Difference between revisions of "User:Tohline/ThreeDimensionalConfigurations/MeetsCOLLADAandOculusRiftS"
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</table> | </table> | ||
The subscript "EFE" on Ω and λ means that the relevant frequency is given in units that have been adopted in [<b>[[User:Tohline/Appendix/References#EFE|<font color="red">EFE</font>]]</b>], that is, in units of <math>~[\pi G\rho]^{1 / 2}</math>. In Figure 1a, the yellow circular marker, that has been placed where the pair of purple dashed lines cross, identifies the location of this model in the "c/a versus b/a" | The subscript "EFE" on Ω and λ means that the relevant frequency is given in units that have been adopted in [<b>[[User:Tohline/Appendix/References#EFE|<font color="red">EFE</font>]]</b>], that is, in units of <math>~[\pi G\rho]^{1 / 2}</math>. In Figure 1a, the yellow circular marker, that has been placed where the pair of purple dashed lines cross, identifies the location of this model in the "c/a versus b/a" ''[[User:Tohline/ThreeDimensionalConfigurations/RiemannStype#Fig2|EFE Diagram]]'' that appears as Figure 2 on p. 902 of [http://adsabs.harvard.edu/abs/1965ApJ...142..890C S. Chandrasekhar (1965)]; essentially the same diagram appears in §49 (p. 147) of [<b>[[User:Tohline/Appendix/References#EFE|<font color="red">EFE</font>]]</b>]. | ||
In a [[User:Tohline/ThreeDimensionalConfigurations/JacobiEllipsoids#Jacobi_Ellipsoids|separate chapter]] we have discussed various properties of uniformly rotating, ''Jacobi'' ellipsoids; they are equilibrium configurations that lie along the sequence that runs from "M<sub>2</sub>" (on the b/a = 1, Maclaurin sequence) to the origin of this diagram. Our chosen model lies off of — 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 |Ω<sub>EFE</sub>|, each Lagrangian fluid element inside as well as on the surface of the ellipsoid is traveling retrograde (clockwise) along an elliptical path with a frequency given by |λ<sub>EFE</sub>|. | In a [[User:Tohline/ThreeDimensionalConfigurations/JacobiEllipsoids#Jacobi_Ellipsoids|separate chapter]] we have discussed various properties of uniformly rotating, ''Jacobi'' ellipsoids; they are equilibrium configurations that lie along the sequence that runs from "M<sub>2</sub>" (on the b/a = 1, Maclaurin sequence) to the origin of this diagram. Our chosen model lies off of — 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 |Ω<sub>EFE</sub>|, each Lagrangian fluid element inside as well as on the surface of the ellipsoid is traveling retrograde (clockwise) along an elliptical path with a frequency given by |λ<sub>EFE</sub>|. | ||
Revision as of 21:25, 13 June 2020
Riemann Meets COLLADA & Oculus Rift S
If you want to jump straight to the fun part, copy the ASCII text file that is contained below within the scrollable box named, Inertial17.dae, and read the accompanying instructions regarding how to view this example model on a Mac. A second file — presenting the same example model, but as viewed from a rotating frame of reference — can be extracted from a separate scrollable box named, MultiLagrange18.dae.
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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 |
|
<math>~\frac{b}{a} = 0.41</math> |
|
Figure 1b |
||
|
<math>~\frac{c}{a} = 0.385</math> |
||||||
|
Direct |
|
Adjoint |
||||
|
<math>~\Omega_\mathrm{EFE} = 0.547874</math> |
<math>~\Omega_\mathrm{EFE} = - 0.079886</math> |
|||||
|
<math>~\lambda_\mathrm{EFE} = 0.079886</math> |
<math>~\lambda_\mathrm{EFE} = - 0.547874</math> |
|||||
|
<math>~f = - 0.415418</math> |
<math>~f = - 19.53923</math> |
|||||
The subscript "EFE" on Ω and λ means that the relevant frequency is given in units that have been adopted in [EFE], that is, in units of <math>~[\pi G\rho]^{1 / 2}</math>. In Figure 1a, the yellow circular marker, that has been placed where the pair of purple dashed lines cross, identifies the location of this model in the "c/a versus b/a" EFE Diagram that appears as Figure 2 on p. 902 of S. Chandrasekhar (1965); essentially the same diagram appears in §49 (p. 147) of [EFE].
In a separate chapter we have discussed various properties of uniformly rotating, Jacobi ellipsoids; they are equilibrium configurations that lie along the sequence that runs from "M2" (on the b/a = 1, Maclaurin sequence) to the origin of this diagram. Our chosen model lies off of — just above — the Jacobi-ellipsoid sequence, which means that it is not rotating as a solid body. Instead, as we focus first on the direct (as opposed to the adjoint) configuration, we appreciate that while the ellipsoid is spinning prograde (counter-clockwise) with a frequency given by |ΩEFE|, each Lagrangian fluid element inside as well as on the surface of the ellipsoid is traveling retrograde (clockwise) along an elliptical path with a frequency given by |λEFE|.
The COLLADA Code & Initial 3D Scene
The following scrollable box titled, Inertial17.dae, contains an <xml>-formatted COLLADA code that, when properly executed, uses the interactive, 3D animation capabilities of video game drivers to illustrate, in a quantitatively precise fashion, the dynamical flows that are associated with our chosen example model of an equilibrium S-type Riemann ellipsoid. On a Macintosh computer platform, all of the features of this animated and interactive model can be accessed by simply opening the file using Apple's in-house "Preview" application. Figure 1b provides a snapshot of the Preview app's window immediately (TIME = 0.0) after the COLLADA code has been read into the app. More elements of this 3D visual scene will be identified and discussed below, but for now we simply point out that the center of the opaque, purple ellipsoid coincides with the origin of the principal underlying "laboratory" coordinate frame — that is, at (X0, Y0, Z0) = (0, 0, 0) — and the ellipsoid has the desired axis ratios (b/a, c/a) = (0.41, 0.385).
Inertial17.dae … a COLLADA code containing 7968 lines of <xml>-formatted ASCII text
<?xml version="1.0" encoding="UTF-8" standalone="no" ?>
<COLLADA xmlns="http://www.collada.org/2005/11/COLLADASchema" version="1.4.1">
<asset>
<contributor>
<author>jet53man</author>
<authoring_tool>Raw XML</authoring_tool>
</contributor>
<created>2020-04-28</created>
<modified>2020-05-20</modified>
<unit meter="0.0254" name="inch" />
<up_axis>Z_UP</up_axis>
<!--
This file originally was named FullLast45X.dae ...
here its assigned name is Inertial17.dae (etc.)
we are inserting various objects, drawn from b41c385_DI.dae
<node> <geometry> <material> <effect>
*** firstclock: ID3 Clock_OuterEdge ID6 ID5
*** : Clock_InnerEdge InnerID6 InnerID5
*** Jetman : ArrowID3 Clock_ArrowEdge ArrowID6 ArrowID5
*** HourHand : HourID3 Clock_HourEdge HourID6 HourID5
-->
</asset>
<library_effects>
<effect id="DiffusePurple_00">
<profile_COMMON>
<technique sid="COMMON">
<phong>
<diffuse>
<color>0.5 0.0 0.99 1.0</color>
</diffuse>
<transparency>
<float sid="transparency">1.0</float>
</transparency>
</phong>
</technique>
</profile_COMMON>
</effect>
<effect id="DiffuseRed_EFE">
<profile_COMMON>
<technique sid="COMMON">
<lambert>
<diffuse>
<color>1.0 0.0 0.0 1.0</color>
</diffuse>
</lambert>
</technique>
</profile_COMMON>
</effect>
<!-- effect: MidPlane Frame -->
<effect id="MidPlaneID5">
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<lambert>
<diffuse>
<color>0.0 0.0 0.6 0.5</color>
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</profile_COMMON>
</effect>
<!-- effect: Cylindrical Pointer -->
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<lambert>
<diffuse>
<color>0.0 0.0 0.0 1.0</color>
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<lambert>
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<color>1 1 0 1</color>
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<lambert>
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<!-- material: Four Clock Components -->
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<material id="InnerID6" name="Inner_material">
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<instance_effect url="#ArrowID5" />
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<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" />
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<instance_effect url="#MarkersID5" />
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<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" />
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<!-- node: Three clock components -->
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<instance_geometry url="#Clock_OuterEdge">
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<!-- node: MidPlane Frame -->
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<instance_geometry url="#EquatorialPlane">
<bind_material>
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<instance_material symbol="Material2" target="#MidPlaneID6">
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<!-- node: Cylindrical Pointer -->
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<instance_geometry url="#Cylinder">
<bind_material>
<technique_common>
<instance_material symbol="Material2" target="#CylID6">
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<bind_material>
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<instance_material symbol="Material2" target="#ZupID6">
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<!--
**********************************************
*
* Insert first portion of clock's structure
*
**********************************************
-->
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</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" />
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</technique_common>
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<source id="Clock_ArrowNormals">
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<technique_common>
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<param name="X" type="float" />
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<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"/>
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</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" />
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<param name="X" type="float" />
<param name="Y" type="float" />
<param name="Z" type="float" />
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<vertices id="Clock_HourVertices">
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</vertices>
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<input semantic="VERTEX" source="#Clock_HourVertices" offset="0" />
<input semantic="NORMAL" source="#Clock_HourNormals" offset="1"/>
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</mesh>
</geometry>
<!-- geometry: Letters -->
<geometry id="CubeID4">
<mesh>
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0.5 -0.5 -0.5
0.5 -0.5 0.5
0.5 0.5 -0.5
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<technique_common>
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<param name="X" type="float" />
<param name="Y" type="float" />
<param name="Z" type="float" />
</accessor>
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<source id="CubeID8_Normals">
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0 0 1
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<param name="X" type="float" />
<param name="Y" type="float" />
<param name="Z" type="float" />
</accessor>
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<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>
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</mesh>
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<geometry id="DiagonalID4">
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0.5 -0.5 -0.5
0.5 -0.5 0.5
0.5 0.5 -0.5
0.5 0.5 0.5
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<technique_common>
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<param name="X" type="float" />
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<param name="Z" type="float" />
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</source>
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<technique_common>
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<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" />
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<p>
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0 4 3 4 2 4 4 5 6 5 7 5
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</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
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0.5 -0.5 -0.5
0.5 -0.5 0.5
0.5 0.5 -0.5
0.5 0.5 0.5
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<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">
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0 0 -1
0 0 1
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</float_array>
<technique_common>
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<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" />
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<p>
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</p>
</polylist>
</mesh>
</geometry>
<!-- geometry: Cylindrical Pointer -->
<geometry id="Cylinder">
<mesh>
<source id="Cyl_Positions">
<float_array id="CylCoords01" count="54">
