# 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.

## 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 ${\displaystyle ~{\frac {b}{a}}=0.41}$ Figure 1b ${\displaystyle ~{\frac {c}{a}}=0.385}$ Direct Adjoint ${\displaystyle ~\Omega _{\mathrm {EFE} }=0.547874}$ ${\displaystyle ~\Omega _{\mathrm {EFE} }=-0.079886}$ ${\displaystyle ~\lambda _{\mathrm {EFE} }=0.079886}$ ${\displaystyle ~\lambda _{\mathrm {EFE} }=-0.547874}$ ${\displaystyle ~f=-0.415418}$ ${\displaystyle ~f=-19.53923}$

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 ${\displaystyle ~[\pi G\rho ]^{1/2}}$. 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" ?>
<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
-->
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<color>0.5 0.0 0.99  1.0</color>
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<effect id="DiffuseRed_EFE">
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<!-- effect:  MidPlane Frame -->
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<library_materials>
<!-- material:  Four Clock Components -->
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<instance_effect url="#ID5" />
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<material id="ID6_EFE" name="material">
<instance_effect url="#DiffusePurple_00" />
</material>
<!-- material:  MidPlane Frame -->
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<instance_effect url="#MidPlaneID5" />
</material>
<!-- material:  Cylindrical Pointer -->
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<!-- material:  Letters -->
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<instance_effect url="#Black_DiagonalID5" />
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<!-- node:  Three clock components -->
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<!-- node:  MidPlane Frame -->
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<!-- node:  Cylindrical Pointer -->
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<instance_geometry url="#Cylinder">
<bind_material>
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<instance_material symbol="Material2" target="#CylID6">
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<!-- geometry:  Four Clock Components -->
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<mesh>
<!--
**********************************************
*
*  Insert first portion of clock's structure
*
**********************************************
-->
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<!--
**********************************************
*
*  Insert second portion of clock's structure
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-->
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<!--
**********************************************
*
*  Insert arrow portion of clock's structure
*
**********************************************
-->
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<input semantic="NORMAL" source="#Clock_ArrowNormals" offset="1"/>
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<p> 0 0 8 0 1 0 1 0 8 0 2 0 2 0 8 0 3 0 3 0 8 0 0 0 4 1 5 1 9 1 5 1 6 1 9 1 6 1 7 1 9 1 7 1 4 1 9 1 0 2 1 2 5 2 4 2 1 3 2 3 6 3 5 3 2 4 3 4 7 4 6 4 3 5 0 5 4 5 7 5 </p>
</polylist>
</mesh>
</geometry>
<geometry id="Clock_HourEdge">
<mesh>
<!--
**********************************************
*
*  Insert hour_hand portion of clock's structure
*
**********************************************
-->
<source id="Clock_HourPositions">
<float_array id="HourCoordinates01" count="30"> 0.0  0.85 0.25 0.1  0.0 0.25 0.0 -0.2 0.25 -0.1  0.0 0.25 0.0  0.85 0.05 0.1  0.0 0.05 0.0 -0.2 0.05 -0.1  0.0 0.05 0.0  0.0 0.25 0.0  0.0 0.05 </float_array>
<technique_common>
<accessor source="#HourCoordinates01" count="10" stride="3">
<param name="X" type="float" />
<param name="Y" type="float" />
<param name="Z" type="float" />
</accessor>
</technique_common>
</source>
<source id="Clock_HourNormals">
<float_array id="HourNormals01" count="18">
0  0  1
0  0 -1
0.993151  0.116841 0.0
0.447214 -0.894427 0.0
-0.447214 -0.894427 0.0
-0.993151  0.116841 0.0
</float_array>
<technique_common>
<accessor source="#HourNormals01" count="6" stride="3">
<param name="X" type="float" />
<param name="Y" type="float" />
<param name="Z" type="float" />
</accessor>
</technique_common>
</source>
<vertices id="Clock_HourVertices">
<input semantic="POSITION" source="#Clock_HourPositions" />
</vertices>
<polylist count="12" material="Material2">
<input semantic="VERTEX" source="#Clock_HourVertices" offset="0" />
<input semantic="NORMAL" source="#Clock_HourNormals" offset="1"/>
<vcount>3 3 3 3 3 3 3 3 4 4 4 4</vcount>
<p> 0 0 8 0 1 0 1 0 8 0 2 0 2 0 8 0 3 0 3 0 8 0 0 0 4 1 5 1 9 1 5 1 6 1 9 1 6 1 7 1 9 1 7 1 4 1 9 1 0 2 1 2 5 2 4 2 1 3 2 3 6 3 5 3 2 4 3 4 7 4 6 4 3 5 0 5 4 5 7 5 </p>
</polylist>
</mesh>
</geometry>
<!-- geometry:  Letters -->
<geometry id="CubeID4">
<mesh>
<source id="CubeID7_Positions">
<float_array id="CoordinatesID10" count="24">
-0.5  -0.5  -0.5
-0.5  -0.5   0.5
-0.5   0.5  -0.5
-0.5   0.5   0.5
0.5  -0.5  -0.5
0.5  -0.5   0.5
0.5   0.5  -0.5
0.5   0.5   0.5
</float_array>
<technique_common>
<accessor source="#CoordinatesID10" count="8" stride="3">
<param name="X" type="float" />
<param name="Y" type="float" />
<param name="Z" type="float" />
</accessor>
</technique_common>
</source>
<source id="CubeID8_Normals">
<float_array id="NormalsID11" count="18">
0  0 -1
0  0  1
0 -1  0
0  1  0
-1  0  0
1  0  0
</float_array>
<technique_common>
<accessor source="#NormalsID11" count="6" stride="3">
<param name="X" type="float" />
<param name="Y" type="float" />
<param name="Z" type="float" />
</accessor>
</technique_common>
</source>
<vertices id="CubeID9_Vertices">
<input semantic="POSITION" source="#CubeID7_Positions" />
</vertices>
<polylist count="12" material="Material2">
<input semantic="VERTEX" source="#CubeID9_Vertices" offset="0" />
<input semantic="NORMAL" source="#CubeID8_Normals" offset="1" />
<vcount>3 3 3 3  3 3 3 3  3 3 3 3</vcount>
<p>
0 0 2 0 6 0  0 0 6 0 4 0
1 1 7 1 3 1  1 1 5 1 7 1
0 2 4 2 5 2  0 2 5 2 1 2
2 3 3 3 7 3  2 3 7 3 6 3
0 4 1 4 3 4  0 4 3 4 2 4
4 5 6 5 7 5  4 5 7 5 5 5
</p>
</polylist>
</mesh>
</geometry>
<geometry id="DiagonalID4">
<mesh>
<source id="DiagonalID7_Positions">
<float_array id="Diag_CoordinatesID10" count="24">
-0.5  -0.5  -0.5
-0.5  -0.5   0.5
-0.5   0.5  -0.5
-0.5   0.5   0.5
0.5  -0.5  -0.5
0.5  -0.5   0.5
0.5   0.5  -0.5
0.5   0.5   0.5
</float_array>
<technique_common>
<accessor source="#Diag_CoordinatesID10" count="8" stride="3">
<param name="X" type="float" />
<param name="Y" type="float" />
<param name="Z" type="float" />
</accessor>
</technique_common>
</source>
<source id="DiagonalID8_Normals">
<float_array id="Diagonal_NormalsID11" count="21">
0  0 -1
0  0  1
0 -1  0
0  1  0
-1  0  0
1  0  0
0  -0.707 0.707
</float_array>
<technique_common>
<accessor source="#Diagonal_NormalsID11" count="7" stride="3">
<param name="X" type="float" />
<param name="Y" type="float" />
<param name="Z" type="float" />
</accessor>
</technique_common>
</source>
<vertices id="DiagonalID9_Vertices">
<input semantic="POSITION" source="#DiagonalID7_Positions" />
</vertices>
<polylist count="8" material="Material2">
<input semantic="VERTEX" source="#DiagonalID9_Vertices" offset="0" />
<input semantic="NORMAL" source="#DiagonalID8_Normals" offset="1" />
<vcount>3 3 3 3  3 3 3 3</vcount>
<p>
0 0 2 0 6 0  0 0 6 0 4 0
2 3 3 3 7 3  2 3 7 3 6 3
0 4 3 4 2 4  4 5 6 5 7 5
0 6 7 6 3 6  0 6 4 6 7 6
</p>
</polylist>
</mesh>
</geometry>
<!-- geometry:  Cubes for Lagrangian Markers -->
<geometry id="CubeID4">
<mesh>
<source id="CubeID7_Positions">
<float_array id="CoordinatesID10" count="24">
-0.5  -0.5  -0.5
-0.5  -0.5   0.5
-0.5   0.5  -0.5
-0.5   0.5   0.5
0.5  -0.5  -0.5
0.5  -0.5   0.5
0.5   0.5  -0.5
0.5   0.5   0.5
</float_array>
<technique_common>
<accessor source="#CoordinatesID10" count="8" stride="3">
<param name="X" type="float" />
<param name="Y" type="float" />
<param name="Z" type="float" />
</accessor>
</technique_common>
</source>
<source id="CubeID8_Normals">
<float_array id="NormalsID11" count="18">
0  0 -1
0  0  1
0 -1  0
0  1  0
-1  0  0
1  0  0
</float_array>
<technique_common>
<accessor source="#NormalsID11" count="6" stride="3">
<param name="X" type="float" />
<param name="Y" type="float" />
<param name="Z" type="float" />
</accessor>
</technique_common>
</source>
<vertices id="CubeID9_Vertices">
<input semantic="POSITION" source="#CubeID7_Positions" />
</vertices>
<polylist count="12" material="Material2">
<input semantic="VERTEX" source="#CubeID9_Vertices" offset="0" />
<input semantic="NORMAL" source="#CubeID8_Normals" offset="1" />
<vcount>3 3 3 3  3 3 3 3  3 3 3 3</vcount>
<p>
0 0 2 0 6 0  0 0 6 0 4 0
1 1 7 1 3 1  1 1 5 1 7 1
0 2 4 2 5 2  0 2 5 2 1 2
2 3 3 3 7 3  2 3 7 3 6 3
0 4 1 4 3 4  0 4 3 4 2 4
4 5 6 5 7 5  4 5 7 5 5 5
</p>
</polylist>
</mesh>
</geometry>
<!-- geometry:  Cylindrical Pointer -->
<geometry id="Cylinder">
<mesh>
<source id="Cyl_Positions">
<float_array id="CylCoords01" count="54">
-1.0  -0.9239   0.3827
-1.0  -0.3827   0.9239
-1.0   0.3827   0.9239
-1.0   0.9239   0.3827
-1.0   0.9239  -0.3827
-1.0   0.3827  -0.9239
-1.0  -0.3827  -0.9239
-1.0  -0.9239  -0.3827
-1.0   0.0000   0.0000
1.0  -0.9239   0.3827
1.0  -0.3827   0.9239
1.0   0.3827   0.9239
1.0   0.9239   0.3827
1.0   0.9239  -0.3827
1.0   0.3827  -0.9239
1.0  -0.3827  -0.9239
1.0  -0.9239  -0.3827
1.5   0.0000   0.0000
</float_array>
<technique_common>
<accessor source="#CylCoords01" count="18" stride="3">
<param name="X" type="float" />
<param name="Y" type="float" />
<param name="Z" type="float" />
</accessor>
</technique_common>
</source>
<source id="Cyl_Normals">
<float_array id="CylNormals01" count="54">
1.0  0.0  0.0
-1.0  0.0  0.0
0.0  1.0  0.0
0.0 -1.0  0.0
0.0  0.0  1.0
0.0  0.0 -1.0
0.0  0.7071  0.7071
0.0  0.7071 -0.7071
0.0 -0.7071  0.7071
0.0 -0.7071 -0.7071
0.8795  -0.3365   0.3365
0.8795   0.0000   0.4760
0.8795   0.3365   0.3365
0.8795   0.4760   0.0000
0.8795   0.3365  -0.3365
0.8795   0.0000  -0.4760
0.8795  -0.3365  -0.3365
0.8795  -0.4760   0.0000
</float_array>
<technique_common>
<accessor source="#CylNormals01" count="18" stride="3">
<param name="X" type="float" />
<param name="Y" type="float" />
<param name="Z" type="float" />
</accessor>
</technique_common>
</source>
<vertices id="Cyl_Vertices">
<input semantic="POSITION" source="#Cyl_Positions" />
</vertices>
<polylist count="32" material="Material2">
<input semantic="VERTEX" source="#Cyl_Vertices" offset="0" />
<input semantic="NORMAL" source="#Cyl_Normals" offset="1" />
<vcount>3 3 3 3  3 3 3 3  3 3 3 3  3 3 3 3  3 3 3 3  3 3 3 3  3 3 3 3  3 3 3 3</vcount>
<p>
0 1  1 1  8 1
1 1  2 1  8 1
2 1  3 1  8 1
3 1  4 1  8 1
4 1  5 1  8 1
5 1  6 1  8 1
6 1  7 1  8 1
7 1  0 1  8 1
10 10   9 10  17 10
11 11  10 11  17 11
12 12  11 12  17 12
13 13  12 13  17 13
14 14  13 14  17 14
15 15  14 15  17 15
16 16  15 16  17 16
9 17  16 17  17 17
0 8   9 8   1 8
1 8   9 8  10 8
1 4  10 4   2 4
2 4  10 4  11 4
2 6  11 6   3 6
3 6  11 6  12 6
3 2  12 2   4 2
4 2  12 2  13 2
4 7  13 7   5 7
5 7  13 7  14 7
5 5  14 5   6 5
6 5  14 5  15 5
6 9  15 9   7 9
7 9  15 9  16 9
7 3  16 3   0 3
0 3  16 3   9 3
</p>
</polylist>
</mesh>
</geometry>
<!--
**********************************************
*
*  Insert Geometry of Ellipsoid Octant
*
**********************************************
-->
<geometry id="EllipsoidOctant">
<mesh>
<source id="Ellipsoid_Positions">
<float_array id="Ellipsoid_Coordinates" count=" 1563">
0.0000    0.0000    0.3850
0.0000    0.4100    0.0000
0.0400    0.4097    0.0000
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<technique_common>
<accessor source="#Ellipsoid_Coordinates" count="  521" stride="3">
<param name="X" type="float" />
<param name="Y" type="float" />
<param name="Z" type="float" />
</accessor>
</technique_common>
</source>
<source id="Ellipsoid_Normals">
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<param name="Y" type="float" />
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</technique_common>
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3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
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3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
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3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
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3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
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0    7  503    7  502    7
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0   12  508   12  507   12
0   13  509   13  508   13
0   14  510   14  509   14
0   15  511   15  510   15
0   16  512   16  511   16
0   17  513   17  512   17
0   18  514   18  513   18
0   19  515   19  514   19
0   20  516   20  515   20
0   21  517   21  516   21
0   22  518   22  517   22
0   23  519   23  518   23
0   24  520   24  519   24
495   25  470   25  469   25
495   26  496   26  470   26
496   27  471   27  470   27
496   28  497   28  471   28
497   29  472   29  471   29
497   30  498   30  472   30
498   31  473   31  472   31
498   32  499   32  473   32
499   33  474   33  473   33
499   34  500   34  474   34
500   35  475   35  474   35
500   36  501   36  475   36
501   37  476   37  475   37
501   38  502   38  476   38
502   39  477   39  476   39
502   40  503   40  477   40
503   41  478   41  477   41
503   42  504   42  478   42
504   43  479   43  478   43
504   44  505   44  479   44
505   45  480   45  479   45
505   46  506   46  480   46
506   47  481   47  480   47
506   48  507   48  481   48
507   49  482   49  481   49
507   50  508   50  482   50
508   51  483   51  482   51
508   52  509   52  483   52
509   53  484   53  483   53
509   54  510   54  484   54
510   55  485   55  484   55
510   56  511   56  485   56
511   57  486   57  485   57
511   58  512   58  486   58
512   59  487   59  486   59
512   60  513   60  487   60
513   61  488   61  487   61
513   62  514   62  488   62
514   63  489   63  488   63
514   64  515   64  489   64
515   65  490   65  489   65
515   66  516   66  490   66
516   67  491   67  490   67
516   68  517   68  491   68
517   69  492   69  491   69
517   70  518   70  492   70
518   71  493   71  492   71
518   72  519   72  493   72
519   73  494   73  493   73
519   74  520   74  494   74
469   75  444   75  443   75
469   76  470   76  444   76
470   77  445   77  444   77
470   78  471   78  445   78
471   79  446   79  445   79
471   80  472   80  446   80
472   81  447   81  446   81
472   82  473   82  447   82
473   83  448   83  447   83
473   84  474   84  448   84
474   85  449   85  448   85
474   86  475   86  449   86
475   87  450   87  449   87
475   88  476   88  450   88
476   89  451   89  450   89
476   90  477   90  451   90
477   91  452   91  451   91
477   92  478   92  452   92
478   93  453   93  452   93
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492  121  467  121  466  121
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493  123  468  123  467  123
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445  129  420  129  419  129
445  130  446  130  420  130
446  131  421  131  420  131
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448  135  423  135  422  135
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451  141  426  141  425  141
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<technique_common>
<accessor source="#Reflect_Coordinates" count="  521" stride="3">
<param name="X" type="float" />
<param name="Y" type="float" />
<param name="Z" type="float" />
</accessor>
</technique_common>
</source>
<source id="Reflect_Normals">
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<param name="Y" type="float" />
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</technique_common>
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3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
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3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
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0    3  498    3  499    3
0    4  499    4  500    4
0    5  500    5  501    5
0    6  501    6  502    6
0    7  502    7  503    7
0    8  503    8  504    8
0    9  504    9  505    9
0   10  505   10  506   10
0   11  506   11  507   11
0   12  507   12  508   12
0   13  508   13  509   13
0   14  509   14  510   14
0   15  510   15  511   15
0   16  511   16  512   16
0   17  512   17  513   17
0   18  513   18  514   18
0   19  514   19  515   19
0   20  515   20  516   20
0   21  516   21  517   21
0   22  517   22  518   22
0   23  518   23  519   23
0   24  519   24  520   24
495   25  469   25  470   25
495   26  470   26  496   26
496   27  470   27  471   27
496   28  471   28  497   28
497   29  471   29  472   29
497   30  472   30  498   30
498   31  472   31  473   31
498   32  473   32  499   32
499   33  473   33  474   33
499   34  474   34  500   34
500   35  474   35  475   35
500   36  475   36  501   36
501   37  475   37  476   37
501   38  476   38  502   38
502   39  476   39  477   39
502   40  477   40  503   40
503   41  477   41  478   41
503   42  478   42  504   42
504   43  478   43  479   43
504   44  479   44  505   44
505   45  479   45  480   45
505   46  480   46  506   46
506   47  480   47  481   47
506   48  481   48  507   48
507   49  481   49  482   49
507   50  482   50  508   50
508   51  482   51  483   51
508   52  483   52  509   52
509   53  483   53  484   53
