_common>
    </physics_scene>
  </library_physics_scenes>
  <library_lights>
    <light ... pointLightShape1 ...>
    </light>
    <light ... ambientLightShape1 ...>
    </light>
  </library_lights>
  <library_images>
    <image id="file9" name="file9">
      ...
    </image>
  </library_images><!-- THRU line 3687 -->
  <library_materials>
...
  </library_materials>
  <library_effects>
    <effect id="matte-fx">
...
    </effect><!-- THRU line 3782 -->
    <effect id="shiny-fx">
...
    </effect><!-- THRU line 3861 -->
    <effect id="face-fx">
...
    </effect><!-- THRU line 3940 -->
    <effect id="glass-fx">
...
    </effect><!-- THRU line 4019 -->
  </library_effects>
<library_geometries>
    <geometry id="boyShape" name="boyShape">
      <mesh> 
        <source id="boyShape-positions" name="position">
          <float_array id="boyShape-positions-array" count = "7857">                        <!--    3 x 2619 = 7857   -->
          <technique_common>
            <accessor source="#boyShape-positions-array" count="2619" stride="3">
              <param name="X" type="float"/>
              <param name="Y" type="float"/>
              <param name="Z" type="float"/>
            </accessor>
          </technique_common>
        </source>
        <source id="boyShape-normals" name="normal">
          <float_array id="boyShape-normals-array" count="9519">                           <!--    3 x 3173 = 9519   -->
          <technique_common>
            <accessor source="#boyShape-normals-array" count="3173" stride="3">
              <param name="X" type="float"/>
              <param name="Y" type="float"/>
              <param name="Z" type="float"/>
            </accessor>
          </technique_common>
        </source>
        <source id="boyShape-map1" name="map1">
          <float_array id="boyShape-map1-array" count="6444">                              <!--    3 x 2148 = 6444   -->
          <technique_common>
            <accessor source="#boyShape-map1-array" count="3222" stride="2">
              <param name="S" type="float"/>
              <param name="T" type="float"/>
            </accessor>
          </technique_common>
        </source>
        <vertices id="boyShape-vertices">
          <input semantic="POSITION" source="#boyShape-positions"/>
        </vertices>                                                                                                           <!--  Line 4056  -->
        <polylist material="faceSG" count="508">
          <input semantic="VERTEX" source="#boyShape-vertices" offset="0"/>
          <input semantic="NORMAL" source="#boyShape-normals" offset="1"/>
          <input semantic="TEXCOORD" source="#boyShape-map1" offset="2" set="0"/>
          <vcount>
...
          </vcount>
          <p>
...
          </p>
        </polylist>
        <polylist material="glassSG" count="12">
          <input semantic="VERTEX" source="#boyShape-vertices" offset="0"/>
          <input semantic="NORMAL" source="#boyShape-normals" offset="1"/>
          <input semantic="TEXCOORD" source="#boyShape-map1" offset="2" set="0"/>
          <vcount>4 4 4 4 4 4 4 4 4 4 4 4</vcount>
          <p>
...
          </p>
        </polylist>
        <polylist material="shinnySG" count="1454">
          <input semantic="VERTEX" source="#boyShape-vertices" offset="0"/>
          <input semantic="NORMAL" source="#boyShape-normals" offset="1"/>
          <input semantic="TEXCOORD" source="#boyShape-map1" offset="2" set="0"/>
          <vcount>
...
          </vcount>
          <p>
...
          </p>
        </polylist>
        <polylist material="matteSG" count="574">
          <input semantic="VERTEX" source="#boyShape-vertices" offset="0"/>
          <input semantic="NORMAL" source="#boyShape-normals" offset="1"/>
          <input semantic="TEXCOORD" source="#boyShape-map1" offset="2" set="0"/>
          <vcount>
...
          </vcount>
          <p>
...
          </p>
        </polylist>
      </mesh>
      <extra>
...
      </extra>
    </geometry>
  </library_geometries>                                 <!--   THRU line 4103   -->
  <library_controllers>
    <controller id="boyShape-skin" name="skinCluster1">
      <skin source="#boyShape">
        <bind_shape_matrix>1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1</bind_shape_matrix>
        <source id="boyShape-skin-joints">
...
        </source>
        <source id="boyShape-skin-bind_poses">
...
        </source>
        <source id="boyShape-skin-bind_poses">
          <float_array id="boyShape-skin-bind_poses-array" count="704">
...
          </float_array>
...
        </source>
        <source id="boyShape-skin-weights">
          <float_array id="boyShape-skin-weights-array" count="1160">
...
          </float_array>
...
        </source>
        <joints>
          <input semantic="JOINT" source="#boyShape-skin-joints"/>
          <input semantic="INV_BIND_MATRIX" source="#boyShape-skin-bind_poses"/>
        </joints>
        <vertex_weights count="2619">
          <input semantic="JOINT" source="#boyShape-skin-joints" offset="0"/>
          <input semantic="WEIGHT" source="#boyShape-skin-weights" offset="1"/>
          <vcount> ... </vcounts>
          <v> ... </v>
        </vertex_weights>
      </skin>
    </controller>
  </library_controllers>                                                        <!--   THRU line 4147   -->
  <library_visual_scenes>
    <visual_scene id="VisualSceneNode" name="astroBoy_walkbake">
...
<!-- LOTS OF COMMANDS -->
...
      </visual_scene>
    </library_visual_scenes>                                                        <!--   THRU line 4960   -->
  <scene>
    <instance_physics_scene url="#MayaNativePhysicsScene"/>
    <instance_visual_scene url="#VisualSceneNode"/>
  </scene>
</COLLADA>
astroBoy_walk

Here are a few additional items of note regarding Example #5:

  • Check out …
    • Part 1 of Step by Step Skeletal Animation in C++ and OpenGL, Using COLLADA (circa 2010)
    • Part 2 of Step by Step Skeletal Animation in C++ and OpenGL, Using COLLADA (circa 2010) — especially the subsection titled, "How skeletal Animation Works?"


Whitworth's (1981) Isothermal Free-Energy Surface

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