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1.0 -0.3827 0.9239
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1.0 -0.3827 -0.9239
1.0 -0.9239 -0.3827
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</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">
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0.0 1.0 0.0
0.0 -1.0 0.0
0.0 0.0 1.0
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0.0 0.7071 0.7071
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<technique_common>
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<param name="X" type="float" />
<param name="Y" type="float" />
<param name="Z" type="float" />
</accessor>
</technique_common>
</source>
<vertices id="Cyl_Vertices">
<input semantic="POSITION" source="#Cyl_Positions" />
</vertices>
<polylist count="32" material="Material2">
<input semantic="VERTEX" source="#Cyl_Vertices" offset="0" />
<input semantic="NORMAL" source="#Cyl_Normals" offset="1" />
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<p>
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3 1 4 1 8 1
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5 1 6 1 8 1
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11 11 10 11 17 11
12 12 11 12 17 12
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</p>
</polylist>
</mesh>
</geometry>
<!--
**********************************************
*
* Insert Geometry of Ellipsoid Octant
*
**********************************************
-->
<geometry id="EllipsoidOctant">
<mesh>
<source id="Ellipsoid_Positions">
<float_array id="Ellipsoid_Coordinates" count=" 1563">
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</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">
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</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>
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</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
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5.0
5.0
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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
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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
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</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
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-0.1509
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</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
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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
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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">
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253.125
251.25
249.375
247.5
245.625
243.75
241.875
240.0
238.125
236.25
234.375
232.5
230.625
228.75
226.875
225.0
223.125
221.25
219.375
217.5
215.625
213.75
211.875
210.0
208.125
206.25
204.375
202.5
200.625
198.75
196.875
195.0
193.125
191.25
189.375
187.5
185.625
183.75
181.875
180.0
178.125
176.25
174.375
172.5
170.625
168.75
166.875
165.0
163.125
161.25
159.375
157.5
155.625
153.75
151.875
150.0
148.125
146.25
144.375
142.5
140.625
138.75
136.875
135.0
133.125
131.25
129.375
127.5
125.625
123.75
121.875
120.0
118.125
116.25
114.375
112.5
110.625
108.75
106.875
105.0
103.125
101.25
99.375
97.5
95.625
93.75
91.875
90.0
88.125
86.25
84.375
82.5
80.625
78.75
76.875
75.0
73.125
71.25
69.375
67.5
65.625
63.75
61.875
60.0
58.125
56.25
54.375
52.5
50.625
48.75
46.875
45.0
43.125
41.25
39.375
37.5
35.625
33.75
31.875
30.0
28.125
26.25
24.375
22.5
20.625
18.75
16.875
15.0
13.125
11.25
9.375
7.5
5.625
3.75
1.875
0.0
-1.875
-3.75
</float_array>
<technique_common>
<accessor source="#HourHand_euler_Z-output-array" count=" 147" stride="1">
<param name="ANGLE" type="float"/>
</accessor>
</technique_common>
</source>
<sampler id="HourHand_euler_Z-sampler">
<input semantic="INPUT" source="#HourHand_euler_Z-input"/>
<input semantic="OUTPUT" source="#HourHand_euler_Z-output"/>
</sampler>
<channel source="#HourHand_euler_Z-sampler" target="HourHand/rotationZ.ANGLE"/>
</animation>
</library_animations>
<library_controllers/>
<library_visual_scenes>
<visual_scene id="ID1">
<node id="EntireEllipsoid" name="OculusRift_EFE">
<translate>0.0 0.0 0.0</translate>
<rotate sid="rotationX">1.0 0.0 0.0 0.0</rotate>
<rotate sid="rotationY">0.0 1.0 0.0 0.0</rotate>
<rotate sid="rotationZ">0.0 0.0 1.0 3.0</rotate>
<scale sid="scale">5.0 5.0 5.0</scale>
<node id="First" name="First_instance_EFE">
<translate>0.0 0.0 0.0</translate>
<rotate sid="rotationX">1.0 0.0 0.0 0.0</rotate>
<rotate sid="rotationY">0.0 1.0 0.0 0.0</rotate>
<rotate sid="rotationZ">0.0 0.0 1.0 0.0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<instance_node url="#ID3_EFE" />
</node>
<node id="Second" name="Second_instance_EFE">
<translate>0.0 0.0 0.0</translate>
<rotate sid="rotationX">1.0 0.0 0.0 180.0</rotate>
<rotate sid="rotationY">0.0 1.0 0.0 0.0</rotate>
<rotate sid="rotationZ">0.0 0.0 1.0 0.0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<instance_node url="#ID3_EFE" />
</node>
<node id="Third" name="Third_instance_EFE">
<translate>0.0 0.0 0.0</translate>
<rotate sid="rotationX">1.0 0.0 0.0 0.0</rotate>
<rotate sid="rotationY">0.0 1.0 0.0 180.0</rotate>
<rotate sid="rotationZ">0.0 0.0 1.0 0.0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<instance_node url="#ID3_EFE" />
</node>
<node id="Fourth" name="Fourth_instance_EFE">
<translate>0.0 0.0 0.0</translate>
<rotate sid="rotationX">1.0 0.0 0.0 180.0</rotate>
<rotate sid="rotationY">0.0 1.0 0.0 180.0</rotate>
<rotate sid="rotationZ">0.0 0.0 1.0 0.0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<instance_node url="#ID3_EFE" />
</node>
<!-- instance: Cylindrical Pointer -->
<node id="CylinderPointer" name="instance_cylinder">
<translate sid="location">-1.0 0.0 0.0</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 180</rotate>
<scale sid="scale">0.05 0.025 0.025</scale>
<instance_node url="#CylPointer" />
</node>
<!-- Begin LAGRANGE markers -->
<node id="Lagrange01" name="instance_Lagrange01">
<translate sid="location">1.0000 0.0000 0.0</translate>
<rotate sid="rotationX">1.0 0.0 0.0 0.0</rotate>
<rotate sid="rotationY">0.0 1.0 0.0 0.0</rotate>
<rotate sid="rotationZ">0.0 0.0 1.0 0.0</rotate>
<scale sid="scale">0.075 0.075 0.075</scale>
<instance_node url="#Primary_MarkerID3" />
</node>
<node id="Marker01" name="instance_marker01">
<matrix>0.025 0.0 0.0 1.0000 0.0 0.025 0.0 -0.0000 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker02" name="instance_marker02">
<matrix>0.025 0.0 0.0 0.9921 0.0 0.025 0.0 -0.0514 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker03" name="instance_marker03">
<matrix>0.025 0.0 0.0 0.9686 0.0 0.025 0.0 -0.1020 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker04" name="instance_marker04">
<matrix>0.025 0.0 0.0 0.9298 0.0 0.025 0.0 -0.1509 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker05" name="instance_marker05">
<matrix>0.025 0.0 0.0 0.8763 0.0 0.025 0.0 -0.1975 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker06" name="instance_marker06">
<matrix>0.025 0.0 0.0 0.8090 0.0 0.025 0.0 -0.2410 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker07" name="instance_marker07">
<matrix>0.025 0.0 0.0 0.7290 0.0 0.025 0.0 -0.2807 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker08" name="instance_marker08">
<matrix>0.025 0.0 0.0 0.6374 0.0 0.025 0.0 -0.3159 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker09" name="instance_marker09">
<matrix>0.025 0.0 0.0 0.5358 0.0 0.025 0.0 -0.3462 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker10" name="instance_marker10">
<matrix>0.025 0.0 0.0 0.4258 0.0 0.025 0.0 -0.3710 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker11" name="instance_marker11">
<matrix>0.025 0.0 0.0 0.3090 0.0 0.025 0.0 -0.3899 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker12" name="instance_marker12">
<matrix>0.025 0.0 0.0 0.1874 0.0 0.025 0.0 -0.4027 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker13" name="instance_marker13">
<matrix>0.025 0.0 0.0 0.0628 0.0 0.025 0.0 -0.4092 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker14" name="instance_marker14">
<matrix>0.025 0.0 0.0 -0.0628 0.0 0.025 0.0 -0.4092 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker15" name="instance_marker15">
<matrix>0.025 0.0 0.0 -0.1874 0.0 0.025 0.0 -0.4027 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker16" name="instance_marker16">
<matrix>0.025 0.0 0.0 -0.3090 0.0 0.025 0.0 -0.3899 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker17" name="instance_marker17">
<matrix>0.025 0.0 0.0 -0.4258 0.0 0.025 0.0 -0.3710 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker18" name="instance_marker18">
<matrix>0.025 0.0 0.0 -0.5358 0.0 0.025 0.0 -0.3462 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker19" name="instance_marker19">
<matrix>0.025 0.0 0.0 -0.6374 0.0 0.025 0.0 -0.3159 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker20" name="instance_marker20">
<matrix>0.025 0.0 0.0 -0.7290 0.0 0.025 0.0 -0.2807 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker21" name="instance_marker21">
<matrix>0.025 0.0 0.0 -0.8090 0.0 0.025 0.0 -0.2410 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker22" name="instance_marker22">
<matrix>0.025 0.0 0.0 -0.8763 0.0 0.025 0.0 -0.1975 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker23" name="instance_marker23">
<matrix>0.025 0.0 0.0 -0.9298 0.0 0.025 0.0 -0.1509 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker24" name="instance_marker24">
<matrix>0.025 0.0 0.0 -0.9686 0.0 0.025 0.0 -0.1020 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker25" name="instance_marker25">
<matrix>0.025 0.0 0.0 -0.9921 0.0 0.025 0.0 -0.0514 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker26" name="instance_marker26">
<matrix>0.025 0.0 0.0 -1.0000 0.0 0.025 0.0 -0.0000 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<!-- Second Half -->
<node id="Marker28" name="instance_marker28">
<matrix>0.025 0.0 0.0 -0.9921 0.0 0.025 0.0 0.0514 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker29" name="instance_marker29">
<matrix>0.025 0.0 0.0 -0.9686 0.0 0.025 0.0 0.1020 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker30" name="instance_marker30">
<matrix>0.025 0.0 0.0 -0.9298 0.0 0.025 0.0 0.1509 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker31" name="instance_marker31">
<matrix>0.025 0.0 0.0 -0.8763 0.0 0.025 0.0 0.1975 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker32" name="instance_marker32">
<matrix>0.025 0.0 0.0 -0.8090 0.0 0.025 0.0 0.2410 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker33" name="instance_marker33">
<matrix>0.025 0.0 0.0 -0.7290 0.0 0.025 0.0 0.2807 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker34" name="instance_marker34">
<matrix>0.025 0.0 0.0 -0.6374 0.0 0.025 0.0 0.3159 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker35" name="instance_marker35">
<matrix>0.025 0.0 0.0 -0.5358 0.0 0.025 0.0 0.3462 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker36" name="instance_marker36">
<matrix>0.025 0.0 0.0 -0.4258 0.0 0.025 0.0 0.3710 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker37" name="instance_marker37">
<matrix>0.025 0.0 0.0 -0.3090 0.0 0.025 0.0 0.3899 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker38" name="instance_marker38">
<matrix>0.025 0.0 0.0 -0.1874 0.0 0.025 0.0 0.4027 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker39" name="instance_marker39">
<matrix>0.025 0.0 0.0 -0.0628 0.0 0.025 0.0 0.4092 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker40" name="instance_marker40">
<matrix>0.025 0.0 0.0 0.0628 0.0 0.025 0.0 0.4092 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker41" name="instance_marker41">
<matrix>0.025 0.0 0.0 0.1874 0.0 0.025 0.0 0.4027 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker42" name="instance_marker42">
<matrix>0.025 0.0 0.0 0.3090 0.0 0.025 0.0 0.3899 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker43" name="instance_marker43">
<matrix>0.025 0.0 0.0 0.4258 0.0 0.025 0.0 0.3710 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker44" name="instance_marker44">
<matrix>0.025 0.0 0.0 0.5358 0.0 0.025 0.0 0.3462 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker45" name="instance_marker45">
<matrix>0.025 0.0 0.0 0.6374 0.0 0.025 0.0 0.3159 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker46" name="instance_marker46">
<matrix>0.025 0.0 0.0 0.7290 0.0 0.025 0.0 0.2807 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker47" name="instance_marker47">
<matrix>0.025 0.0 0.0 0.8090 0.0 0.025 0.0 0.2410 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker48" name="instance_marker48">
<matrix>0.025 0.0 0.0 0.8763 0.0 0.025 0.0 0.1975 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker49" name="instance_marker49">
<matrix>0.025 0.0 0.0 0.9298 0.0 0.025 0.0 0.1509 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker50" name="instance_marker50">
<matrix>0.025 0.0 0.0 0.9686 0.0 0.025 0.0 0.1020 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker51" name="instance_marker51">
<matrix>0.025 0.0 0.0 0.9921 0.0 0.025 0.0 0.0514 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<!-- End LAGRANGE markers -->