509   54  484   54  510   54
510   55  484   55  485   55
510   56  485   56  511   56
511   57  485   57  486   57
511   58  486   58  512   58
512   59  486   59  487   59
512   60  487   60  513   60
513   61  487   61  488   61
513   62  488   62  514   62
514   63  488   63  489   63
514   64  489   64  515   64
515   65  489   65  490   65
515   66  490   66  516   66
516   67  490   67  491   67
516   68  491   68  517   68
517   69  491   69  492   69
517   70  492   70  518   70
518   71  492   71  493   71
518   72  493   72  519   72
519   73  493   73  494   73
519   74  494   74  520   74
469   75  443   75  444   75
469   76  444   76  470   76
470   77  444   77  445   77
470   78  445   78  471   78
471   79  445   79  446   79
471   80  446   80  472   80
472   81  446   81  447   81
472   82  447   82  473   82
473   83  447   83  448   83
473   84  448   84  474   84
474   85  448   85  449   85
474   86  449   86  475   86
475   87  449   87  450   87
475   88  450   88  476   88
476   89  450   89  451   89
476   90  451   90  477   90
477   91  451   91  452   91
477   92  452   92  478   92
478   93  452   93  453   93
478   94  453   94  479   94
479   95  453   95  454   95
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480   97  454   97  455   97
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488  113  462  113  463  113
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491  119  465  119  466  119
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492  121  466  121  467  121
492  122  467  122  493  122
493  123  467  123  468  123
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443  126  418  126  444  126
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445  129  419  129  420  129
445  130  420  130  446  130
446  131  420  131  421  131
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448  135  422  135  423  135
448  136  423  136  449  136
449  137  423  137  424  137
449  138  424  138  450  138
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450  140  425  140  451  140
451  141  425  141  426  141
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452  143  426  143  427  143
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453  145  427  145  428  145
453  146  428  146  454  146
454  147  428  147  429  147
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70  909   44  909   45  909
70  910   45  910   71  910
71  911   45  911   46  911
71  912   46  912   72  912
72  913   46  913   47  913
72  914   47  914   73  914
73  915   47  915   48  915
73  916   48  916   74  916
74  917   48  917   49  917
74  918   49  918   75  918
75  919   49  919   50  919
75  920   50  920   76  920
76  921   50  921   51  921
76  922   51  922   77  922
77  923   51  923   52  923
77  924   52  924   78  924
27  925    1  925    2  925
27  926    2  926   28  926
28  927    2  927    3  927
28  928    3  928   29  928
29  929    3  929    4  929
29  930    4  930   30  930
30  931    4  931    5  931
30  932    5  932   31  932
31  933    5  933    6  933
31  934    6  934   32  934
32  935    6  935    7  935
32  936    7  936   33  936
33  937    7  937    8  937
33  938    8  938   34  938
34  939    8  939    9  939
34  940    9  940   35  940
35  941    9  941   10  941
35  942   10  942   36  942
36  943   10  943   11  943
36  944   11  944   37  944
37  945   11  945   12  945
37  946   12  946   38  946
38  947   12  947   13  947
38  948   13  948   39  948
39  949   13  949   14  949
39  950   14  950   40  950
40  951   14  951   15  951
40  952   15  952   41  952
41  953   15  953   16  953
41  954   16  954   42  954
42  955   16  955   17  955
42  956   17  956   43  956
43  957   17  957   18  957
43  958   18  958   44  958
44  959   18  959   19  959
44  960   19  960   45  960
45  961   19  961   20  961
45  962   20  962   46  962
46  963   20  963   21  963
46  964   21  964   47  964
47  965   21  965   22  965
47  966   22  966   48  966
48  967   22  967   23  967
48  968   23  968   49  968
49  969   23  969   24  969
49  970   24  970   50  970
50  971   24  971   25  971
50  972   25  972   51  972
51  973   25  973   26  973
51  974   26  974   52  974
</p>
</polylist>
</mesh>
</geometry>
<!-- EquatorialPlane (begin) -->
<geometry id="EquatorialPlane">
<mesh>
<source id="EquatorialPlane_Positions">
<float_array id="EquatorialPlane_Coordinates" count="48">
-5.5000    -5.5000    0.2000
5.5000    -5.5000    0.2000
5.5000     5.5000    0.2000
-5.5000     5.5000    0.2000
-5.7500    -5.7500    0.2000
5.7500    -5.7500    0.2000
5.7500     5.7500    0.2000
-5.7500     5.7500    0.2000
-5.5000    -5.5000   -0.2000
5.5000    -5.5000   -0.2000
5.5000     5.5000   -0.2000
-5.5000     5.5000   -0.2000
-5.7500    -5.7500   -0.2000
5.7500    -5.7500   -0.2000
5.7500     5.7500   -0.2000
-5.7500     5.7500   -0.2000
</float_array>
<technique_common>
<accessor source="#EquatorialPlane_Coordinates" count="  16" stride="3">
<param name="X" type="float" />
<param name="Y" type="float" />
<param name="Z" type="float" />
</accessor>
</technique_common>
</source>
<source id="EquatorialPlane_Normals">
<float_array id="EquatorialPlane_Normals01" count="18">
0.0000    0.0000     1.0000
0.0000    0.0000    -1.0000
0.0000   -1.0000     0.0000
0.0000    1.0000     0.0000
-1.0000    0.0000     0.0000
1.0000    0.0000     0.0000
</float_array>
<technique_common>
<accessor source="#EquatorialPlane_Normals01" count="6" stride="3">
<param name="X" type="float" />
<param name="Y" type="float" />
<param name="Z" type="float" />
</accessor>
</technique_common>
</source>
<vertices id="EquatorialPlane_Vertices">
<input semantic="POSITION" source="#EquatorialPlane_Positions" />
</vertices>
<polylist count="  12" material="Material2">
<input semantic="VERTEX" source="#EquatorialPlane_Vertices" offset="0" />
<input semantic="NORMAL" source="#EquatorialPlane_Normals" offset="1" />
<vcount>
4 4 4 4
4 4 4 4
4 4 4 4
</vcount>
<p>
4 0  5 0  1 0  0 0
5 0  6 0  2 0  1 0
6 0  7 0  3 0  2 0
7 0  4 0  0 0  3 0
8 1   9 1  13 1  12 1
9 1  10 1  14 1  13 1
10 1  11 1  15 1  14 1
11 1   8 1  12 1  15 1
12 2  13 2   5 2   4 2
14 3  15 3   7 3   6 3
15 4  12 4   4 4   7 4
13 5  14 5   6 5   5 5
</p>
</polylist>
</mesh>
</geometry>
<!-- EquatorialPlane (end)   -->
</library_geometries>
<library_animations>
<animation id="First_rotation_euler_Z">
<!-- for EFE/Ou model b41c385, clockstop = 36.5047 and anglestop = 1800.0 -->
<!-- this means that one 360 degree turn of the ellipsoid takes 7.3009 clock units -->
<source id="First_rotation_euler_Z-input">
<float_array id="First_rotation_euler_Z-input-array" count="31">
0.00
1.22
2.43
3.65
4.87
6.08
7.30
8.52
9.73
10.95
12.17
13.39
14.60
15.82
17.04
18.25
19.47
20.69
21.90
23.12
24.34
25.55
26.77
27.99
29.20
30.42
31.64
32.85
34.07
35.29
36.50
</float_array>
<technique_common>
<accessor source="#First_rotation_euler_Z-input-array" count="31" stride="1">
<param name="TIME" type="float"/>
</accessor>
</technique_common>
</source>
<!-- This sets the spin rate of the "Entire" ellipsoid -->
<source id="First_rotation_euler_Z-output">
<float_array id="First_rotation_euler_Z-output-array" count="31">
3.0
63.0
123.0
183.0
243.0
303.0
363.0
423.0
483.0
543.0
603.0
663.0
723.0
783.0
843.0
903.0
963.0
1023.0
1083.0
1143.0
1203.0
1263.0
1323.0
1383.0
1443.0
1503.0
1563.0
1623.0
1683.0
1743.0
1803.0
</float_array>
<technique_common>
<accessor source="#First_rotation_euler_Z-output-array" count="31" stride="1">
<param name="ANGLE" type="float"/>
</accessor>
</technique_common>
</source>
<!-- This sets the spin rate of the "MidPlane" Frame of reference -->
<source id="Frame_rotation_euler_Z-output">
<float_array id="Frame_rotation_euler_Z-output-array" count="31">
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
</float_array>
<technique_common>
<accessor source="#Frame_rotation_euler_Z-output-array" count="31" stride="1">
<param name="ANGLE" type="float"/>
</accessor>
</technique_common>
</source>
<sampler id="First_rotation_euler_Z-sampler">
<input semantic="INPUT" source="#First_rotation_euler_Z-input"/>
<input semantic="OUTPUT" source="#First_rotation_euler_Z-output"/>
</sampler>
<sampler id="Frame_rotation_euler_Z-sampler">
<input semantic="INPUT" source="#First_rotation_euler_Z-input"/>
<input semantic="OUTPUT" source="#Frame_rotation_euler_Z-output"/>
</sampler>
<channel source="#First_rotation_euler_Z-sampler" target="EntireEllipsoid/rotationZ.ANGLE"/>
<channel source="#Frame_rotation_euler_Z-sampler" target="Inertial/rotationZ.ANGLE"/>
</animation>
<!-- FLUID ELEMENT 1 -->
<animation id="FluidElement1_location">
<source id="Lagrange1_location_X-input">
<float_array id="Lagrange1_location_X-input-array" count="   37">
0.0000
1.0014
2.0029
3.0043
4.0057
5.0071
6.0086
7.0100
8.0114
9.0129
10.0143
11.0157
12.0171
13.0186
14.0200
15.0214
16.0229
17.0243
18.0257
19.0271
20.0286
21.0300
22.0314
23.0329
24.0343
25.0357
26.0371
27.0386
28.0400
29.0414
30.0429
31.0443
32.0457
33.0472
34.0486
35.0500
36.0514
</float_array>
<technique_common>
<accessor source="#Lagrange1_location_X-input-array" count="   37" stride="1">
<param name="TIME" type="float"/>
</accessor>
</technique_common>
</source>
<source id="Lagrange1_location_X-output">
<float_array id="Lagrange1_location_X-output-array" count="   37">
1.0000
0.9921
0.9686
0.9298
0.8763
0.8090
0.7290
0.6374
0.5358
0.4258
0.3090
0.1874
0.0628
-0.0628
-0.1874
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-1.0000
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-0.5358
-0.4258
-0.3090
-0.1874
</float_array>
<technique_common>
<accessor source="#Lagrange1_location_X-output-array" count="   37" stride="1">
<param name="X" type="float"/>
</accessor>
</technique_common>
</source>
<sampler id="Lagrange1_location_X-sampler">
<input semantic="INPUT" source="#Lagrange1_location_X-input"/>
<input semantic="OUTPUT" source="#Lagrange1_location_X-output"/>
</sampler>
<source id="Lagrange1_location_Y-output">
<float_array id="Lagrange1_location_Y-output-array" count="   37">
-0.0000
-0.0514
-0.1020
-0.1509
-0.1975
-0.2410
-0.2807
-0.3159
-0.3462
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-0.3899
-0.4027
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-0.4092
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0.0000
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0.1020
0.1509
0.1975
0.2410
0.2807
0.3159
0.3462
0.3710
0.3899
0.4027
</float_array>
<technique_common>
<accessor source="#Lagrange1_location_Y-output-array" count="   37" stride="1">
<param name="Y" type="float"/>
</accessor>
</technique_common>
</source>
<sampler id="Lagrange1_location_Y-sampler">
<input semantic="INPUT" source="#Lagrange1_location_X-input"/>
<input semantic="OUTPUT" source="#Lagrange1_location_Y-output"/>
</sampler>
<channel source="#Lagrange1_location_X-sampler" target="Lagrange01/location.X"/>
<channel source="#Lagrange1_location_Y-sampler" target="Lagrange01/location.Y"/>
</animation>
<!-- CLOCK (clockstop = 36.5047)
One spin of ellipsoid (or frame) is 1.8252 EFE sqrt(pi * G * rho) units;
Want 1 EFE unit to take 4.0 seconds of TIME;
Hence, one spin of ellipsoid (360 degrees) is 7.3009 seconds of TIME;
and 5 ellipsoid spins is 36.5047 seconds of TIME.
Divide one spin (360) into 12 pieces
==> 30 degrees = 1 timestep = 4 x 0.1521 = 0.6084 seconds of TIME.
-->
<animation id="Cube_quaternion_Z">
<source id="Cube_quaternion_Z-input">
<float_array id="Cube_quaternion_Z-input-array" count=" 147">
0.00  0.25  0.50  0.75  1.00  1.25  1.50  1.75  2.00  2.25  2.50  2.75  3.00  3.25  3.50  3.75
4.00  4.25  4.50  4.75  5.00  5.25  5.50  5.75  6.00  6.25  6.50  6.75  7.00  7.25  7.50  7.75
8.00  8.25  8.50  8.75  9.00  9.25  9.50  9.75 10.00 10.25 10.50 10.75 11.00 11.25 11.50 11.75
12.00 12.25 12.50 12.75 13.00 13.25 13.50 13.75 14.00 14.25 14.50 14.75 15.00 15.25 15.50 15.75
16.00 16.25 16.50 16.75 17.00 17.25 17.50 17.75 18.00 18.25 18.50 18.75 19.00 19.25 19.50 19.75
20.00 20.25 20.50 20.75 21.00 21.25 21.50 21.75 22.00 22.25 22.50 22.75 23.00 23.25 23.50 23.75
24.00 24.25 24.50 24.75 25.00 25.25 25.50 25.75 26.00 26.25 26.50 26.75 27.00 27.25 27.50 27.75
28.00 28.25 28.50 28.75 29.00 29.25 29.50 29.75 30.00 30.25 30.50 30.75 31.00 31.25 31.50 31.75
32.00 32.25 32.50 32.75 33.00 33.25 33.50 33.75 34.00 34.25 34.50 34.75 35.00 35.25 35.50 35.75
36.00 36.25 36.50
</float_array>
<technique_common>
<accessor source="#Cube_quaternion_Z-input-array" count="   147" stride="1">
<param name="TIME" type="float"/>
</accessor>
</technique_common>
</source>
<source id="Cube_quaternion_Z-output">
<float_array id="Cube_quaternion_Z-output-array" count="2352">
0.000  0.000 -1.00  0.00  -1.0000  0.0000  0.000  0.000   0.0000  1.0000  0.000  0.00   0.000  0.000  0.000  1.000
0.000  0.000 -1.00  0.00  -0.9239 -0.3827  0.000  0.000  -0.3827  0.9239  0.000  0.00   0.000  0.000  0.000  1.000
0.000  0.000 -1.00  0.00  -0.7071 -0.7071  0.000  0.000  -0.7071  0.7071  0.000  0.00   0.000  0.000  0.000  1.000
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0.000  0.000 -1.00  0.00   0.7071 -0.7071  0.000  0.000  -0.7071 -0.7071  0.000  0.00   0.000  0.000  0.000  1.000
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0.000  0.000 -1.00  0.00   0.7071  0.7071  0.000  0.000   0.7071 -0.7071  0.000  0.00   0.000  0.000  0.000  1.000
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36.00 36.25 36.50
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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  3.0</rotate>
<scale sid="scale">5.0 5.0 5.0</scale>
<node id="First" name="First_instance_EFE">
<translate>0.0 0.0 0.0</translate>
<rotate sid="rotationX">1.0 0.0 0.0  0.0</rotate>
<rotate sid="rotationY">0.0 1.0 0.0  0.0</rotate>
<rotate sid="rotationZ">0.0 0.0 1.0  0.0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<instance_node url="#ID3_EFE" />
</node>
<node id="Second" name="Second_instance_EFE">
<translate>0.0 0.0 0.0</translate>
<rotate sid="rotationX">1.0 0.0 0.0  180.0</rotate>
<rotate sid="rotationY">0.0 1.0 0.0    0.0</rotate>
<rotate sid="rotationZ">0.0 0.0 1.0    0.0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<instance_node url="#ID3_EFE" />
</node>
<node id="Third" name="Third_instance_EFE">
<translate>0.0 0.0 0.0</translate>
<rotate sid="rotationX">1.0 0.0 0.0    0.0</rotate>
<rotate sid="rotationY">0.0 1.0 0.0  180.0</rotate>
<rotate sid="rotationZ">0.0 0.0 1.0    0.0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<instance_node url="#ID3_EFE" />
</node>
<node id="Fourth" name="Fourth_instance_EFE">
<translate>0.0 0.0 0.0</translate>
<rotate sid="rotationX">1.0 0.0 0.0  180.0</rotate>
<rotate sid="rotationY">0.0 1.0 0.0  180.0</rotate>
<rotate sid="rotationZ">0.0 0.0 1.0    0.0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<instance_node url="#ID3_EFE" />
</node>
<!-- instance:  Cylindrical Pointer -->
<node id="CylinderPointer" name="instance_cylinder">
<translate sid="location">-1.0 0.0 0.0</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 180</rotate>
<scale sid="scale">0.05 0.025 0.025</scale>
<instance_node url="#CylPointer" />
</node>
<!-- Begin LAGRANGE markers -->
<node id="Lagrange01" name="instance_Lagrange01">
<translate sid="location">1.0000 0.0000 0.0</translate>
<rotate sid="rotationX">1.0 0.0 0.0  0.0</rotate>
<rotate sid="rotationY">0.0 1.0 0.0  0.0</rotate>
<rotate sid="rotationZ">0.0 0.0 1.0  0.0</rotate>
<scale sid="scale">0.075 0.075 0.075</scale>
<instance_node url="#Primary_MarkerID3" />
</node>
<node id="Marker01" name="instance_marker01">
<matrix>0.025 0.0 0.0 1.0000  0.0 0.025 0.0 -0.0000  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker02" name="instance_marker02">
<matrix>0.025 0.0 0.0 0.9921  0.0 0.025 0.0 -0.0514  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker03" name="instance_marker03">
<matrix>0.025 0.0 0.0 0.9686  0.0 0.025 0.0 -0.1020  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker04" name="instance_marker04">
<matrix>0.025 0.0 0.0 0.9298  0.0 0.025 0.0 -0.1509  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker05" name="instance_marker05">
<matrix>0.025 0.0 0.0 0.8763  0.0 0.025 0.0 -0.1975  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker06" name="instance_marker06">
<matrix>0.025 0.0 0.0 0.8090  0.0 0.025 0.0 -0.2410  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker07" name="instance_marker07">
<matrix>0.025 0.0 0.0 0.7290  0.0 0.025 0.0 -0.2807  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker08" name="instance_marker08">
<matrix>0.025 0.0 0.0 0.6374  0.0 0.025 0.0 -0.3159  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker09" name="instance_marker09">
<matrix>0.025 0.0 0.0 0.5358  0.0 0.025 0.0 -0.3462  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker10" name="instance_marker10">
<matrix>0.025 0.0 0.0 0.4258  0.0 0.025 0.0 -0.3710  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker11" name="instance_marker11">
<matrix>0.025 0.0 0.0 0.3090  0.0 0.025 0.0 -0.3899  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker12" name="instance_marker12">
<matrix>0.025 0.0 0.0 0.1874  0.0 0.025 0.0 -0.4027  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker13" name="instance_marker13">
<matrix>0.025 0.0 0.0 0.0628  0.0 0.025 0.0 -0.4092  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker14" name="instance_marker14">
<matrix>0.025 0.0 0.0 -0.0628  0.0 0.025 0.0 -0.4092  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker15" name="instance_marker15">