</node> <!-- END EntireEllipsoid -->
<node id="Inertial" name="instance_inertial"> <!-- Start Inertial Grouping of Objects -->
<translate>0.0 0.0 0.0</translate>
<rotate sid="rotationX">1.0 0.0 0.0 0.0</rotate>
<rotate sid="rotationY">0.0 1.0 0.0 0.0</rotate>
<rotate sid="rotationZ">0.0 0.0 1.0 3.0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<node id="Zup_Pointer" name="instance_zupPointer">
<translate>0.0 0.0 5.0</translate>
<rotate sid="rotationX">1 0 0 0.0</rotate>
<rotate sid="rotationY">0 1 0 0.0</rotate>
<rotate sid="rotationZ">0 0 1 0.0</rotate>
<scale sid="scale">0.125 0.5 1.5</scale>
<instance_node url="#ZupPointer" />
</node>
<!-- instance: MidPlane Frame (MidPlane flips with rotationX = 180 for clockwise spin)-->
<node id="MidPlane" name="instance_MidPlane">
<translate>0.0 0.0 0.0</translate>
<rotate sid="rotationX">1.0 0.0 0.0 0.0</rotate>
<rotate sid="rotationY">0.0 1.0 0.0 0.0</rotate>
<rotate sid="rotationZ">0.0 0.0 1.0 0.0</rotate>
<scale sid="scale">1.25 1.25 1.25</scale>
<instance_node url="#EqPlane" />
</node>
<!-- BEGIN LABELING HERE -->
<node name="Labels">
<translate>7.0 -2.0 5.0</translate>
<rotate sid="rotationX">1 0 0 0.0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 180</rotate>
<scale sid="scale">0.1 0.1 0.1</scale>
<!-- Equals sign #1 -->
<node name="Equals1">
<translate>0.0 15.0 1.0</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<node id="IDd51" name="instance_51">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 2.4 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDd52" name="instance_52">
<matrix>0.25 0 0 0.0 0 1 0 1.1 0 0 1 2.4 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDd53" name="instance_53">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 2.4 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDd55" name="instance_55">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 4.2 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDd56" name="instance_56">
<matrix>0.25 0 0 0.0 0 1 0 1.1 0 0 1 4.2 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDd57" name="instance_57">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 4.2 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
</node>
<!-- Equals sign #2 -->
<node name="Equals2">
<translate>0.0 15.0 -8.5</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<node id="IDd51" name="instance_51">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 2.4 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDd52" name="instance_52">
<matrix>0.25 0 0 0.0 0 1 0 1.1 0 0 1 2.4 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDd53" name="instance_53">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 2.4 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDd55" name="instance_55">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 4.2 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDd56" name="instance_56">
<matrix>0.25 0 0 0.0 0 1 0 1.1 0 0 1 4.2 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDd57" name="instance_57">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 4.2 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
</node>
<!-- Division sign #1 -->
<node name="Divide1">
<translate>0.0 4.4 1.0</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 0.75 1.0</scale>
<node id="IDd21" name="instance_21">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 0.0 0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
<node id="IDd22" name="instance_22">
<matrix>0.25 0 0 0.0 0 -1 0 1.1 0 0 -1 0.0 0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
<node id="IDd23" name="instance_23">
<matrix>0.25 0 0 0.0 0 1 0 1.1 0 0 1 1.1 0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
<node id="IDd24" name="instance_24">
<matrix>0.25 0 0 0.0 0 -1 0 2.2 0 0 -1 1.1 0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
<node id="IDd25" name="instance_25">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 2.2 0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
<node id="IDd26" name="instance_26">
<matrix>0.25 0 0 0.0 0 -1 0 3.3 0 0 -1 2.2 0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
<node id="IDd27" name="instance_27">
<matrix>0.25 0 0 0.0 0 1 0 3.3 0 0 1 3.3 0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
</node>
<!-- Division sign #2 -->
<node name="Divide2">
<translate>0.0 4.4 -8.5</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 0.75 1.0</scale>
<node id="IDd21" name="instance_21">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 0.0 0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
<node id="IDd22" name="instance_22">
<matrix>0.25 0 0 0.0 0 -1 0 1.1 0 0 -1 0.0 0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
<node id="IDd23" name="instance_23">
<matrix>0.25 0 0 0.0 0 1 0 1.1 0 0 1 1.1 0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
<node id="IDd24" name="instance_24">
<matrix>0.25 0 0 0.0 0 -1 0 2.2 0 0 -1 1.1 0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
<node id="IDd25" name="instance_25">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 2.2 0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
<node id="IDd26" name="instance_26">
<matrix>0.25 0 0 0.0 0 -1 0 3.3 0 0 -1 2.2 0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
<node id="IDd27" name="instance_27">
<matrix>0.25 0 0 0.0 0 1 0 3.3 0 0 1 3.3 0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
</node>
<!-- Letter "a" #1 -->
<node name="Letter_a1">
<translate>0.0 8.0 1.0</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<node id="IDa01" name="instance_1">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 1.1 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa06" name="instance_6">
<matrix>0.25 0 0 0.0 0 1 0 1.1 0 0 1 2.2 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa07" name="instance_7">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 2.2 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa10" name="instance_10">
<matrix>0.25 0 0 0.0 0 1 0 1.1 0 0 1 0.0 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa11" name="instance_11">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 0.0 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa18" name="instance_18">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 2.2 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDa19" name="instance_19">
<matrix>0.25 0 0 0.0 0 0 1 4.4 0 -1 0 0.0 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDa19" name="instance_19">
<matrix>0.25 0 0 0.0 0 0 -1 3.3 0 1 0 0.0 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDa11" name="instance_11">
<matrix>0.25 0 0 0.0 0 1 0 3.3 0 0 1 1.1 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa31" name="instance_11">
<matrix>0.25 0 0 0.0 0 1 0 3.3 0 0 1 2.2 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa20" name="instance_20">
<matrix>0.25 0 0 0.0 0 0 1 3.3 0 -1 0 3.3 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDa21" name="instance_21">
<matrix>0.25 0 0 0.0 0 0 -1 0.0 0 1 0 0.0 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
</node>
<!-- Letter "a" #2 -->
<node name="Letter_a2">
<translate>0.0 8.0 -8.5</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<node id="IDa01" name="instance_1">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 1.1 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa06" name="instance_6">
<matrix>0.25 0 0 0.0 0 1 0 1.1 0 0 1 2.2 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa07" name="instance_7">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 2.2 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa10" name="instance_10">
<matrix>0.25 0 0 0.0 0 1 0 1.1 0 0 1 0.0 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa11" name="instance_11">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 0.0 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa18" name="instance_18">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 2.2 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDa19" name="instance_19">
<matrix>0.25 0 0 0.0 0 0 1 4.4 0 -1 0 0.0 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDa19" name="instance_19">
<matrix>0.25 0 0 0.0 0 0 -1 3.3 0 1 0 0.0 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDa11" name="instance_11">
<matrix>0.25 0 0 0.0 0 1 0 3.3 0 0 1 1.1 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa31" name="instance_11">
<matrix>0.25 0 0 0.0 0 1 0 3.3 0 0 1 2.2 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa20" name="instance_20">
<matrix>0.25 0 0 0.0 0 0 1 3.3 0 -1 0 3.3 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDa21" name="instance_21">
<matrix>0.25 0 0 0.0 0 0 -1 0.0 0 1 0 0.0 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
</node>
<!-- Letter "a" #2 -->
<node name="Letter_a2">
<translate>0.0 8.0 -8.5</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<node id="IDa01" name="instance_1">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 1.1 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa06" name="instance_6">
<matrix>0.25 0 0 0.0 0 1 0 1.1 0 0 1 2.2 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa07" name="instance_7">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 2.2 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa10" name="instance_10">
<matrix>0.25 0 0 0.0 0 1 0 1.1 0 0 1 0.0 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa11" name="instance_11">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 0.0 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa18" name="instance_18">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 2.2 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDa19" name="instance_19">
<matrix>0.25 0 0 0.0 0 0 1 4.4 0 -1 0 0.0 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDa19" name="instance_19">
<matrix>0.25 0 0 0.0 0 0 -1 3.3 0 1 0 0.0 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDa11" name="instance_11">
<matrix>0.25 0 0 0.0 0 1 0 3.3 0 0 1 1.1 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa31" name="instance_11">
<matrix>0.25 0 0 0.0 0 1 0 3.3 0 0 1 2.2 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa20" name="instance_20">
<matrix>0.25 0 0 0.0 0 0 1 3.3 0 -1 0 3.3 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDa21" name="instance_21">
<matrix>0.25 0 0 0.0 0 0 -1 0.0 0 1 0 0.0 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
</node>
<!-- Letter "c" -->
<node name="Letter_c">
<translate>0.0 0.0 -8.5</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<node id="ID001" name="instance_1">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 1.1 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID002" name="instance_2">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 2.2 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID006" name="instance_6">
<matrix>0.25 0 0 0.0 0 1 0 1.1 0 0 1 3.3 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID007" name="instance_7">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 3.3 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID010" name="instance_10">
<matrix>0.25 0 0 0.0 0 1 0 1.1 0 0 1 0.0 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID011" name="instance_11">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 0.0 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID018" name="instance_18">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 3.3 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="ID019" name="instance_19">
<matrix>0.25 0 0 0.0 0 -1 0 3.3 0 0 -1 0.0 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="ID020" name="instance_20">
<matrix>0.25 0 0 0.0 0 0 1 3.3 0 -1 0 3.3 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="ID021" name="instance_21">
<matrix>0.25 0 0 0.0 0 0 -1 0.0 0 1 0 0.0 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
</node>
<!-- Letter "b" ... has 8 + (4 x 15) = 68 lines -->
<node name="Letter_b">
<translate>0.0 0.0 1.0</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<node id="IDb01" name="instance_1">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 1.1 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb02" name="instance_2">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 2.2 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb03" name="instance_3">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 3.3 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb04" name="instance_4">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 4.4 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb05" name="instance_5">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 5.5 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb12" name="instance_12">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 6.6 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb06" name="instance_6">
<matrix>0.25 0 0 0.0 0 1 0 1.1 0 0 1 3.3 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb07" name="instance_7">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 3.3 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb08" name="instance_8">
<matrix>0.25 0 0 0.0 0 1 0 3.3 0 0 1 2.2 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb09" name="instance_9">
<matrix>0.25 0 0 0.0 0 1 0 3.3 0 0 1 1.1 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb10" name="instance_10">
<matrix>0.25 0 0 0.0 0 1 0 1.1 0 0 1 0.0 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb11" name="instance_11">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 0.0 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb19" name="instance_19">
<matrix>0.25 0 0 0.0 0 -1 0 3.3 0 0 -1 0.0 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDb20" name="instance_20">
<matrix>0.25 0 0 0.0 0 0 1 3.3 0 -1 0 3.3 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDb21" name="instance_21">
<matrix>0.25 0 0 0.0 0 0 -1 0.0 0 1 0 0.0 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
</node>
<!-- DECIMAL POINTS -->
<node id="IDD01" name="Decimal_1">
<matrix>0.25 0 0 0.0 0 1 0 25.0 0 0 1 1.0 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDD02" name="Decimal_2">
<matrix>0.25 0 0 0.0 0 1 0 25.0 0 0 1 -8.5 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<!-- Number "0" #1 ... has 8 + (4 x 18) = 80 lines -->
<node name="Number_0">
<translate>0.0 20.0 1.0</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<node id="IDb01" name="instance_1">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 1.1 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb02" name="instance_2">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 2.2 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb03" name="instance_3">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 3.3 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb04" name="instance_4">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 4.4 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb05" name="instance_5">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 5.5 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDz19" name="instance_z19">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 6.6 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDb06" name="instance_6">
<matrix>0.25 0 0 0.0 0 1 0 1.1 0 0 1 6.6 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb07" name="instance_7">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 6.6 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb08" name="instance_8">
<matrix>0.25 0 0 0.0 0 1 0 3.3 0 0 1 2.2 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb09" name="instance_9">
<matrix>0.25 0 0 0.0 0 1 0 3.3 0 0 1 1.1 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb10" name="instance_10">
<matrix>0.25 0 0 0.0 0 1 0 1.1 0 0 1 0.0 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb11" name="instance_11">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 0.0 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb19" name="instance_19">
<matrix>0.25 0 0 0.0 0 -1 0 3.3 0 0 -1 0.0 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDb20" name="instance_20">
<matrix>0.25 0 0 0.0 0 0 1 3.3 0 -1 0 6.6 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDb21" name="instance_21">
<matrix>0.25 0 0 0.0 0 0 -1 0.0 0 1 0 0.0 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDz11" name="instance_z11">
<matrix>0.25 0 0 0.0 0 1 0 3.3 0 0 1 3.3 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDz12" name="instance_z12">
<matrix>0.25 0 0 0.0 0 1 0 3.3 0 0 1 4.4 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDz13" name="instance_z13">
<matrix>0.25 0 0 0.0 0 1 0 3.3 0 0 1 5.5 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
</node>
<!-- Number "0" #2 ... has 8 + (4 x 18) = 80 lines -->
<node name="Number_0b">
<translate>0.0 20.0 -8.5</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<node id="IDb01" name="instance_1">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 1.1 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb02" name="instance_2">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 2.2 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb03" name="instance_3">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 3.3 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb04" name="instance_4">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 4.4 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb05" name="instance_5">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 5.5 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDz19" name="instance_z19">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 6.6 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDb06" name="instance_6">
<matrix>0.25 0 0 0.0 0 1 0 1.1 0 0 1 6.6 0 0 0 1.0</matrix>
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<!-- 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 -->
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<scale sid="scale">1.0 1.0 1.0</scale>
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<instance_node url="#LettersID3" />
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<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" />
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<matrix>0.25 0 0 0.0 0 1 0 3.3 0 0 1 6.6 0 0 0 1.0</matrix>
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<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" />
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<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" />
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<instance_node url="#LettersID3" />
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<scale sid="scale">1.0 1.0 1.0</scale>
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<instance_node url="#LettersID3" />
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<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" />
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<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" />
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<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" />
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<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" />
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<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" />
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<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" -->
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<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" />
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<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" />
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<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 6.6 0 0 0 1.0</matrix>
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<instance_node url="#LettersID3" />
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<instance_node url="#LettersID3" />
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<instance_node url="#LettersID3" />
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<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" />
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<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" />
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<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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<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" />
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<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" />
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<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" />
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<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" />
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<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" />
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<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" />
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<instance_node url="#DiagonalID3" />
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<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" />
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<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" />
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<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" />
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<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" />
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<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" />
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<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" />
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<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" />
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<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" />
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<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" />
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<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" />
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<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 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" />
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<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" />
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<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" />
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<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" />
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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" />
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<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" />
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<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" />
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<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" />
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<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" />
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<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" />
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<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" />
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<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" />
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<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" />
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<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" />
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<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" />
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<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" />
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<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 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" />
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<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" />
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<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:
Instructions for Viewing the Example Model on a Windows 10 PC:
|
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:
- We use the motion of the hands on the wall-mounted clock to identify the natural oscillation frequency of the physical system, namely, <math>~\Omega_0 \equiv [\pi G \rho]^{1 / 2}</math>. More specifically, by declaration, one oscillation period of the red "minute" hand — that is to say, one wall-clock "hour" — is <math>~P_0 = 2\pi[\pi G \rho]^{-1 / 2} = [4\pi/(G \rho)]^{1 / 2}</math>. One full cycle of the wall-clock's black "hour" hand is therefore 12P0. For pedagogical purposes, in all of our COLLADA-driven animations we have equated P0 with a COLLADA TIME interval of 4.0, which means that during each animation, one wall-clock hour passes every (approximately) 4 seconds of real time.‡
- The purple ellipsoid spins in a prograde direction about its shortest axis — that is, about the Z0-axis — on a timescale set by the value of <math>~\Omega_\mathrm{EFE}</math>, which has already been normalized to Ω0. Specifically, as viewed from the inertial frame of reference, the ellipsoid will complete one full spin in a time, <math>~P_\mathrm{spin} = |\Omega_\mathrm{EFE}|^{-1} = [0.5479]^{-1} = 1.825</math> wall-clock hours, which is approximately 7.3 seconds of real time.
- As viewed from a frame of reference that is spinning with the ellipsoid, each Lagrangian fluid element inside as well as on the surface of the ellipsoid moves in a retro-grade direction along an elliptical trajectory that has the same ellipticity as does the equatorial surface of the 3D ellipsoid. Each and every Lagrangian fluid element completes one full elliptical orbit in a time, <math>~P_\mathrm{Lagrange} = \lambda_\mathrm{EFE}^{-1} = [0.0799]^{-1} = 12.52</math> wall-clock hours, which is about 50 seconds of real time.
In the COLLADA-based code (Inertial17.dae) that has been provided above in the scrollable box, we have instructed the animation sequence to follow the system's evolution through five complete spins of the purple ellipsoid. (Unless the pause button is clicked, the animation will actually loop repeatedly, but the time on the wall-mounted clock will reset to 0h0m after every fifth spin period.) In practice, this animation sequence lasts (5 × 1.825) × 4 = 36.5 seconds of real time.