<matrix>0.025 0.0 0.0 -0.1874  0.0 0.025 0.0 -0.4027  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker16" name="instance_marker16">
<matrix>0.025 0.0 0.0 -0.3090  0.0 0.025 0.0 -0.3899  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker17" name="instance_marker17">
<matrix>0.025 0.0 0.0 -0.4258  0.0 0.025 0.0 -0.3710  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker18" name="instance_marker18">
<matrix>0.025 0.0 0.0 -0.5358  0.0 0.025 0.0 -0.3462  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker19" name="instance_marker19">
<matrix>0.025 0.0 0.0 -0.6374  0.0 0.025 0.0 -0.3159  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker20" name="instance_marker20">
<matrix>0.025 0.0 0.0 -0.7290  0.0 0.025 0.0 -0.2807  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker21" name="instance_marker21">
<matrix>0.025 0.0 0.0 -0.8090  0.0 0.025 0.0 -0.2410  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker22" name="instance_marker22">
<matrix>0.025 0.0 0.0 -0.8763  0.0 0.025 0.0 -0.1975  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker23" name="instance_marker23">
<matrix>0.025 0.0 0.0 -0.9298  0.0 0.025 0.0 -0.1509  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker24" name="instance_marker24">
<matrix>0.025 0.0 0.0 -0.9686  0.0 0.025 0.0 -0.1020  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker25" name="instance_marker25">
<matrix>0.025 0.0 0.0 -0.9921  0.0 0.025 0.0 -0.0514  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker26" name="instance_marker26">
<matrix>0.025 0.0 0.0 -1.0000  0.0 0.025 0.0 -0.0000  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<!-- Second Half -->
<node id="Marker28" name="instance_marker28">
<matrix>0.025 0.0 0.0 -0.9921  0.0 0.025 0.0 0.0514  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker29" name="instance_marker29">
<matrix>0.025 0.0 0.0 -0.9686  0.0 0.025 0.0 0.1020  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker30" name="instance_marker30">
<matrix>0.025 0.0 0.0 -0.9298  0.0 0.025 0.0 0.1509  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker31" name="instance_marker31">
<matrix>0.025 0.0 0.0 -0.8763  0.0 0.025 0.0 0.1975  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker32" name="instance_marker32">
<matrix>0.025 0.0 0.0 -0.8090  0.0 0.025 0.0 0.2410  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker33" name="instance_marker33">
<matrix>0.025 0.0 0.0 -0.7290  0.0 0.025 0.0 0.2807  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker34" name="instance_marker34">
<matrix>0.025 0.0 0.0 -0.6374  0.0 0.025 0.0 0.3159  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker35" name="instance_marker35">
<matrix>0.025 0.0 0.0 -0.5358  0.0 0.025 0.0 0.3462  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker36" name="instance_marker36">
<matrix>0.025 0.0 0.0 -0.4258  0.0 0.025 0.0 0.3710  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker37" name="instance_marker37">
<matrix>0.025 0.0 0.0 -0.3090  0.0 0.025 0.0 0.3899  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker38" name="instance_marker38">
<matrix>0.025 0.0 0.0 -0.1874  0.0 0.025 0.0 0.4027  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker39" name="instance_marker39">
<matrix>0.025 0.0 0.0 -0.0628  0.0 0.025 0.0 0.4092  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker40" name="instance_marker40">
<matrix>0.025 0.0 0.0 0.0628  0.0 0.025 0.0 0.4092  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker41" name="instance_marker41">
<matrix>0.025 0.0 0.0 0.1874  0.0 0.025 0.0 0.4027  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker42" name="instance_marker42">
<matrix>0.025 0.0 0.0 0.3090  0.0 0.025 0.0 0.3899  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker43" name="instance_marker43">
<matrix>0.025 0.0 0.0 0.4258  0.0 0.025 0.0 0.3710  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker44" name="instance_marker44">
<matrix>0.025 0.0 0.0 0.5358  0.0 0.025 0.0 0.3462  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker45" name="instance_marker45">
<matrix>0.025 0.0 0.0 0.6374  0.0 0.025 0.0 0.3159  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker46" name="instance_marker46">
<matrix>0.025 0.0 0.0 0.7290  0.0 0.025 0.0 0.2807  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker47" name="instance_marker47">
<matrix>0.025 0.0 0.0 0.8090  0.0 0.025 0.0 0.2410  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker48" name="instance_marker48">
<matrix>0.025 0.0 0.0 0.8763  0.0 0.025 0.0 0.1975  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker49" name="instance_marker49">
<matrix>0.025 0.0 0.0 0.9298  0.0 0.025 0.0 0.1509  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker50" name="instance_marker50">
<matrix>0.025 0.0 0.0 0.9686  0.0 0.025 0.0 0.1020  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker51" name="instance_marker51">
<matrix>0.025 0.0 0.0 0.9921  0.0 0.025 0.0 0.0514  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<!-- End LAGRANGE markers -->
</node>                           <!-- END EntireEllipsoid -->
<node id="Inertial" name="instance_inertial">  <!-- Start Inertial Grouping of Objects -->
<translate>0.0 0.0 0.0</translate>
<rotate sid="rotationX">1.0 0.0 0.0  0.0</rotate>
<rotate sid="rotationY">0.0 1.0 0.0  0.0</rotate>
<rotate sid="rotationZ">0.0 0.0 1.0  3.0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<node id="Zup_Pointer" name="instance_zupPointer">
<translate>0.0 0.0 5.0</translate>
<rotate sid="rotationX">1 0 0  0.0</rotate>
<rotate sid="rotationY">0 1 0  0.0</rotate>
<rotate sid="rotationZ">0 0 1  0.0</rotate>
<scale sid="scale">0.125 0.5 1.5</scale>
<instance_node url="#ZupPointer" />
</node>
<!-- instance:  MidPlane Frame (MidPlane flips with rotationX = 180 for clockwise spin)-->
<node id="MidPlane" name="instance_MidPlane">
<translate>0.0 0.0 0.0</translate>
<rotate sid="rotationX">1.0 0.0 0.0  0.0</rotate>
<rotate sid="rotationY">0.0 1.0 0.0  0.0</rotate>
<rotate sid="rotationZ">0.0 0.0 1.0  0.0</rotate>
<scale sid="scale">1.25 1.25 1.25</scale>
<instance_node url="#EqPlane" />
</node>
<!-- BEGIN LABELING HERE -->
<node name="Labels">
<translate>7.0 -2.0 5.0</translate>
<rotate sid="rotationX">1 0 0 0.0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 180</rotate>
<scale sid="scale">0.1 0.1 0.1</scale>
<!--  Equals sign #1  -->
<node name="Equals1">
<translate>0.0 15.0 1.0</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<node id="IDd51" name="instance_51">
<matrix>0.25  0 0 0.0   0 1  0 0.0  0 0 1 2.4  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDd52" name="instance_52">
<matrix>0.25  0 0 0.0   0 1  0 1.1  0 0 1 2.4  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDd53" name="instance_53">
<matrix>0.25  0 0 0.0   0 1  0 2.2  0 0 1 2.4  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDd55" name="instance_55">
<matrix>0.25  0 0 0.0   0 1  0 0.0  0 0 1 4.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDd56" name="instance_56">
<matrix>0.25  0 0 0.0   0 1  0 1.1  0 0 1 4.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDd57" name="instance_57">
<matrix>0.25  0 0 0.0   0 1  0 2.2  0 0 1 4.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
</node>
<!--  Equals sign #2  -->
<node name="Equals2">
<translate>0.0 15.0 -8.5</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<node id="IDd51" name="instance_51">
<matrix>0.25  0 0 0.0   0 1  0 0.0  0 0 1 2.4  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDd52" name="instance_52">
<matrix>0.25  0 0 0.0   0 1  0 1.1  0 0 1 2.4  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDd53" name="instance_53">
<matrix>0.25  0 0 0.0   0 1  0 2.2  0 0 1 2.4  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDd55" name="instance_55">
<matrix>0.25  0 0 0.0   0 1  0 0.0  0 0 1 4.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDd56" name="instance_56">
<matrix>0.25  0 0 0.0   0 1  0 1.1  0 0 1 4.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDd57" name="instance_57">
<matrix>0.25  0 0 0.0   0 1  0 2.2  0 0 1 4.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
</node>
<!--  Division sign #1  -->
<node name="Divide1">
<translate>0.0 4.4 1.0</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 0.75 1.0</scale>
<node id="IDd21" name="instance_21">
<matrix>0.25  0 0 0.0   0 1  0 0.0  0 0 1 0.0  0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
<node id="IDd22" name="instance_22">
<matrix>0.25  0 0 0.0   0 -1  0 1.1  0 0 -1 0.0  0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
<node id="IDd23" name="instance_23">
<matrix>0.25  0 0 0.0   0 1  0 1.1  0 0 1 1.1  0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
<node id="IDd24" name="instance_24">
<matrix>0.25  0 0 0.0   0 -1  0 2.2  0 0 -1 1.1  0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
<node id="IDd25" name="instance_25">
<matrix>0.25  0 0 0.0   0 1  0 2.2  0 0 1 2.2  0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
<node id="IDd26" name="instance_26">
<matrix>0.25  0 0 0.0   0 -1  0 3.3  0 0 -1 2.2  0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
<node id="IDd27" name="instance_27">
<matrix>0.25  0 0 0.0   0 1  0 3.3  0 0 1 3.3  0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
</node>
<!--  Division sign #2  -->
<node name="Divide2">
<translate>0.0 4.4 -8.5</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 0.75 1.0</scale>
<node id="IDd21" name="instance_21">
<matrix>0.25  0 0 0.0   0 1  0 0.0  0 0 1 0.0  0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
<node id="IDd22" name="instance_22">
<matrix>0.25  0 0 0.0   0 -1  0 1.1  0 0 -1 0.0  0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
<node id="IDd23" name="instance_23">
<matrix>0.25  0 0 0.0   0 1  0 1.1  0 0 1 1.1  0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
<node id="IDd24" name="instance_24">
<matrix>0.25  0 0 0.0   0 -1  0 2.2  0 0 -1 1.1  0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
<node id="IDd25" name="instance_25">
<matrix>0.25  0 0 0.0   0 1  0 2.2  0 0 1 2.2  0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
<node id="IDd26" name="instance_26">
<matrix>0.25  0 0 0.0   0 -1  0 3.3  0 0 -1 2.2  0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
<node id="IDd27" name="instance_27">
<matrix>0.25  0 0 0.0   0 1  0 3.3  0 0 1 3.3  0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
</node>
<!--  Letter "a" #1  -->
<node name="Letter_a1">
<translate>0.0 8.0 1.0</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<node id="IDa01" name="instance_1">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa06" name="instance_6">
<matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 2.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa07" name="instance_7">
<matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 2.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa10" name="instance_10">
<matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa11" name="instance_11">
<matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa18" name="instance_18">
<matrix>0.25  0 0 0.0  0 1 0 0.0  0 0  1 2.2  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDa19" name="instance_19">
<matrix>0.25  0 0 0.0  0 0 1 4.4  0 -1 0 0.0  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDa19" name="instance_19">
<matrix>0.25  0 0 0.0  0 0 -1 3.3  0 1 0 0.0  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDa11" name="instance_11">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa31" name="instance_11">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa20" name="instance_20">
<matrix>0.25  0 0 0.0   0 0 1 3.3  0 -1 0 3.3  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDa21" name="instance_21">
<matrix>0.25  0 0 0.0   0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
</node>
<!--  Letter "a" #2  -->
<node name="Letter_a2">
<translate>0.0 8.0 -8.5</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<node id="IDa01" name="instance_1">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa06" name="instance_6">
<matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 2.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa07" name="instance_7">
<matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 2.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa10" name="instance_10">
<matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa11" name="instance_11">
<matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa18" name="instance_18">
<matrix>0.25  0 0 0.0  0 1 0 0.0  0 0  1 2.2  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDa19" name="instance_19">
<matrix>0.25  0 0 0.0  0 0 1 4.4  0 -1 0 0.0  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDa19" name="instance_19">
<matrix>0.25  0 0 0.0  0 0 -1 3.3  0 1 0 0.0  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDa11" name="instance_11">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa31" name="instance_11">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa20" name="instance_20">
<matrix>0.25  0 0 0.0   0 0 1 3.3  0 -1 0 3.3  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDa21" name="instance_21">
<matrix>0.25  0 0 0.0   0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
</node>
<!--  Letter "a" #2  -->
<node name="Letter_a2">
<translate>0.0 8.0 -8.5</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<node id="IDa01" name="instance_1">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa06" name="instance_6">
<matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 2.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa07" name="instance_7">
<matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 2.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa10" name="instance_10">
<matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa11" name="instance_11">
<matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa18" name="instance_18">
<matrix>0.25  0 0 0.0  0 1 0 0.0  0 0  1 2.2  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDa19" name="instance_19">
<matrix>0.25  0 0 0.0  0 0 1 4.4  0 -1 0 0.0  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDa19" name="instance_19">
<matrix>0.25  0 0 0.0  0 0 -1 3.3  0 1 0 0.0  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDa11" name="instance_11">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa31" name="instance_11">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa20" name="instance_20">
<matrix>0.25  0 0 0.0   0 0 1 3.3  0 -1 0 3.3  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDa21" name="instance_21">
<matrix>0.25  0 0 0.0   0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
</node>
<!--  Letter "c"  -->
<node name="Letter_c">
<translate>0.0 0.0 -8.5</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<node id="ID001" name="instance_1">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID002" name="instance_2">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 2.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID006" name="instance_6">
<matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 3.3  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID007" name="instance_7">
<matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 3.3  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID010" name="instance_10">
<matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID011" name="instance_11">
<matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID018" name="instance_18">
<matrix>0.25  0 0 0.0  0 1 0 0.0  0 0  1 3.3  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="ID019" name="instance_19">
<matrix>0.25  0 0 0.0  0 -1 0 3.3  0 0  -1 0.0  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="ID020" name="instance_20">
<matrix>0.25  0 0 0.0   0 0 1 3.3  0 -1 0 3.3  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="ID021" name="instance_21">
<matrix>0.25  0 0 0.0   0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
</node>
<!--  Letter "b"  ... has 8 + (4 x 15) = 68 lines -->
<node name="Letter_b">
<translate>0.0 0.0 1.0</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<node id="IDb01" name="instance_1">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb02" name="instance_2">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 2.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb03" name="instance_3">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 3.3  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb04" name="instance_4">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 4.4  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb05" name="instance_5">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 5.5  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb12" name="instance_12">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 6.6  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb06" name="instance_6">
<matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 3.3  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb07" name="instance_7">
<matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 3.3  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb08" name="instance_8">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb09" name="instance_9">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb10" name="instance_10">
<matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb11" name="instance_11">
<matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb19" name="instance_19">
<matrix>0.25  0 0 0.0  0 -1 0 3.3  0 0  -1 0.0  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDb20" name="instance_20">
<matrix>0.25  0 0 0.0   0 0 1 3.3  0 -1 0 3.3  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDb21" name="instance_21">
<matrix>0.25  0 0 0.0   0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
</node>
<!-- DECIMAL POINTS -->
<node id="IDD01" name="Decimal_1">
<matrix>0.25 0 0 0.0  0 1 0 25.0  0 0 1 1.0  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDD02" name="Decimal_2">
<matrix>0.25 0 0 0.0  0 1 0 25.0  0 0 1 -8.5  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<!--  Number "0" #1  ... has 8 + (4 x 18) = 80 lines -->
<node name="Number_0">
<translate>0.0 20.0 1.0</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<node id="IDb01" name="instance_1">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb02" name="instance_2">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 2.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb03" name="instance_3">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 3.3  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb04" name="instance_4">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 4.4  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb05" name="instance_5">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 5.5  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDz19" name="instance_z19">
<matrix>0.25  0 0 0.0  0 1 0 0.0  0 0 1 6.6  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDb06" name="instance_6">
<matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 6.6  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb07" name="instance_7">
<matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 6.6  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb08" name="instance_8">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb09" name="instance_9">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb10" name="instance_10">
<matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb11" name="instance_11">
<matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb19" name="instance_19">
<matrix>0.25  0 0 0.0  0 -1 0 3.3  0 0  -1 0.0  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDb20" name="instance_20">
<matrix>0.25  0 0 0.0   0 0 1 3.3  0 -1 0 6.6  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDb21" name="instance_21">
<matrix>0.25  0 0 0.0   0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDz11" name="instance_z11">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 3.3  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDz12" name="instance_z12">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 4.4  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDz13" name="instance_z13">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 5.5  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
</node>
<!--  Number "0" #2  ... has 8 + (4 x 18) = 80 lines -->
<node name="Number_0b">
<translate>0.0 20.0 -8.5</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<node id="IDb01" name="instance_1">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb02" name="instance_2">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 2.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb03" name="instance_3">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 3.3  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb04" name="instance_4">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 4.4  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb05" name="instance_5">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 5.5  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDz19" name="instance_z19">
<matrix>0.25  0 0 0.0  0 1 0 0.0  0 0 1 6.6  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDb06" name="instance_6">
<matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 6.6  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb07" name="instance_7">
<matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 6.6  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb08" name="instance_8">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb09" name="instance_9">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb10" name="instance_10">
<matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb11" name="instance_11">
<matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb19" name="instance_19">
<matrix>0.25  0 0 0.0  0 -1 0 3.3  0 0  -1 0.0  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDb20" name="instance_20">
<matrix>0.25  0 0 0.0   0 0 1 3.3  0 -1 0 6.6  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDb21" name="instance_21">
<matrix>0.25  0 0 0.0   0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDz11" name="instance_z11">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 3.3  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDz12" name="instance_z12">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 4.4  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDz13" name="instance_z13">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 5.5  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
</node>
<!--  Number "1" ... has 8 + (4 x 8) = 40 lines -->
<!--  Number "2" #1 ... has 8 + (4 x 17) = 76 lines -->
<!--  Number "2" #2 ... has 8 + (4 x 17) = 76 lines -->
<!--  Number "3"  ... has 8 + (4 x 18) = 80 lines -->
<!--  Number "4" ... has 8 + (4 x 13) = 60 lines -->
<!--  Number "5"  ... has 8 + (4 x 17) = 76 lines -->
<!--  Number "6" ... has 8 + (4 x 18) = 80 lines -->
<!--  Number "7" ... has 8 + (4 x 14) = 64 lines -->
<!--  Number "8" ... has 8 + (4 x 22) = 96 lines -->
<!--  Number "9"  ... has 8 + (4 x 15) = 68 lines -->
<!-- bovera_Digit1 is "4" -->
<node name="bovera_Digit1">
<translate>0.0 26.8 1.0</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<!--  Number "4" ... has 8 + (4 x 13) = 60 lines -->
<node id="IDe01" name="instance_e01">
<matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 3.3  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDe02" name="instance_e02">
<matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 3.3  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDe02" name="instance_e02">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 3.3  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb04" name="instance_4">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 4.4  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb05" name="instance_5">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 5.5  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb06" name="instance_6">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 6.6  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb08" name="instance_8">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb09" name="instance_9">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDn09" name="instance_9">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 0.0  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDf12" name="instance_n12">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 6.6  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDn12" name="instance_n12">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 3.3  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDz12" name="instance_z12">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 4.4  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDz13" name="instance_z13">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 5.5  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
</node>
<!-- bovera_Digit2 is "1" -->
<node name="bovera_Digit2">
<translate>0.0 31.8 1.0</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<!--  Number "1" ... has 8 + (4 x 8) = 40 lines -->
<node id="ID101" name="instance_1">
<matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID102" name="instance_1">
<matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 1.1  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID103" name="instance_1">
<matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 2.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID104" name="instance_1">
<matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 3.3  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID105" name="instance_1">
<matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 4.4  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID106" name="instance_1">
<matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 5.5  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID107" name="instance_1">
<matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 6.6  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID109" name="instance_z19">
<matrix>0.25  0 0 0.0  0 1 0 1.1  0 0 1 6.6  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
</node>
<!-- covera_Digit1 is "3" -->
<node name="covera_Digit1">
<translate>0.0 26.8 -8.5</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<!--  Number "3"  ... has 8 + (4 x 18) = 80 lines -->
<node id="ID301" name="instance_e01">
<matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 3.3  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID302" name="instance_e02">
<matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 3.3  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID303" name="instance_1">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID304" name="instance_5">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 5.5  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID305" name="instance_z19">
<matrix>0.25  0 0 0.0  0 1 0 0.0  0 0 1 6.6  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="ID306" name="instance_6">
<matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 6.6  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID307" name="instance_7">
<matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 6.6  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID308" name="instance_8">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID309" name="instance_9">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID310" name="instance_10">
<matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID311" name="instance_11">
<matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID312" name="instance_19">
<matrix>0.25  0 0 0.0  0 -1 0 3.3  0 0  -1 0.0  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="ID313" name="instance_20">
<matrix>0.25  0 0 0.0   0 0 1 3.3  0 -1 0 6.6  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="ID314" name="instance_21">
<matrix>0.25  0 0 0.0   0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="ID315" name="instance_e19">
<matrix>0.25  0 0 0.0  0 -1 0 3.3  0 0  -1 3.3  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="ID316" name="instance_e20">
<matrix>0.25  0 0 0.0   0 0 1 3.3  0 -1 0 3.3  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="ID317" name="instance_z12">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 4.4  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID318" name="instance_z13">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 5.5  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
</node>
<!-- covera_Digit2 is "8" -->
<node name="covera_Digit2">
<translate>0.0 31.8 -8.5</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<!--  Number "8" ... has 8 + (4 x 22) = 96 lines -->
<node id="IDe01" name="instance_e01">
<matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 3.3  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDe02" name="instance_e02">
<matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 3.3  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb01" name="instance_1">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb02" name="instance_2">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 2.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDe19" name="instance_e19">
<matrix>0.25  0 0 0.0  0 1 0 0.0  0 0 1 3.3  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDe21" name="instance_e21">
<matrix>0.25  0 0 0.0   0 0 -1 0.0  0 1 0 3.3  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDb04" name="instance_4">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 4.4  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb05" name="instance_5">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 5.5  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDz19" name="instance_z19">
<matrix>0.25  0 0 0.0  0 1 0 0.0  0 0 1 6.6  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDb06" name="instance_6">
<matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 6.6  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb07" name="instance_7">
<matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 6.6  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb08" name="instance_8">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb09" name="instance_9">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb10" name="instance_10">
<matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb11" name="instance_11">
<matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb19" name="instance_19">
<matrix>0.25  0 0 0.0  0 -1 0 3.3  0 0  -1 0.0  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDb20" name="instance_20">
<matrix>0.25  0 0 0.0   0 0 1 3.3  0 -1 0 6.6  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDb21" name="instance_21">
<matrix>0.25  0 0 0.0   0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDe19" name="instance_e19">
<matrix>0.25  0 0 0.0  0 -1 0 3.3  0 0  -1 3.3  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDe20" name="instance_e20">
<matrix>0.25  0 0 0.0   0 0 1 3.3  0 -1 0 3.3  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDz12" name="instance_z12">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 4.4  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDz13" name="instance_z13">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 5.5  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
</node>
<!-- covera_Digit3 is "5" -->
<node name="covera_Digit3">
<translate>0.0 37.1 -8.5</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<!--  Number "5"  ... has 8 + (4 x 17) = 76 lines -->
<node id="IDb01" name="instance_1">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb04" name="instance_4">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 4.4  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb05" name="instance_5">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 5.5  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDf06" name="instance_f6">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 6.6  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb06" name="instance_6">
<matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 6.6  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb07" name="instance_7">
<matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 6.6  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb08" name="instance_8">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb09" name="instance_9">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb10" name="instance_10">
<matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb11" name="instance_11">
<matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb19" name="instance_19">
<matrix>0.25  0 0 0.0  0 -1 0 3.3  0 0  -1 0.0  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDb20" name="instance_20">
<matrix>0.25  0 0 0.0   0 0 1 3.3  0 -1 0 3.3  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDf11" name="instance_f11">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 6.6  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb21" name="instance_21">
<matrix>0.25  0 0 0.0   0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDf21" name="instance_f21">
<matrix>0.25  0 0 0.0   0 0 -1 0.0  0 1 0 3.3  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDz12" name="instance_z12">
<matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 3.3  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDz13" name="instance_z13">
<matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 3.3  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
</node>
<!-- END LABELING HERE -->
</node>
<!-- BEGIN CLOCK -->
<node id="EntireClock" name="instance_Clock">
<translate>7.0 0.0 5.0</translate>
<rotate sid="rotationX">1.0 0.0 0.0 0.0</rotate>
<rotate sid="rotationY">0.0 1.0 0.0 0.0</rotate>
<rotate sid="rotationZ">0.0 0.0 1.0 0.0</rotate>
<scale sid="scale">1.00 1.00 1.00</scale>
<node id="firstclock" name="instance_1">        <!-- TWO -->
<translate>0.0 0.0 0.0</translate>
<rotate sid="rotationX">1.0 0.0 0.0 0.0</rotate>
<rotate sid="rotationY">0.0 1.0 0.0 -90.0</rotate>
<rotate sid="rotationZ">0.0 0.0 1.0 0.0</rotate>
<scale sid="scale">1.00 1.00 1.00</scale>
<instance_node url="#ID3" />
</node>                                         <!-- /TWO -->
<node id="Jetman" name="instance_Arrow">        <!-- TWO -->
<matrix sid="transformation"> 0.000  0.000 -1.00  0.00  -1.0000  0.0000  0.000  0.000   0.0000  1.0000  0.000  0.00   0.000  0.000  0.000  1.000</matrix>
<instance_node url="#ArrowID3" />
</node>                                         <!-- /TWO -->
<node id="HourHand" name="instance_Hour">       <!-- TWO -->
<translate>0.0 0.0 0.0</translate>
<rotate sid="rotationX">1.0 0.0 0.0 0.0</rotate>
<rotate sid="rotationY">0.0 1.0 0.0 -90.0</rotate>
<rotate sid="rotationZ">0.0 0.0 1 270.0</rotate>
<scale sid="scale">0.75 0.75 0.75</scale>
<instance_node url="#HourID3" />
</node>                                         <!-- /TWO -->
</node>
<!-- END CLOCK   -->
</node> <!-- End Inertial Grouping of Objects -->
</visual_scene>
</library_visual_scenes>
<scene>
<instance_visual_scene url="#ID1" />
</scene>