Figure 2 displays a pair of still-frame images of our example (purple) ellipsoidal configuration after the ellipsoid has completed precisely five (counter-clockwise) spin cycles. (The snapshots have been taken at the same point in time, but from two different camera viewing angles.) In the left-hand image (Figure 2a), the time on the clock appears to be about 9h8m. This means that as the ellipsoid has completed five spin cycles, the "minute" hand of the clock has completed approximately [9 + 8/60] ≈ 9.13 cycles. Dividing this number by 5 gives a value of <math>~P_\mathrm{spin} \approx 1.827</math>, which is indeed the spin period we identified earlier. This illustrates that the proper physical timescales governing oscillations of the wall-mounted clock and of the spinning ellipsoid have been implemented in a quantitatively accurate manner within the COLLADA code.
| Figure 2a | Figure 2b |
|---|---|
|
|
|
In Figure 1b, above, we have used a small red cube to mark the Lagrangian fluid element that is initially (TIME = 0.0) located at the end of the longest axis of the ellipsoid (in the +X direction). In Figure 2b we can see where this fluid element is located after the ellipsoid has completed five complete spins. After moving in a retrograde (clockwise) direction along its assigned elliptical trajectory while the ellipsoid completed five full spins, we see that the red-tagged Lagrangian fluid element has completed a little less than 3/4 of one full orbit; let's call it 73% of one orbit. We therefore infer from the COLLADA-driven animation that <math>~0.73 P_\mathrm{Lagrange}\approx~5 P_\mathrm{spin}</math>, that is, <math>~P_\mathrm{Lagrange}\approx 6.849 P_\mathrm{spin}</math>. This is indeed a proper reflection of the physical properties of our chosen example Riemann S-type ellipsoid, as its mathematically determined equilibrium frequency ratio is, <math>~|\Omega_\mathrm{EFE}|/|\lambda_\mathrm{EFE}| = 6.8582</math>. This, too, illustrates that the proper physical timescales governing oscillations of our chosen example Riemann ellipsoid have been implemented in a quantitatively accurate manner within the COLLADA code.
Rotating Reference Frame
|
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:
- 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.
- 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
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**********************************************
*
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</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">
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<technique_common>
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<param name="X" type="float" />
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<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"/>
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</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" />
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</source>
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<technique_common>
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<param name="X" type="float" />
<param name="Y" type="float" />
<param name="Z" type="float" />
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<vertices id="Clock_HourVertices">
<input semantic="POSITION" source="#Clock_HourPositions" />
</vertices>
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<input semantic="VERTEX" source="#Clock_HourVertices" offset="0" />
<input semantic="NORMAL" source="#Clock_HourNormals" offset="1"/>
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</mesh>
</geometry>
<!-- geometry: Letters -->
<geometry id="CubeID4">
<mesh>
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0.5 -0.5 0.5
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<technique_common>
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<param name="X" type="float" />
<param name="Y" type="float" />
<param name="Z" type="float" />
</accessor>
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</source>
<source id="CubeID8_Normals">
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0 0 1
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<param name="X" type="float" />
<param name="Y" type="float" />
<param name="Z" type="float" />
</accessor>
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<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>
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<geometry id="DiagonalID4">
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0.5 -0.5 -0.5
0.5 -0.5 0.5
0.5 0.5 -0.5
0.5 0.5 0.5
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<technique_common>
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<param name="X" type="float" />
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<param name="Z" type="float" />
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</source>
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<technique_common>
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<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" />
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<p>
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0 4 3 4 2 4 4 5 6 5 7 5
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</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
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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">
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0 0 -1
0 0 1
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</float_array>
<technique_common>
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<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" />
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<p>
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</p>
</polylist>
</mesh>
</geometry>
<!-- geometry: Cylindrical Pointer -->
<geometry id="Cylinder">
<mesh>
<source id="Cyl_Positions">
<float_array id="CylCoords01" count="54">
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1.0 -0.3827 0.9239
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1.0 -0.3827 -0.9239
1.0 -0.9239 -0.3827
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</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">
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-1.0 0.0 0.0
0.0 1.0 0.0
0.0 -1.0 0.0
0.0 0.0 1.0
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0.0 0.7071 0.7071
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<technique_common>
<accessor source="#CylNormals01" count="18" stride="3">
<param name="X" type="float" />
<param name="Y" type="float" />
<param name="Z" type="float" />
</accessor>
</technique_common>
</source>
<vertices id="Cyl_Vertices">
<input semantic="POSITION" source="#Cyl_Positions" />
</vertices>
<polylist count="32" material="Material2">
<input semantic="VERTEX" source="#Cyl_Vertices" offset="0" />
<input semantic="NORMAL" source="#Cyl_Normals" offset="1" />
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<p>
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3 1 4 1 8 1
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5 1 6 1 8 1
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11 11 10 11 17 11
12 12 11 12 17 12
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</p>
</polylist>
</mesh>
</geometry>
<!--
**********************************************
*
* Insert Geometry of Ellipsoid Octant
*
**********************************************
-->
<geometry id="EllipsoidOctant">
<mesh>
<source id="Ellipsoid_Positions">
<float_array id="Ellipsoid_Coordinates" count=" 1563">
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</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
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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">
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</float_array>
<technique_common>
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<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>
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4 4 4 4
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</vcount>
<p>
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</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
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5.0
5.0
5.0
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5.0
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5.0
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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
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1323.0
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1143.0
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603.0
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363.0
303.0
243.0
183.0
123.0
63.0
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</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
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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
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</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">
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</float_array>
<technique_common>
<accessor source="#Lagrange1_location_Y-output-array" count=" 37" stride="1">
<param name="Y" type="float"/>
</accessor>
</technique_common>
</source>
<sampler id="Lagrange1_location_Y-sampler">
<input semantic="INPUT" source="#Lagrange1_location_X-input"/>
<input semantic="OUTPUT" source="#Lagrange1_location_Y-output"/>
</sampler>
<channel source="#Lagrange1_location_X-sampler" target="Lagrange01/location.X"/>
<channel source="#Lagrange1_location_Y-sampler" target="Lagrange01/location.Y"/>
<channel source="#Lagrange1_location_X-sampler" target="Lagrange02/location.X"/>
<channel source="#Lagrange1_location_Y-sampler" target="Lagrange02/location.Y"/>
<channel source="#Lagrange1_location_X-sampler" target="Lagrange03/location.X"/>
<channel source="#Lagrange1_location_Y-sampler" target="Lagrange03/location.Y"/>
</animation>
<!-- CLOCK (clockstop = 36.5047)
One spin of ellipsoid (or frame) is 1.8252 EFE sqrt(pi * G * rho) units;
Want 1 EFE unit to take 4.0 seconds of TIME;
Hence, one spin of ellipsoid (360 degrees) is 7.3009 seconds of TIME;
and 5 ellipsoid spins is 36.5047 seconds of TIME.
Divide one spin (360) into 12 pieces
==> 30 degrees = 1 timestep = 4 x 0.1521 = 0.6084 seconds of TIME.
-->
<animation id="Cube_quaternion_Z">
<source id="Cube_quaternion_Z-input">
<float_array id="Cube_quaternion_Z-input-array" count=" 147">
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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
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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">
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<!-- HOURHAND (clockstop = 36.5047) -->
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<source id="HourHand_euler_Z-output">
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270.0
268.125
266.25
264.375
262.5
260.625
258.75
256.875
255.0
253.125
251.25
249.375
247.5
245.625
243.75
241.875
240.0
238.125
236.25
234.375
232.5
230.625
228.75
226.875
225.0
223.125
221.25
219.375
217.5
215.625
213.75
211.875
210.0
208.125
206.25
204.375
202.5
200.625
198.75
196.875
195.0
193.125
191.25
189.375
187.5
185.625
183.75
181.875
180.0
178.125
176.25
174.375
172.5
170.625
168.75
166.875
165.0
163.125
161.25
159.375
157.5
155.625
153.75
151.875
150.0
148.125
146.25
144.375
142.5
140.625
138.75
136.875
135.0
133.125
131.25
129.375
127.5
125.625
123.75
121.875
120.0
118.125
116.25
114.375
112.5
110.625
108.75
106.875
105.0
103.125
101.25
99.375
97.5
95.625
93.75
91.875
90.0
88.125
86.25
84.375
82.5
80.625
78.75
76.875
75.0
73.125
71.25
69.375
67.5
65.625
63.75
61.875
60.0
58.125
56.25
54.375
52.5
50.625
48.75
46.875
45.0
43.125
41.25
39.375
37.5
35.625
33.75
31.875
30.0
28.125
26.25
24.375
22.5
20.625
18.75
16.875
15.0
13.125
11.25
9.375
7.5
5.625
3.75
1.875
0.0
-1.875
-3.75
</float_array>
<technique_common>
<accessor source="#HourHand_euler_Z-output-array" count=" 147" stride="1">
<param name="ANGLE" type="float"/>
</accessor>
</technique_common>
</source>
<sampler id="HourHand_euler_Z-sampler">
<input semantic="INPUT" source="#HourHand_euler_Z-input"/>
<input semantic="OUTPUT" source="#HourHand_euler_Z-output"/>
</sampler>
<channel source="#HourHand_euler_Z-sampler" target="HourHand/rotationZ.ANGLE"/>
</animation>
</library_animations>
<library_controllers/>
<library_visual_scenes>
<visual_scene id="ID1">