 Instructions for Viewing the Example Model on a Mac: Click, then drag your cursor down through the scrollable box to highlight and select all 7968 lines of the COLLADA code. Make a copy (⌘-c) of the entire code. Paste (⌘-v) the code into an empty, plain text file (using, for example, Apple's TextEdit app) and save it with the name, Inertial17.dae. [NOTE: ".dae" is the file name suffix that is universally associated with an executable COLLADA file.] Open this file using Apple's Preview app; the static 3D model of our (opaque purple) ellipsoid should appear at TIME = 0.0 — see Figure 1b. To view the 3D (TIME = 0.0) model from different angles, place your mouse cursor anywhere near the center of the Preview app's image, then click and drag the cursor in different directions. The play/pause buttons — shown at the bottom of Figure 1b — become visible if the cursor is simply placed near the bottom of the image being displayed by the Preview app; the animation will start (on a continuous loop) when the play button is clicked. Instructions for Viewing the Example Model on a Windows 10 PC: We have not yet figured out how to similarly (at no cost) view COLLADA-based (.dae) 3D scenes on a PC. On my Lenovo system, the Windows 10 startup menu includes a "3D Viewer" app, but this app does not recognize .dae-formatted files. However, the app appears to read .glb-formatted files satisfactorily. As is discussed below, the Oculus Rift S system will import our COLLADA-based models only if each model file has been translated from a ".dae" format to a ".glb" format. Hence, after this translation has been made principally to facilitate the importation of our model into the Oculus Rift S virtual-reality environment — see our description, below, of the Khronos Group's COLLADA2GLTF Converter — we have also been able to straightforwardly view the 3D scene on our Lenovo PC using its "3D Viewer" app.