<node id="EntireEllipsoid" name="OculusRift_EFE">
<translate>0.0 0.0 0.0</translate>
<rotate sid="rotationX">1.0 0.0 0.0 0.0</rotate>
<rotate sid="rotationY">0.0 1.0 0.0 0.0</rotate>
<rotate sid="rotationZ">0.0 0.0 1.0 5.0</rotate>
<scale sid="scale">5.0 5.0 5.0</scale>
<node id="First" name="First_instance_EFE">
<translate>0.0 0.0 0.0</translate>
<rotate sid="rotationX">1.0 0.0 0.0 0.0</rotate>
<rotate sid="rotationY">0.0 1.0 0.0 0.0</rotate>
<rotate sid="rotationZ">0.0 0.0 1.0 0.0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<instance_node url="#ID3_EFE" />
</node>
<node id="Second" name="Second_instance_EFE">
<translate>0.0 0.0 0.0</translate>
<rotate sid="rotationX">1.0 0.0 0.0 180.0</rotate>
<rotate sid="rotationY">0.0 1.0 0.0 0.0</rotate>
<rotate sid="rotationZ">0.0 0.0 1.0 0.0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<instance_node url="#ID3_EFE" />
</node>
<node id="Third" name="Third_instance_EFE">
<translate>0.0 0.0 0.0</translate>
<rotate sid="rotationX">1.0 0.0 0.0 0.0</rotate>
<rotate sid="rotationY">0.0 1.0 0.0 180.0</rotate>
<rotate sid="rotationZ">0.0 0.0 1.0 0.0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<instance_node url="#ID3_EFE" />
</node>
<node id="Fourth" name="Fourth_instance_EFE">
<translate>0.0 0.0 0.0</translate>
<rotate sid="rotationX">1.0 0.0 0.0 180.0</rotate>
<rotate sid="rotationY">0.0 1.0 0.0 180.0</rotate>
<rotate sid="rotationZ">0.0 0.0 1.0 0.0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<instance_node url="#ID3_EFE" />
</node>
<!-- instance: Cylindrical Pointer -->
<node id="CylinderPointer" name="instance_cylinder">
<translate sid="location">-1.0 0.0 0.0</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 180</rotate>
<scale sid="scale">0.05 0.025 0.025</scale>
<instance_node url="#CylPointer" />
</node>
<!-- Begin LAGRANGE markers -->
<node id="Lagrange01" name="instance_Lagrange01">
<translate sid="location">1.0000 0.0000 0.0</translate>
<rotate sid="rotationX">1.0 0.0 0.0 0.0</rotate>
<rotate sid="rotationY">0.0 1.0 0.0 0.0</rotate>
<rotate sid="rotationZ">0.0 0.0 1.0 0.0</rotate>
<scale sid="scale">0.06 0.06 0.06</scale>
<instance_node url="#Primary_MarkerID3" />
</node>
<node id="Shrink02" name="instance_Shrink02">
<scale sid="scale">0.8 0.8 0.8</scale>
<node id="Lagrange02" name="instance_Lagrange02">
<translate sid="location">1.0000 0.0000 0.0</translate>
<rotate sid="rotationX">1.0 0.0 0.0 0.0</rotate>
<rotate sid="rotationY">0.0 1.0 0.0 0.0</rotate>
<rotate sid="rotationZ">0.0 0.0 1.0 0.0</rotate>
<scale sid="scale">0.075 0.075 0.075</scale>
<instance_node url="#Primary_MarkerID3" />
</node>
</node>
<node id="Shrink03" name="instance_Shrink03">
<scale sid="scale">0.6 0.6 0.6</scale>
<node id="Lagrange03" name="instance_Lagrange03">
<translate sid="location">1.0000 0.0000 0.0</translate>
<rotate sid="rotationX">1.0 0.0 0.0 0.0</rotate>
<rotate sid="rotationY">0.0 1.0 0.0 0.0</rotate>
<rotate sid="rotationZ">0.0 0.0 1.0 0.0</rotate>
<scale sid="scale">0.1 0.1 0.1</scale>
<instance_node url="#Primary_MarkerID3" />
</node>
</node>
<node id="Marker01" name="instance_marker01">
<matrix>0.025 0.0 0.0 1.0000 0.0 0.025 0.0 -0.0000 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker02" name="instance_marker02">
<matrix>0.025 0.0 0.0 0.9921 0.0 0.025 0.0 -0.0514 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker03" name="instance_marker03">
<matrix>0.025 0.0 0.0 0.9686 0.0 0.025 0.0 -0.1020 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker04" name="instance_marker04">
<matrix>0.025 0.0 0.0 0.9298 0.0 0.025 0.0 -0.1509 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker05" name="instance_marker05">
<matrix>0.025 0.0 0.0 0.8763 0.0 0.025 0.0 -0.1975 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker06" name="instance_marker06">
<matrix>0.025 0.0 0.0 0.8090 0.0 0.025 0.0 -0.2410 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker07" name="instance_marker07">
<matrix>0.025 0.0 0.0 0.7290 0.0 0.025 0.0 -0.2807 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker08" name="instance_marker08">
<matrix>0.025 0.0 0.0 0.6374 0.0 0.025 0.0 -0.3159 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker09" name="instance_marker09">
<matrix>0.025 0.0 0.0 0.5358 0.0 0.025 0.0 -0.3462 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker10" name="instance_marker10">
<matrix>0.025 0.0 0.0 0.4258 0.0 0.025 0.0 -0.3710 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker11" name="instance_marker11">
<matrix>0.025 0.0 0.0 0.3090 0.0 0.025 0.0 -0.3899 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker12" name="instance_marker12">
<matrix>0.025 0.0 0.0 0.1874 0.0 0.025 0.0 -0.4027 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker13" name="instance_marker13">
<matrix>0.025 0.0 0.0 0.0628 0.0 0.025 0.0 -0.4092 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker14" name="instance_marker14">
<matrix>0.025 0.0 0.0 -0.0628 0.0 0.025 0.0 -0.4092 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker15" name="instance_marker15">
<matrix>0.025 0.0 0.0 -0.1874 0.0 0.025 0.0 -0.4027 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker16" name="instance_marker16">
<matrix>0.025 0.0 0.0 -0.3090 0.0 0.025 0.0 -0.3899 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker17" name="instance_marker17">
<matrix>0.025 0.0 0.0 -0.4258 0.0 0.025 0.0 -0.3710 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker18" name="instance_marker18">
<matrix>0.025 0.0 0.0 -0.5358 0.0 0.025 0.0 -0.3462 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker19" name="instance_marker19">
<matrix>0.025 0.0 0.0 -0.6374 0.0 0.025 0.0 -0.3159 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker20" name="instance_marker20">
<matrix>0.025 0.0 0.0 -0.7290 0.0 0.025 0.0 -0.2807 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker21" name="instance_marker21">
<matrix>0.025 0.0 0.0 -0.8090 0.0 0.025 0.0 -0.2410 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker22" name="instance_marker22">
<matrix>0.025 0.0 0.0 -0.8763 0.0 0.025 0.0 -0.1975 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker23" name="instance_marker23">
<matrix>0.025 0.0 0.0 -0.9298 0.0 0.025 0.0 -0.1509 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker24" name="instance_marker24">
<matrix>0.025 0.0 0.0 -0.9686 0.0 0.025 0.0 -0.1020 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker25" name="instance_marker25">
<matrix>0.025 0.0 0.0 -0.9921 0.0 0.025 0.0 -0.0514 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker26" name="instance_marker26">
<matrix>0.025 0.0 0.0 -1.0000 0.0 0.025 0.0 -0.0000 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<!-- Second Half -->
<node id="Marker28" name="instance_marker28">
<matrix>0.025 0.0 0.0 -0.9921 0.0 0.025 0.0 0.0514 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker29" name="instance_marker29">
<matrix>0.025 0.0 0.0 -0.9686 0.0 0.025 0.0 0.1020 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker30" name="instance_marker30">
<matrix>0.025 0.0 0.0 -0.9298 0.0 0.025 0.0 0.1509 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker31" name="instance_marker31">
<matrix>0.025 0.0 0.0 -0.8763 0.0 0.025 0.0 0.1975 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker32" name="instance_marker32">
<matrix>0.025 0.0 0.0 -0.8090 0.0 0.025 0.0 0.2410 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker33" name="instance_marker33">
<matrix>0.025 0.0 0.0 -0.7290 0.0 0.025 0.0 0.2807 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker34" name="instance_marker34">
<matrix>0.025 0.0 0.0 -0.6374 0.0 0.025 0.0 0.3159 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker35" name="instance_marker35">
<matrix>0.025 0.0 0.0 -0.5358 0.0 0.025 0.0 0.3462 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker36" name="instance_marker36">
<matrix>0.025 0.0 0.0 -0.4258 0.0 0.025 0.0 0.3710 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker37" name="instance_marker37">
<matrix>0.025 0.0 0.0 -0.3090 0.0 0.025 0.0 0.3899 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker38" name="instance_marker38">
<matrix>0.025 0.0 0.0 -0.1874 0.0 0.025 0.0 0.4027 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker39" name="instance_marker39">
<matrix>0.025 0.0 0.0 -0.0628 0.0 0.025 0.0 0.4092 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker40" name="instance_marker40">
<matrix>0.025 0.0 0.0 0.0628 0.0 0.025 0.0 0.4092 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker41" name="instance_marker41">
<matrix>0.025 0.0 0.0 0.1874 0.0 0.025 0.0 0.4027 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker42" name="instance_marker42">
<matrix>0.025 0.0 0.0 0.3090 0.0 0.025 0.0 0.3899 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker43" name="instance_marker43">
<matrix>0.025 0.0 0.0 0.4258 0.0 0.025 0.0 0.3710 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker44" name="instance_marker44">
<matrix>0.025 0.0 0.0 0.5358 0.0 0.025 0.0 0.3462 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker45" name="instance_marker45">
<matrix>0.025 0.0 0.0 0.6374 0.0 0.025 0.0 0.3159 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker46" name="instance_marker46">
<matrix>0.025 0.0 0.0 0.7290 0.0 0.025 0.0 0.2807 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker47" name="instance_marker47">
<matrix>0.025 0.0 0.0 0.8090 0.0 0.025 0.0 0.2410 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker48" name="instance_marker48">
<matrix>0.025 0.0 0.0 0.8763 0.0 0.025 0.0 0.1975 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker49" name="instance_marker49">
<matrix>0.025 0.0 0.0 0.9298 0.0 0.025 0.0 0.1509 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker50" name="instance_marker50">
<matrix>0.025 0.0 0.0 0.9686 0.0 0.025 0.0 0.1020 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker51" name="instance_marker51">
<matrix>0.025 0.0 0.0 0.9921 0.0 0.025 0.0 0.0514 0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<!-- End LAGRANGE markers -->
</node> <!-- END EntireEllipsoid -->
<node id="Inertial" name="instance_inertial"> <!-- Start Inertial Grouping of Objects -->
<translate>0.0 0.0 0.0</translate>
<rotate sid="rotationX">1.0 0.0 0.0 0.0</rotate>
<rotate sid="rotationY">0.0 1.0 0.0 0.0</rotate>
<rotate sid="rotationZ">0.0 0.0 1.0 1803.0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<node id="Zup_Pointer" name="instance_zupPointer">
<translate>0.0 0.0 5.0</translate>
<rotate sid="rotationX">1 0 0 0.0</rotate>
<rotate sid="rotationY">0 1 0 0.0</rotate>
<rotate sid="rotationZ">0 0 1 0.0</rotate>
<scale sid="scale">0.125 0.5 1.5</scale>
<instance_node url="#ZupPointer" />
</node>
<!-- instance: MidPlane Frame (MidPlane flips with rotationX = 180 for clockwise spin)-->
<node id="MidPlane" name="instance_MidPlane">
<translate>0.0 0.0 0.0</translate>
<rotate sid="rotationX">1.0 0.0 0.0 0.0</rotate>
<rotate sid="rotationY">0.0 1.0 0.0 0.0</rotate>
<rotate sid="rotationZ">0.0 0.0 1.0 0.0</rotate>
<scale sid="scale">1.25 1.25 1.25</scale>
<instance_node url="#EqPlane" />
</node>
<!-- BEGIN LABELING HERE -->
<node name="Labels">
<translate>7.0 -2.0 5.0</translate>
<rotate sid="rotationX">1 0 0 0.0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 180</rotate>
<scale sid="scale">0.1 0.1 0.1</scale>
<!-- Equals sign #1 -->
<node name="Equals1">
<translate>0.0 15.0 1.0</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<node id="IDd51" name="instance_51">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 2.4 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDd52" name="instance_52">
<matrix>0.25 0 0 0.0 0 1 0 1.1 0 0 1 2.4 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDd53" name="instance_53">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 2.4 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDd55" name="instance_55">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 4.2 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDd56" name="instance_56">
<matrix>0.25 0 0 0.0 0 1 0 1.1 0 0 1 4.2 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDd57" name="instance_57">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 4.2 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
</node>
<!-- Equals sign #2 -->
<node name="Equals2">
<translate>0.0 15.0 -8.5</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<node id="IDd51" name="instance_51">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 2.4 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDd52" name="instance_52">
<matrix>0.25 0 0 0.0 0 1 0 1.1 0 0 1 2.4 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDd53" name="instance_53">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 2.4 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDd55" name="instance_55">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 4.2 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDd56" name="instance_56">
<matrix>0.25 0 0 0.0 0 1 0 1.1 0 0 1 4.2 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDd57" name="instance_57">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 4.2 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
</node>
<!-- Division sign #1 -->
<node name="Divide1">
<translate>0.0 4.4 1.0</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 0.75 1.0</scale>
<node id="IDd21" name="instance_21">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 0.0 0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
<node id="IDd22" name="instance_22">
<matrix>0.25 0 0 0.0 0 -1 0 1.1 0 0 -1 0.0 0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
<node id="IDd23" name="instance_23">
<matrix>0.25 0 0 0.0 0 1 0 1.1 0 0 1 1.1 0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
<node id="IDd24" name="instance_24">
<matrix>0.25 0 0 0.0 0 -1 0 2.2 0 0 -1 1.1 0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
<node id="IDd25" name="instance_25">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 2.2 0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
<node id="IDd26" name="instance_26">
<matrix>0.25 0 0 0.0 0 -1 0 3.3 0 0 -1 2.2 0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
<node id="IDd27" name="instance_27">
<matrix>0.25 0 0 0.0 0 1 0 3.3 0 0 1 3.3 0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
</node>
<!-- Division sign #2 -->
<node name="Divide2">
<translate>0.0 4.4 -8.5</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 0.75 1.0</scale>
<node id="IDd21" name="instance_21">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 0.0 0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
<node id="IDd22" name="instance_22">
<matrix>0.25 0 0 0.0 0 -1 0 1.1 0 0 -1 0.0 0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
<node id="IDd23" name="instance_23">
<matrix>0.25 0 0 0.0 0 1 0 1.1 0 0 1 1.1 0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
<node id="IDd24" name="instance_24">
<matrix>0.25 0 0 0.0 0 -1 0 2.2 0 0 -1 1.1 0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
<node id="IDd25" name="instance_25">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 2.2 0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
<node id="IDd26" name="instance_26">
<matrix>0.25 0 0 0.0 0 -1 0 3.3 0 0 -1 2.2 0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
<node id="IDd27" name="instance_27">
<matrix>0.25 0 0 0.0 0 1 0 3.3 0 0 1 3.3 0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
</node>
<!-- Letter "a" #1 -->
<node name="Letter_a1">
<translate>0.0 8.0 1.0</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<node id="IDa01" name="instance_1">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 1.1 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa06" name="instance_6">
<matrix>0.25 0 0 0.0 0 1 0 1.1 0 0 1 2.2 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa07" name="instance_7">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 2.2 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa10" name="instance_10">
<matrix>0.25 0 0 0.0 0 1 0 1.1 0 0 1 0.0 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa11" name="instance_11">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 0.0 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa18" name="instance_18">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 2.2 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDa19" name="instance_19">
<matrix>0.25 0 0 0.0 0 0 1 4.4 0 -1 0 0.0 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDa19" name="instance_19">
<matrix>0.25 0 0 0.0 0 0 -1 3.3 0 1 0 0.0 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDa11" name="instance_11">
<matrix>0.25 0 0 0.0 0 1 0 3.3 0 0 1 1.1 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa31" name="instance_11">
<matrix>0.25 0 0 0.0 0 1 0 3.3 0 0 1 2.2 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa20" name="instance_20">
<matrix>0.25 0 0 0.0 0 0 1 3.3 0 -1 0 3.3 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDa21" name="instance_21">
<matrix>0.25 0 0 0.0 0 0 -1 0.0 0 1 0 0.0 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
</node>
<!-- Letter "a" #2 -->
<node name="Letter_a2">
<translate>0.0 8.0 -8.5</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<node id="IDa01" name="instance_1">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 1.1 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa06" name="instance_6">
<matrix>0.25 0 0 0.0 0 1 0 1.1 0 0 1 2.2 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa07" name="instance_7">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 2.2 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa10" name="instance_10">
<matrix>0.25 0 0 0.0 0 1 0 1.1 0 0 1 0.0 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa11" name="instance_11">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 0.0 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa18" name="instance_18">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 2.2 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDa19" name="instance_19">
<matrix>0.25 0 0 0.0 0 0 1 4.4 0 -1 0 0.0 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDa19" name="instance_19">
<matrix>0.25 0 0 0.0 0 0 -1 3.3 0 1 0 0.0 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDa11" name="instance_11">
<matrix>0.25 0 0 0.0 0 1 0 3.3 0 0 1 1.1 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa31" name="instance_11">
<matrix>0.25 0 0 0.0 0 1 0 3.3 0 0 1 2.2 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa20" name="instance_20">
<matrix>0.25 0 0 0.0 0 0 1 3.3 0 -1 0 3.3 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDa21" name="instance_21">
<matrix>0.25 0 0 0.0 0 0 -1 0.0 0 1 0 0.0 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
</node>
<!-- Letter "a" #2 -->
<node name="Letter_a2">
<translate>0.0 8.0 -8.5</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<node id="IDa01" name="instance_1">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 1.1 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa06" name="instance_6">
<matrix>0.25 0 0 0.0 0 1 0 1.1 0 0 1 2.2 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa07" name="instance_7">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 2.2 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa10" name="instance_10">
<matrix>0.25 0 0 0.0 0 1 0 1.1 0 0 1 0.0 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa11" name="instance_11">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 0.0 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa18" name="instance_18">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 2.2 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDa19" name="instance_19">
<matrix>0.25 0 0 0.0 0 0 1 4.4 0 -1 0 0.0 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDa19" name="instance_19">
<matrix>0.25 0 0 0.0 0 0 -1 3.3 0 1 0 0.0 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDa11" name="instance_11">
<matrix>0.25 0 0 0.0 0 1 0 3.3 0 0 1 1.1 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa31" name="instance_11">
<matrix>0.25 0 0 0.0 0 1 0 3.3 0 0 1 2.2 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa20" name="instance_20">
<matrix>0.25 0 0 0.0 0 0 1 3.3 0 -1 0 3.3 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDa21" name="instance_21">
<matrix>0.25 0 0 0.0 0 0 -1 0.0 0 1 0 0.0 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
</node>
<!-- Letter "c" -->
<node name="Letter_c">
<translate>0.0 0.0 -8.5</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<node id="ID001" name="instance_1">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 1.1 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID002" name="instance_2">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 2.2 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID006" name="instance_6">
<matrix>0.25 0 0 0.0 0 1 0 1.1 0 0 1 3.3 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID007" name="instance_7">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 3.3 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID010" name="instance_10">
<matrix>0.25 0 0 0.0 0 1 0 1.1 0 0 1 0.0 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID011" name="instance_11">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 0.0 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID018" name="instance_18">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 3.3 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="ID019" name="instance_19">
<matrix>0.25 0 0 0.0 0 -1 0 3.3 0 0 -1 0.0 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="ID020" name="instance_20">
<matrix>0.25 0 0 0.0 0 0 1 3.3 0 -1 0 3.3 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="ID021" name="instance_21">
<matrix>0.25 0 0 0.0 0 0 -1 0.0 0 1 0 0.0 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
</node>
<!-- Letter "b" ... has 8 + (4 x 15) = 68 lines -->
<node name="Letter_b">
<translate>0.0 0.0 1.0</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<node id="IDb01" name="instance_1">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 1.1 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb02" name="instance_2">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 2.2 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb03" name="instance_3">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 3.3 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb04" name="instance_4">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 4.4 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb05" name="instance_5">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 5.5 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb12" name="instance_12">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 6.6 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb06" name="instance_6">
<matrix>0.25 0 0 0.0 0 1 0 1.1 0 0 1 3.3 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb07" name="instance_7">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 3.3 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb08" name="instance_8">
<matrix>0.25 0 0 0.0 0 1 0 3.3 0 0 1 2.2 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb09" name="instance_9">
<matrix>0.25 0 0 0.0 0 1 0 3.3 0 0 1 1.1 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb10" name="instance_10">
<matrix>0.25 0 0 0.0 0 1 0 1.1 0 0 1 0.0 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb11" name="instance_11">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 0.0 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb19" name="instance_19">
<matrix>0.25 0 0 0.0 0 -1 0 3.3 0 0 -1 0.0 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDb20" name="instance_20">
<matrix>0.25 0 0 0.0 0 0 1 3.3 0 -1 0 3.3 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDb21" name="instance_21">
<matrix>0.25 0 0 0.0 0 0 -1 0.0 0 1 0 0.0 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
</node>
<!-- DECIMAL POINTS -->
<node id="IDD01" name="Decimal_1">
<matrix>0.25 0 0 0.0 0 1 0 25.0 0 0 1 1.0 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDD02" name="Decimal_2">
<matrix>0.25 0 0 0.0 0 1 0 25.0 0 0 1 -8.5 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<!-- Number "0" #1 ... has 8 + (4 x 18) = 80 lines -->
<node name="Number_0">
<translate>0.0 20.0 1.0</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<node id="IDb01" name="instance_1">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 1.1 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb02" name="instance_2">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 2.2 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb03" name="instance_3">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 3.3 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb04" name="instance_4">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 4.4 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb05" name="instance_5">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 5.5 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDz19" name="instance_z19">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 6.6 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDb06" name="instance_6">