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

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

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

### Animation

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

1. We use the motion of the hands on the wall-mounted clock to identify the natural oscillation frequency of the physical system, namely, ${\displaystyle ~\Omega _{0}\equiv [\pi G\rho ]^{1/2}}$. More specifically, by declaration, one oscillation period of the red "minute" hand — that is to say, one wall-clock "hour" — is ${\displaystyle ~P_{0}=2\pi [\pi G\rho ]^{-1/2}=[4\pi /(G\rho )]^{1/2}}$. One full cycle of the wall-clock's black "hour" hand is therefore 12P0. For pedagogical purposes, in all of our COLLADA-driven animations we have equated P0 with a COLLADA TIME interval of 4.0, which means that during each animation, one wall-clock hour passes every (approximately) 4 seconds of real time.
2. The purple ellipsoid spins in a prograde direction about its shortest axis — that is, about the Z0-axis — on a timescale set by the value of ${\displaystyle ~\Omega _{\mathrm {EFE} }}$, which has already been normalized to Ω0. Specifically, as viewed from the inertial frame of reference, the ellipsoid will complete one full spin in a time, ${\displaystyle ~P_{\mathrm {spin} }=|\Omega _{\mathrm {EFE} }|^{-1}=[0.5479]^{-1}=1.825}$ wall-clock hours, which is approximately 7.3 seconds of real time.
3. As viewed from a frame of reference that is spinning with the ellipsoid, each Lagrangian fluid element inside as well as on the surface of the ellipsoid moves in a retro-grade direction along an elliptical trajectory that has the same ellipticity as does the equatorial surface of the 3D ellipsoid. Each and every Lagrangian fluid element completes one full elliptical orbit in a time, ${\displaystyle ~P_{\mathrm {Lagrange} }=\lambda _{\mathrm {EFE} }^{-1}=[0.0799]^{-1}=12.52}$ wall-clock hours, which is about 50 seconds of real time.

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

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

Figure 2a Figure 2b

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 ${\displaystyle ~0.73P_{\mathrm {Lagrange} }\approx ~5P_{\mathrm {spin} }}$, that is, ${\displaystyle ~P_{\mathrm {Lagrange} }\approx 6.849P_{\mathrm {spin} }}$. This is indeed a proper reflection of the physical properties of our chosen example Riemann S-type ellipsoid, as its mathematically determined equilibrium frequency ratio is, ${\displaystyle ~|\Omega _{\mathrm {EFE} }|/|\lambda _{\mathrm {EFE} }|=6.8582}$. This, too, illustrates that the proper physical timescales governing oscillations of our chosen example Riemann ellipsoid have been implemented in a quantitatively accurate manner within the COLLADA code.

### Rotating Reference Frame

 Figure 3

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

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

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

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

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

<node>        <geometry>       <material>      <effect>
*** firstclock:    ID3     Clock_OuterEdge         ID6            ID5
***           :            Clock_InnerEdge       InnerID6       InnerID5
***   Jetman  :  ArrowID3  Clock_ArrowEdge       ArrowID6       ArrowID5
***  HourHand :  HourID3   Clock_HourEdge        HourID6        HourID5
-->
</asset>
<library_effects>
<effect id="DiffusePurple_00">
<profile_COMMON>
<technique sid="COMMON">
<phong>
<diffuse>
<color>0.5 0.0 0.99  1.0</color>
</diffuse>
<transparency>
<float sid="transparency">0.6</float>
</transparency>
</phong>
</technique>
</profile_COMMON>
</effect>
<effect id="DiffuseRed_EFE">
<profile_COMMON>
<technique sid="COMMON">
<lambert>
<diffuse>
<color>1.0 0.0 0.0  1.0</color>
</diffuse>
</lambert>
</technique>
</profile_COMMON>
</effect>
<!-- effect:  MidPlane Frame -->
<effect id="MidPlaneID5">
<profile_COMMON>
<technique sid="COMMON">
<lambert>
<diffuse>
<color>0.0 0.0 0.6 0.5</color>
</diffuse>
</lambert>
</technique>
</profile_COMMON>
</effect>
<!-- effect:  Cylindrical Pointer -->
<effect id="CylID5">
<profile_COMMON>
<technique sid="COMMON">
<lambert>
<diffuse>
<color>0.0 0.0 0.0 1.0</color>
</diffuse>
</lambert>
</technique>
</profile_COMMON>
</effect>
<effect id="MarkersID5">
<profile_COMMON>
<technique sid="COMMON">
<lambert>
<diffuse>
<color>1 1 0 1</color>
</diffuse>
</lambert>
</technique>
</profile_COMMON>
</effect>
<!-- effect:  Letters -->
<effect id="LettersID5">
<profile_COMMON>
<technique sid="COMMON">
<lambert>
<diffuse>
<color>0 0 0 1</color>
</diffuse>
</lambert>
</technique>
</profile_COMMON>
</effect>
<effect id="DiagonalID5">
<profile_COMMON>
<technique sid="COMMON">
<lambert>
<diffuse>
<color>0 0 1 1</color>
</diffuse>
</lambert>
</technique>
</profile_COMMON>
</effect>
<effect id="Black_DiagonalID5">
<profile_COMMON>
<technique sid="COMMON">
<lambert>
<diffuse>
<color>0 0 0 1</color>
</diffuse>
</lambert>
</technique>
</profile_COMMON>
</effect>
<!-- effect:  Four Clock Components -->
<effect id="ID5">
<profile_COMMON>
<technique sid="COMMON">
<lambert>
<diffuse>
<color>0 0 1 1</color>
</diffuse>
</lambert>
</technique>
</profile_COMMON>
</effect>
<effect id="InnerID5">
<profile_COMMON>
<technique sid="COMMON">
<lambert>
<diffuse>
<color>0.4 0.0 0.7 0.4</color>
</diffuse>
</lambert>
</technique>
</profile_COMMON>
</effect>
<effect id="ArrowID5">
<profile_COMMON>
<technique sid="COMMON">
<lambert>
<diffuse>
<color>1.0 0.0 0.0 1.0</color>
</diffuse>
</lambert>
</technique>
</profile_COMMON>
</effect>
<effect id="HourID5">
<profile_COMMON>
<technique sid="COMMON">
<lambert>
<diffuse>
<color>0.0 0.0 0.0 1.0</color>
</diffuse>
</lambert>
</technique>
</profile_COMMON>
</effect>
</library_effects>
<library_materials>
<!-- material:  Four Clock Components -->
<material id="ID6" name="material">
<instance_effect url="#ID5" />
</material>
<material id="InnerID6" name="Inner_material">
<instance_effect url="#InnerID5" />
</material>
<material id="ArrowID6" name="Arrow_material">
<instance_effect url="#ArrowID5" />
</material>
<material id="HourID6" name="Hour_material">
<instance_effect url="#HourID5" />
</material>
<material id="ID6_EFE" name="material">
<instance_effect url="#DiffusePurple_00" />
</material>
<!-- material:  MidPlane Frame -->
<material id="MidPlaneID6" name="MidPlane_material">
<instance_effect url="#MidPlaneID5" />
</material>
<!-- material:  Cylindrical Pointer -->
<material id="CylID6" name="Cyl_material">
<instance_effect url="#CylID5" />
</material>
<material id="ZupID6" name="Zup_material">
<instance_effect url="#MidPlaneID5" />
</material>
<material id="MarkersID6" name="markers_material">
<instance_effect url="#MarkersID5" />
</material>
<material id="Primary_MarkerID6" name="primary_marker_material">
<instance_effect url="#DiffuseRed_EFE" />
</material>
<!-- material:  Letters -->
<material id="LettersID6" name="material">
<instance_effect url="#LettersID5" />
</material>
<material id="DiagonalID6" name="material">
<instance_effect url="#DiagonalID5" />
</material>
<material id="Black_DiagonalID6" name="material">
<instance_effect url="#Black_DiagonalID5" />
</material>
</library_materials>
<library_nodes>
<!-- node:  Three clock components -->
<node id="ID3" name="cube_component">
<instance_geometry url="#Clock_OuterEdge">
<bind_material>
<technique_common>
<instance_material symbol="Material2" target="#ID6">
<bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
</instance_material>
</technique_common>
</bind_material>
</instance_geometry>
<instance_geometry url="#Clock_InnerEdge">
<bind_material>
<technique_common>
<instance_material symbol="Material2" target="#InnerID6">
<bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
</instance_material>
</technique_common>
</bind_material>
</instance_geometry>
</node>
<node id="ArrowID3" name="cube_component">
<instance_geometry url="#Clock_ArrowEdge">
<bind_material>
<technique_common>
<instance_material symbol="Material2" target="#ArrowID6">
<bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
</instance_material>
</technique_common>
</bind_material>
</instance_geometry>
</node>
<node id="HourID3" name="hour_hand">
<instance_geometry url="#Clock_HourEdge">
<bind_material>
<technique_common>
<instance_material symbol="Material2" target="#HourID6">
<bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
</instance_material>
</technique_common>
</bind_material>
</instance_geometry>
</node>
<node id="ID3_EFE" name="cube_componentEFE">
<instance_geometry url="#EllipsoidOctant">
<bind_material>
<technique_common>
<instance_material symbol="Material2" target="#ID6_EFE">
<bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
</instance_material>
</technique_common>
</bind_material>
</instance_geometry>
<instance_geometry url="#ReflectOctant">
<bind_material>
<technique_common>
<instance_material symbol="Material2" target="#ID6_EFE">
<bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
</instance_material>
</technique_common>
</bind_material>
</instance_geometry>
</node>
<!-- node:  MidPlane Frame -->
<node id="EqPlane" name="equatorial_plane">
<instance_geometry url="#EquatorialPlane">
<bind_material>
<technique_common>
<instance_material symbol="Material2" target="#MidPlaneID6">
<bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
</instance_material>
</technique_common>
</bind_material>
</instance_geometry>
</node>
<!-- node:  Cylindrical Pointer -->
<node id="CylPointer" name="cylindrical_component">
<instance_geometry url="#Cylinder">
<bind_material>
<technique_common>
<instance_material symbol="Material2" target="#CylID6">
<bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
</instance_material>
</technique_common>
</bind_material>
</instance_geometry>
</node>
<node id="ZupPointer" name="Zup_component">
<instance_geometry url="#CubeID4">
<bind_material>
<technique_common>
<instance_material symbol="Material2" target="#ZupID6">
<bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
</instance_material>
</technique_common>
</bind_material>
</instance_geometry>
</node>
<node id="MarkersID3" name="Lagrange_markers">
<instance_geometry url="#CubeID4">
<bind_material>
<technique_common>
<instance_material symbol="Material2" target="#MarkersID6">
<bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
</instance_material>
</technique_common>
</bind_material>
</instance_geometry>
</node>
<node id="Primary_MarkerID3" name="Primary_marker">
<instance_geometry url="#CubeID4">
<bind_material>
<technique_common>
<instance_material symbol="Material2" target="#Primary_MarkerID6">
<bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
</instance_material>
</technique_common>
</bind_material>
</instance_geometry>
</node>
<!-- node:  Letters -->
<node id="LettersID3" name="cube_component">
<instance_geometry url="#CubeID4">
<bind_material>
<technique_common>
<instance_material symbol="Material2" target="#LettersID6">
<bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
</instance_material>
</technique_common>
</bind_material>
</instance_geometry>
</node>
<node id="DiagonalID3" name="diagonal_component">
<instance_geometry url="#DiagonalID4">
<bind_material>
<technique_common>
<instance_material symbol="Material2" target="#DiagonalID6">
<bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
</instance_material>
</technique_common>
</bind_material>
</instance_geometry>
</node>
<node id="Black_DiagonalID3" name="Blackdiagonal_component">
<instance_geometry url="#DiagonalID4">
<bind_material>
<technique_common>
<instance_material symbol="Material2" target="#Black_DiagonalID6">
<bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
</instance_material>
</technique_common>
</bind_material>
</instance_geometry>
</node>
</library_nodes>
<library_geometries>
<!-- geometry:  Four Clock Components -->
<geometry id="Clock_OuterEdge">
<mesh>
<!--
**********************************************
*
*  Insert first portion of clock's structure
*
**********************************************
-->
<source id="Clock_Positions">
<float_array id="Coordinates01" count="123"> 0.0  1.0  0.2 1.0  1.0  0.2 1.0  0.0  0.2 1.0 -1.0  0.2 0.0 -1.0  0.2 -1.0 -1.0  0.2 -1.0  0.0  0.2 -1.0  1.0  0.2 0.0  1.0 -0.2 1.0  1.0 -0.2 1.0  0.0 -0.2 1.0 -1.0 -0.2 0.0 -1.0 -0.2 -1.0 -1.0 -0.2 -1.0  0.0 -0.2 -1.0  1.0 -0.2 0.9  0.0  0.2 0.779423 0.45 0.2 0.45 0.779423 0.2 0.0  0.9  0.2 -0.45 0.779423 0.2 -0.779423 0.45 0.2 -0.9 0.0 0.2 -0.779423 -0.45 0.2 -0.45 -0.779423 0.2 0.0 -0.9 0.2 0.45 -0.779423 0.2 0.779423 -0.45 0.2 -0.9  0.0  -0.2 -0.779423 0.45 -0.2 -0.45 0.779423 -0.2 -0.0  0.9  -0.2 0.45 0.779423 -0.2 0.779423 0.45 -0.2 0.9 0.0 -0.2 0.779423 -0.45 -0.2 0.45 -0.779423 -0.2 -0.0 -0.9 -0.2 -0.45 -0.779423 -0.2 -0.779423 -0.45 -0.2  0.0 0.0 -0.2</float_array>
<technique_common>
<accessor source="#Coordinates01" count="41" stride="3">
<param name="X" type="float" />
<param name="Y" type="float" />
<param name="Z" type="float" />
</accessor>
</technique_common>
</source>
<source id="Clock_Normals">
<float_array id="InnerNormals01" count="18">
1.0  0.0  0.0
-1.0  0.0  0.0
0.0  1.0  0.0
0.0 -1.0  0.0
0.0  0.0  1.0
0.0  0.0 -1.0
</float_array>
<technique_common>
<accessor source="#InnerNormals01" count="6" stride="3">
<param name="X" type="float" />
<param name="Y" type="float" />
<param name="Z" type="float" />
</accessor>
</technique_common>
</source>
<vertices id="Clock_Vertices">
<input semantic="POSITION" source="#Clock_Positions" />
</vertices>
<polylist count="56" material="Material2">
<input semantic="VERTEX" source="#Clock_Vertices" offset="0" />
<input semantic="NORMAL" source="#Clock_Normals" offset="1" />
<vcount> 3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3</vcount>
<p> 0 2 1 2 8 2  1 2 9 2 8 2  7 2 0 2 15 2  0 2 8 2 15 2 1 0 2 0 9 0  2 0 10 0 9 0  2 0 3 0 10 0  3 0 11 0 10 0 3 3 4 3 11 3  4 3 12 3 11 3  4 3 5 3 12 3  5 3 13 3 12 3 5 1 6 1 13 1  6 1 14 1 13 1  6 1 7 1 14 1  7 1 15 1 14 1 2 4 17 4 16 4  2 4 1 4 17 4  1 4 18 4 17 4  1 4 0 4 18 4  0 4 19 4 18 4 0 4 20 4 19 4  0 4 7 4 20 4  7 4 21 4 20 4  7 4 6 4 21 4  6 4 22 4 21 4 6 4 23 4 22 4  6 4 5 4 23 4  5 4 24 4 23 4  5 4 4 4 24 4  4 4 25 4 24 4 4 4 26 4 25 4  4 4 3 4 26 4  3 4 27 4 26 4  3 4 2 4 27 4  2 4 16 4 27 4 14 5 29 5 28 5  14 5 15 5 29 5  15 5 30 5 29 5  15 5 8 5 30 5  8 5 31 5 30 5 8 5 32 5 31 5  8 5 9 5 32 5  9 5 33 5 32 5  9 5 10 5 33 5  10 5 34 5 33 5 10 5 35 5 34 5  10 5 11 5 35 5  11 5 36 5 35 5  11 5 12 5 36 5  12 5 37 5 36 5 12 5 38 5 37 5  12 5 13 5 38 5  13 5 39 5 38 5  13 5 14 5 39 5  14 5 28 5 39 5 </p>
</polylist>
</mesh>
</geometry>
<geometry id="Clock_InnerEdge">
<mesh>
<!--
**********************************************
*
*  Insert second portion of clock's structure
*
**********************************************
-->
<source id="Clock_InnerPositions">
<float_array id="InnerCoordinates01" count="123">
0.0  1.0  0.2 1.0  1.0  0.2 1.0  0.0  0.2 1.0 -1.0  0.2 0.0 -1.0  0.2 -1.0 -1.0  0.2 -1.0  0.0  0.2 -1.0  1.0  0.2 0.0  1.0 -0.2 1.0  1.0 -0.2 1.0  0.0 -0.2 1.0 -1.0 -0.2 0.0 -1.0 -0.2 -1.0 -1.0 -0.2 -1.0  0.0 -0.2 -1.0  1.0 -0.2 0.9  0.0  0.2 0.779423 0.45 0.2 0.45 0.779423 0.2 0.0  0.9  0.2 -0.45 0.779423 0.2 -0.779423 0.45 0.2 -0.9 0.0 0.2 -0.779423 -0.45 0.2 -0.45 -0.779423 0.2 0.0 -0.9 0.2 0.45 -0.779423 0.2 0.779423 -0.45 0.2 -0.9  0.0  -0.2 -0.779423 0.45 -0.2 -0.45 0.779423 -0.2 -0.0  0.9  -0.2 0.45 0.779423 -0.2 0.779423 0.45 -0.2 0.9 0.0 -0.2 0.779423 -0.45 -0.2 0.45 -0.779423 -0.2 -0.0 -0.9 -0.2 -0.45 -0.779423 -0.2 -0.779423 -0.45 -0.2  0.0 0.0 -0.2</float_array>
<technique_common>
<accessor source="#InnerCoordinates01" count="41" stride="3">
<param name="X" type="float" />
<param name="Y" type="float" />
<param name="Z" type="float" />
</accessor>
</technique_common>
</source>
<source id="Clock_InnerNormals">
<float_array id="InnerNormals01" count="54">
1.0  0.0  0.0
-1.0  0.0  0.0
0.0  1.0  0.0
0.0 -1.0  0.0
0.0  0.0  1.0
0.0  0.0 -1.0
-0.965926 -0.258819 0.0
-0.707107 -0.707107 0.0
-0.258819 -0.965926 0.0
0.258819 -0.965926 0.0
0.707107 -0.707107 0.0
0.965926 -0.258819 0.0
0.965926  0.258819 0.0
0.707107  0.707107 0.0
0.258819  0.965926 0.0
-0.258819  0.965926 0.0