<matrix>0.25 0 0 0.0 0 1 0 1.1 0 0 1 6.6 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb07" name="instance_7">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 6.6 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb08" name="instance_8">
<matrix>0.25 0 0 0.0 0 1 0 3.3 0 0 1 2.2 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb09" name="instance_9">
<matrix>0.25 0 0 0.0 0 1 0 3.3 0 0 1 1.1 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb10" name="instance_10">
<matrix>0.25 0 0 0.0 0 1 0 1.1 0 0 1 0.0 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb11" name="instance_11">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 0.0 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb19" name="instance_19">
<matrix>0.25 0 0 0.0 0 -1 0 3.3 0 0 -1 0.0 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDb20" name="instance_20">
<matrix>0.25 0 0 0.0 0 0 1 3.3 0 -1 0 6.6 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDb21" name="instance_21">
<matrix>0.25 0 0 0.0 0 0 -1 0.0 0 1 0 0.0 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDz11" name="instance_z11">
<matrix>0.25 0 0 0.0 0 1 0 3.3 0 0 1 3.3 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDz12" name="instance_z12">
<matrix>0.25 0 0 0.0 0 1 0 3.3 0 0 1 4.4 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDz13" name="instance_z13">
<matrix>0.25 0 0 0.0 0 1 0 3.3 0 0 1 5.5 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
</node>
<!-- Number "0" #2 ... has 8 + (4 x 18) = 80 lines -->
<node name="Number_0b">
<translate>0.0 20.0 -8.5</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<node id="IDb01" name="instance_1">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 1.1 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb02" name="instance_2">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 2.2 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb03" name="instance_3">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 3.3 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb04" name="instance_4">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 4.4 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb05" name="instance_5">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 5.5 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDz19" name="instance_z19">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 6.6 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDb06" name="instance_6">
<matrix>0.25 0 0 0.0 0 1 0 1.1 0 0 1 6.6 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb07" name="instance_7">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 6.6 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb08" name="instance_8">
<matrix>0.25 0 0 0.0 0 1 0 3.3 0 0 1 2.2 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb09" name="instance_9">
<matrix>0.25 0 0 0.0 0 1 0 3.3 0 0 1 1.1 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb10" name="instance_10">
<matrix>0.25 0 0 0.0 0 1 0 1.1 0 0 1 0.0 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb11" name="instance_11">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 0.0 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb19" name="instance_19">
<matrix>0.25 0 0 0.0 0 -1 0 3.3 0 0 -1 0.0 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDb20" name="instance_20">
<matrix>0.25 0 0 0.0 0 0 1 3.3 0 -1 0 6.6 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDb21" name="instance_21">
<matrix>0.25 0 0 0.0 0 0 -1 0.0 0 1 0 0.0 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDz11" name="instance_z11">
<matrix>0.25 0 0 0.0 0 1 0 3.3 0 0 1 3.3 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDz12" name="instance_z12">
<matrix>0.25 0 0 0.0 0 1 0 3.3 0 0 1 4.4 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDz13" name="instance_z13">
<matrix>0.25 0 0 0.0 0 1 0 3.3 0 0 1 5.5 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
</node>
<!-- Number "1" ... has 8 + (4 x 8) = 40 lines -->
<!-- Number "2" #1 ... has 8 + (4 x 17) = 76 lines -->
<!-- Number "2" #2 ... has 8 + (4 x 17) = 76 lines -->
<!-- Number "3" ... has 8 + (4 x 18) = 80 lines -->
<!-- Number "4" ... has 8 + (4 x 13) = 60 lines -->
<!-- Number "5" ... has 8 + (4 x 17) = 76 lines -->
<!-- Number "6" ... has 8 + (4 x 18) = 80 lines -->
<!-- Number "7" ... has 8 + (4 x 14) = 64 lines -->
<!-- Number "8" ... has 8 + (4 x 22) = 96 lines -->
<!-- Number "9" ... has 8 + (4 x 15) = 68 lines -->
<!-- bovera_Digit1 is "4" -->
<node name="bovera_Digit1">
<translate>0.0 26.8 1.0</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<!-- Number "4" ... has 8 + (4 x 13) = 60 lines -->
<node id="IDe01" name="instance_e01">
<matrix>0.25 0 0 0.0 0 1 0 1.1 0 0 1 3.3 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDe02" name="instance_e02">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 3.3 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDe02" name="instance_e02">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 3.3 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb04" name="instance_4">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 4.4 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb05" name="instance_5">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 5.5 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb06" name="instance_6">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 6.6 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb08" name="instance_8">
<matrix>0.25 0 0 0.0 0 1 0 3.3 0 0 1 2.2 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb09" name="instance_9">
<matrix>0.25 0 0 0.0 0 1 0 3.3 0 0 1 1.1 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDn09" name="instance_9">
<matrix>0.25 0 0 0.0 0 1 0 3.3 0 0 1 0.0 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDf12" name="instance_n12">
<matrix>0.25 0 0 0.0 0 1 0 3.3 0 0 1 6.6 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDn12" name="instance_n12">
<matrix>0.25 0 0 0.0 0 1 0 3.3 0 0 1 3.3 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDz12" name="instance_z12">
<matrix>0.25 0 0 0.0 0 1 0 3.3 0 0 1 4.4 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDz13" name="instance_z13">
<matrix>0.25 0 0 0.0 0 1 0 3.3 0 0 1 5.5 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
</node>
<!-- bovera_Digit2 is "1" -->
<node name="bovera_Digit2">
<translate>0.0 31.8 1.0</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<!-- Number "1" ... has 8 + (4 x 8) = 40 lines -->
<node id="ID101" name="instance_1">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 0.0 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID102" name="instance_1">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 1.1 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID103" name="instance_1">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 2.2 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID104" name="instance_1">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 3.3 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID105" name="instance_1">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 4.4 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID106" name="instance_1">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 5.5 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID107" name="instance_1">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 6.6 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID109" name="instance_z19">
<matrix>0.25 0 0 0.0 0 1 0 1.1 0 0 1 6.6 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
</node>
<!-- covera_Digit1 is "3" -->
<node name="covera_Digit1">
<translate>0.0 26.8 -8.5</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<!-- Number "3" ... has 8 + (4 x 18) = 80 lines -->
<node id="ID301" name="instance_e01">
<matrix>0.25 0 0 0.0 0 1 0 1.1 0 0 1 3.3 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID302" name="instance_e02">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 3.3 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID303" name="instance_1">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 1.1 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID304" name="instance_5">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 5.5 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID305" name="instance_z19">
<matrix>0.25 0 0 0.0 0 1 0 0.0 0 0 1 6.6 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="ID306" name="instance_6">
<matrix>0.25 0 0 0.0 0 1 0 1.1 0 0 1 6.6 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID307" name="instance_7">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 6.6 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID308" name="instance_8">
<matrix>0.25 0 0 0.0 0 1 0 3.3 0 0 1 2.2 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID309" name="instance_9">
<matrix>0.25 0 0 0.0 0 1 0 3.3 0 0 1 1.1 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID310" name="instance_10">
<matrix>0.25 0 0 0.0 0 1 0 1.1 0 0 1 0.0 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID311" name="instance_11">
<matrix>0.25 0 0 0.0 0 1 0 2.2 0 0 1 0.0 0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID312" name="instance_19">
<matrix>0.25 0 0 0.0 0 -1 0 3.3 0 0 -1 0.0 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="ID313" name="instance_20">
<matrix>0.25 0 0 0.0 0 0 1 3.3 0 -1 0 6.6 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="ID314" name="instance_21">
<matrix>0.25 0 0 0.0 0 0 -1 0.0 0 1 0 0.0 0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</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>
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
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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 | |
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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.
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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."
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As is shown here, immediately to the left, the menu panel is updated after the "Inventory" button has been clicked, as directed above.
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. |
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NOTE:
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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.
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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. |
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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.
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| Additional Photos from Inside the Oculus Rift S Home Environment | |
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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. |
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Footnotes
‡Adopting the characteristic mass <math>~(M_\mathrm{Ch} = \mu_e^{-2} \cdot 1.14205 \times 10^{34} ~\mathrm{g})</math> and characteristic length <math>~(\ell_1 = \mu_e^{-1} \cdot 7.71395 \times 10^{8} ~\mathrm{cm})</math> that are associated with a white dwarf equation of state, we can reasonably state that the characteristic mean density of a spherically symmetric white dwarf is,
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<math>~{\bar\rho}_\mathrm{WD}</math> |
<math>~\equiv</math> |
<math>~ \frac{3 M_\mathrm{Ch}}{4\pi \ell_1^3} = \mu_e \cdot 5.93972 \times 10^{6}~\mathrm{g}~{\mathrm{cm}}^{-3} \, . </math> |
Drawing from our above discussion of timescales that arise in the context of our COLLADA-driven animations, we therefore appreciate that the characteristic oscillation period associated with a white dwarf whose molecular weight of electrons is <math>~\mu_e = 2</math>, proves to be,
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<math>~[P_0]_\mathrm{WD}</math> |
<math>~=</math> |
<math>~ \biggl[ \frac{4\pi}{G{\bar\rho}_\mathrm{WD}} \biggr]^{1 / 2} = 3.98~\mathrm{s}\, . </math> |
By presenting animation scenes in which one wall-clock "hour" equates to approximately 4 seconds of real time, we can reasonably assert that our animated models fairly represent how a Riemann-ellipsoid-like white dwarf should behave in real time.
See Also
- Discussion of Ou's Riemann-Like Ellipsoids
- Riemann Meets COLLADA & Oculus Rift S
- Virtual Reality and 3D Printing
- Success Importing Animated Scene into Oculus Rift S
- Carefully (Re)Build Riemann Type S Ellipsoids Inside Oculus Rift Environment: Example (b/a, c/a) = (0.41, 0.385)
- Other Example S-type Riemann Ellipsoids:
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© 2014 - 2021 by Joel E. Tohline |