-0.707107  0.707107 0.0
-0.965926  0.258819 0.0
</float_array>
<technique_common>
<accessor source="#InnerNormals01" count="18" stride="3">
<param name="X" type="float" />
<param name="Y" type="float" />
<param name="Z" type="float" />
</accessor>
</technique_common>
</source>
<vertices id="Clock_InnerVertices">
<input semantic="POSITION" source="#Clock_InnerPositions" />
</vertices>
<polylist count="24" material="Material2">
<input semantic="VERTEX" source="#Clock_InnerVertices" offset="0" />
<input semantic="NORMAL" source="#Clock_InnerNormals" offset="1"/>
<vcount>4 4 4 4  4 4 4 4  4 4 4 4  3 3 3 3  3 3 3 3  3 3 3 3</vcount>
<p> 16 6 17 6 33 6 34 6 17 7 18 7 32 7 33 7 18 8 19 8 31 8 32 8 19 9 20 9 30 9 31 9 20 10 21 10 29 10 30 10 21 11 22 11 28 11 29 11 22 12 23 12 39 12 28 12 23 13 24 13 38 13 39 13 24 14 25 14 37 14 38 14 25 15 26 15 36 15 37 15 26 16 27 16 35 16 36 16 27 17 16 17 34 17 35 17 28 5 29 5 40 5 29 5 30 5 40 5 30 5 31 5 40 5 31 5 32 5 40 5 32 5 33 5 40 5 33 5 34 5 40 5 34 5 35 5 40 5 35 5 36 5 40 5 36 5 37 5 40 5 37 5 38 5 40 5 38 5 39 5 40 5 39 5 28 5 40 5 </p>
</polylist>
</mesh>
</geometry>
<geometry id="Clock_ArrowEdge">
<mesh>
<!--
**********************************************
*
*  Insert arrow portion of clock's structure
*
**********************************************
-->
<source id="Clock_ArrowPositions">
<float_array id="ArrowCoordinates01" count="30"> 0.0  0.85 0.25 0.1  0.0 0.25 0.0 -0.2 0.25 -0.1  0.0 0.25 0.0  0.85 0.05 0.1  0.0 0.05 0.0 -0.2 0.05 -0.1  0.0 0.05 0.0  0.0 0.25 0.0  0.0 0.05 </float_array>
<technique_common>
<accessor source="#ArrowCoordinates01" count="10" stride="3">
<param name="X" type="float" />
<param name="Y" type="float" />
<param name="Z" type="float" />
</accessor>
</technique_common>
</source>
<source id="Clock_ArrowNormals">
<float_array id="ArrowNormals01" count="18">
0  0  1
0  0 -1
0.993151  0.116841 0.0
0.447214 -0.894427 0.0
-0.447214 -0.894427 0.0
-0.993151  0.116841 0.0
</float_array>
<technique_common>
<accessor source="#ArrowNormals01" count="6" stride="3">
<param name="X" type="float" />
<param name="Y" type="float" />
<param name="Z" type="float" />
</accessor>
</technique_common>
</source>
<vertices id="Clock_ArrowVertices">
<input semantic="POSITION" source="#Clock_ArrowPositions" />
</vertices>
<polylist count="12" material="Material2">
<input semantic="VERTEX" source="#Clock_ArrowVertices" offset="0" />
<input semantic="NORMAL" source="#Clock_ArrowNormals" offset="1"/>
<vcount>3 3 3 3 3 3 3 3 4 4 4 4</vcount>
<p> 0 0 8 0 1 0 1 0 8 0 2 0 2 0 8 0 3 0 3 0 8 0 0 0 4 1 5 1 9 1 5 1 6 1 9 1 6 1 7 1 9 1 7 1 4 1 9 1 0 2 1 2 5 2 4 2 1 3 2 3 6 3 5 3 2 4 3 4 7 4 6 4 3 5 0 5 4 5 7 5 </p>
</polylist>
</mesh>
</geometry>
<geometry id="Clock_HourEdge">
<mesh>
<!--
**********************************************
*
*  Insert hour_hand portion of clock's structure
*
**********************************************
-->
<source id="Clock_HourPositions">
<float_array id="HourCoordinates01" count="30"> 0.0  0.85 0.25 0.1  0.0 0.25 0.0 -0.2 0.25 -0.1  0.0 0.25 0.0  0.85 0.05 0.1  0.0 0.05 0.0 -0.2 0.05 -0.1  0.0 0.05 0.0  0.0 0.25 0.0  0.0 0.05 </float_array>
<technique_common>
<accessor source="#HourCoordinates01" count="10" stride="3">
<param name="X" type="float" />
<param name="Y" type="float" />
<param name="Z" type="float" />
</accessor>
</technique_common>
</source>
<source id="Clock_HourNormals">
<float_array id="HourNormals01" count="18">
0  0  1
0  0 -1
0.993151  0.116841 0.0
0.447214 -0.894427 0.0
-0.447214 -0.894427 0.0
-0.993151  0.116841 0.0
</float_array>
<technique_common>
<accessor source="#HourNormals01" count="6" stride="3">
<param name="X" type="float" />
<param name="Y" type="float" />
<param name="Z" type="float" />
</accessor>
</technique_common>
</source>
<vertices id="Clock_HourVertices">
<input semantic="POSITION" source="#Clock_HourPositions" />
</vertices>
<polylist count="12" material="Material2">
<input semantic="VERTEX" source="#Clock_HourVertices" offset="0" />
<input semantic="NORMAL" source="#Clock_HourNormals" offset="1"/>
<vcount>3 3 3 3 3 3 3 3 4 4 4 4</vcount>
<p> 0 0 8 0 1 0 1 0 8 0 2 0 2 0 8 0 3 0 3 0 8 0 0 0 4 1 5 1 9 1 5 1 6 1 9 1 6 1 7 1 9 1 7 1 4 1 9 1 0 2 1 2 5 2 4 2 1 3 2 3 6 3 5 3 2 4 3 4 7 4 6 4 3 5 0 5 4 5 7 5 </p>
</polylist>
</mesh>
</geometry>
<!-- geometry:  Letters -->
<geometry id="CubeID4">
<mesh>
<source id="CubeID7_Positions">
<float_array id="CoordinatesID10" count="24">
-0.5  -0.5  -0.5
-0.5  -0.5   0.5
-0.5   0.5  -0.5
-0.5   0.5   0.5
0.5  -0.5  -0.5
0.5  -0.5   0.5
0.5   0.5  -0.5
0.5   0.5   0.5
</float_array>
<technique_common>
<accessor source="#CoordinatesID10" count="8" stride="3">
<param name="X" type="float" />
<param name="Y" type="float" />
<param name="Z" type="float" />
</accessor>
</technique_common>
</source>
<source id="CubeID8_Normals">
<float_array id="NormalsID11" count="18">
0  0 -1
0  0  1
0 -1  0
0  1  0
-1  0  0
1  0  0
</float_array>
<technique_common>
<accessor source="#NormalsID11" count="6" stride="3">
<param name="X" type="float" />
<param name="Y" type="float" />
<param name="Z" type="float" />
</accessor>
</technique_common>
</source>
<vertices id="CubeID9_Vertices">
<input semantic="POSITION" source="#CubeID7_Positions" />
</vertices>
<polylist count="12" material="Material2">
<input semantic="VERTEX" source="#CubeID9_Vertices" offset="0" />
<input semantic="NORMAL" source="#CubeID8_Normals" offset="1" />
<vcount>3 3 3 3  3 3 3 3  3 3 3 3</vcount>
<p>
0 0 2 0 6 0  0 0 6 0 4 0
1 1 7 1 3 1  1 1 5 1 7 1
0 2 4 2 5 2  0 2 5 2 1 2
2 3 3 3 7 3  2 3 7 3 6 3
0 4 1 4 3 4  0 4 3 4 2 4
4 5 6 5 7 5  4 5 7 5 5 5
</p>
</polylist>
</mesh>
</geometry>
<geometry id="DiagonalID4">
<mesh>
<source id="DiagonalID7_Positions">
<float_array id="Diag_CoordinatesID10" count="24">
-0.5  -0.5  -0.5
-0.5  -0.5   0.5
-0.5   0.5  -0.5
-0.5   0.5   0.5
0.5  -0.5  -0.5
0.5  -0.5   0.5
0.5   0.5  -0.5
0.5   0.5   0.5
</float_array>
<technique_common>
<accessor source="#Diag_CoordinatesID10" count="8" stride="3">
<param name="X" type="float" />
<param name="Y" type="float" />
<param name="Z" type="float" />
</accessor>
</technique_common>
</source>
<source id="DiagonalID8_Normals">
<float_array id="Diagonal_NormalsID11" count="21">
0  0 -1
0  0  1
0 -1  0
0  1  0
-1  0  0
1  0  0
0  -0.707 0.707
</float_array>
<technique_common>
<accessor source="#Diagonal_NormalsID11" count="7" stride="3">
<param name="X" type="float" />
<param name="Y" type="float" />
<param name="Z" type="float" />
</accessor>
</technique_common>
</source>
<vertices id="DiagonalID9_Vertices">
<input semantic="POSITION" source="#DiagonalID7_Positions" />
</vertices>
<polylist count="8" material="Material2">
<input semantic="VERTEX" source="#DiagonalID9_Vertices" offset="0" />
<input semantic="NORMAL" source="#DiagonalID8_Normals" offset="1" />
<vcount>3 3 3 3  3 3 3 3</vcount>
<p>
0 0 2 0 6 0  0 0 6 0 4 0
2 3 3 3 7 3  2 3 7 3 6 3
0 4 3 4 2 4  4 5 6 5 7 5
0 6 7 6 3 6  0 6 4 6 7 6
</p>
</polylist>
</mesh>
</geometry>
<!-- geometry:  Cubes for Lagrangian Markers -->
<geometry id="CubeID4">
<mesh>
<source id="CubeID7_Positions">
<float_array id="CoordinatesID10" count="24">
-0.5  -0.5  -0.5
-0.5  -0.5   0.5
-0.5   0.5  -0.5
-0.5   0.5   0.5
0.5  -0.5  -0.5
0.5  -0.5   0.5
0.5   0.5  -0.5
0.5   0.5   0.5
</float_array>
<technique_common>
<accessor source="#CoordinatesID10" count="8" stride="3">
<param name="X" type="float" />
<param name="Y" type="float" />
<param name="Z" type="float" />
</accessor>
</technique_common>
</source>
<source id="CubeID8_Normals">
<float_array id="NormalsID11" count="18">
0  0 -1
0  0  1
0 -1  0
0  1  0
-1  0  0
1  0  0
</float_array>
<technique_common>
<accessor source="#NormalsID11" count="6" stride="3">
<param name="X" type="float" />
<param name="Y" type="float" />
<param name="Z" type="float" />
</accessor>
</technique_common>
</source>
<vertices id="CubeID9_Vertices">
<input semantic="POSITION" source="#CubeID7_Positions" />
</vertices>
<polylist count="12" material="Material2">
<input semantic="VERTEX" source="#CubeID9_Vertices" offset="0" />
<input semantic="NORMAL" source="#CubeID8_Normals" offset="1" />
<vcount>3 3 3 3  3 3 3 3  3 3 3 3</vcount>
<p>
0 0 2 0 6 0  0 0 6 0 4 0
1 1 7 1 3 1  1 1 5 1 7 1
0 2 4 2 5 2  0 2 5 2 1 2
2 3 3 3 7 3  2 3 7 3 6 3
0 4 1 4 3 4  0 4 3 4 2 4
4 5 6 5 7 5  4 5 7 5 5 5
</p>
</polylist>
</mesh>
</geometry>
<!-- geometry:  Cylindrical Pointer -->
<geometry id="Cylinder">
<mesh>
<source id="Cyl_Positions">
<float_array id="CylCoords01" count="54">
-1.0  -0.9239   0.3827
-1.0  -0.3827   0.9239
-1.0   0.3827   0.9239
-1.0   0.9239   0.3827
-1.0   0.9239  -0.3827
-1.0   0.3827  -0.9239
-1.0  -0.3827  -0.9239
-1.0  -0.9239  -0.3827
-1.0   0.0000   0.0000
1.0  -0.9239   0.3827
1.0  -0.3827   0.9239
1.0   0.3827   0.9239
1.0   0.9239   0.3827
1.0   0.9239  -0.3827
1.0   0.3827  -0.9239
1.0  -0.3827  -0.9239
1.0  -0.9239  -0.3827
1.5   0.0000   0.0000
</float_array>
<technique_common>
<accessor source="#CylCoords01" count="18" stride="3">
<param name="X" type="float" />
<param name="Y" type="float" />
<param name="Z" type="float" />
</accessor>
</technique_common>
</source>
<source id="Cyl_Normals">
<float_array id="CylNormals01" count="54">
1.0  0.0  0.0
-1.0  0.0  0.0
0.0  1.0  0.0
0.0 -1.0  0.0
0.0  0.0  1.0
0.0  0.0 -1.0
0.0  0.7071  0.7071
0.0  0.7071 -0.7071
0.0 -0.7071  0.7071
0.0 -0.7071 -0.7071
0.8795  -0.3365   0.3365
0.8795   0.0000   0.4760
0.8795   0.3365   0.3365
0.8795   0.4760   0.0000
0.8795   0.3365  -0.3365
0.8795   0.0000  -0.4760
0.8795  -0.3365  -0.3365
0.8795  -0.4760   0.0000
</float_array>
<technique_common>
<accessor source="#CylNormals01" count="18" stride="3">
<param name="X" type="float" />
<param name="Y" type="float" />
<param name="Z" type="float" />
</accessor>
</technique_common>
</source>
<vertices id="Cyl_Vertices">
<input semantic="POSITION" source="#Cyl_Positions" />
</vertices>
<polylist count="32" material="Material2">
<input semantic="VERTEX" source="#Cyl_Vertices" offset="0" />
<input semantic="NORMAL" source="#Cyl_Normals" offset="1" />
<vcount>3 3 3 3  3 3 3 3  3 3 3 3  3 3 3 3  3 3 3 3  3 3 3 3  3 3 3 3  3 3 3 3</vcount>
<p>
0 1  1 1  8 1
1 1  2 1  8 1
2 1  3 1  8 1
3 1  4 1  8 1
4 1  5 1  8 1
5 1  6 1  8 1
6 1  7 1  8 1
7 1  0 1  8 1
10 10   9 10  17 10
11 11  10 11  17 11
12 12  11 12  17 12
13 13  12 13  17 13
14 14  13 14  17 14
15 15  14 15  17 15
16 16  15 16  17 16
9 17  16 17  17 17
0 8   9 8   1 8
1 8   9 8  10 8
1 4  10 4   2 4
2 4  10 4  11 4
2 6  11 6   3 6
3 6  11 6  12 6
3 2  12 2   4 2
4 2  12 2  13 2
4 7  13 7   5 7
5 7  13 7  14 7
5 5  14 5   6 5
6 5  14 5  15 5
6 9  15 9   7 9
7 9  15 9  16 9
7 3  16 3   0 3
0 3  16 3   9 3
</p>
</polylist>
</mesh>
</geometry>
<!--
**********************************************
*
*  Insert Geometry of Ellipsoid Octant
*
**********************************************
-->
<geometry id="EllipsoidOctant">
<mesh>
<source id="Ellipsoid_Positions">
<float_array id="Ellipsoid_Coordinates" count=" 1563">
0.0000    0.0000    0.3850
0.0000    0.4100    0.0000
0.0400    0.4097    0.0000
0.0800    0.4087    0.0000
0.1200    0.4070    0.0000
0.1600    0.4047    0.0000
0.2000    0.4017    0.0000
0.2400    0.3980    0.0000
0.2800    0.3936    0.0000
0.3200    0.3884    0.0000
0.3600    0.3825    0.0000
0.4000    0.3758    0.0000
0.4400    0.3682    0.0000
0.4800    0.3597    0.0000
0.5200    0.3502    0.0000
0.5600    0.3397    0.0000
0.6000    0.3280    0.0000
0.6400    0.3150    0.0000
0.6800    0.3006    0.0000
0.7200    0.2845    0.0000
0.7600    0.2665    0.0000
0.8000    0.2460    0.0000
0.8400    0.2225    0.0000
0.8800    0.1947    0.0000
0.9200    0.1607    0.0000
0.9600    0.1148    0.0000
1.0000    0.0000    0.0000
0.0000    0.4095    0.0192
0.0399    0.4092    0.0192
0.0799    0.4082    0.0192
0.1198    0.4065    0.0192
0.1598    0.4042    0.0192
0.1997    0.4012    0.0192
0.2397    0.3975    0.0192
0.2796    0.3931    0.0192
0.3196    0.3880    0.0192
0.3595    0.3820    0.0192
0.3995    0.3753    0.0192
0.4394    0.3677    0.0192
0.4794    0.3592    0.0192
0.5193    0.3498    0.0192
0.5593    0.3393    0.0192
0.5992    0.3276    0.0192
0.6392    0.3146    0.0192
0.6791    0.3002    0.0192
0.7191    0.2842    0.0192
0.7590    0.2661    0.0192
0.7990    0.2457    0.0192
0.8389    0.2222    0.0192
0.8789    0.1945    0.0192
0.9188    0.1605    0.0192
0.9588    0.1147    0.0192
0.9987    0.0000    0.0192
0.0000    0.4079    0.0385
0.0398    0.4076    0.0385
0.0796    0.4066    0.0385
0.1194    0.4050    0.0385
0.1592    0.4027    0.0385
0.1990    0.3997    0.0385
0.2388    0.3960    0.0385
0.2786    0.3916    0.0385
0.3184    0.3865    0.0385
0.3582    0.3806    0.0385
0.3980    0.3739    0.0385
0.4378    0.3663    0.0385
0.4776    0.3579    0.0385
0.5174    0.3485    0.0385
0.5572    0.3380    0.0385
0.5970    0.3264    0.0385
0.6368    0.3135    0.0385
0.6766    0.2991    0.0385
0.7164    0.2831    0.0385
0.7562    0.2651    0.0385
0.7960    0.2448    0.0385
0.8358    0.2213    0.0385
0.8756    0.1938    0.0385
0.9154    0.1599    0.0385
0.9552    0.1142    0.0385
0.9950    0.0000    0.0385
0.0000    0.4054    0.0578
0.0395    0.4050    0.0578
0.0791    0.4041    0.0578
0.1186    0.4024    0.0578
0.1582    0.4001    0.0578
0.1977    0.3972    0.0578
0.2373    0.3935    0.0578
0.2768    0.3891    0.0578
0.3164    0.3840    0.0578
0.3559    0.3782    0.0578
0.3955    0.3715    0.0578
0.4350    0.3640    0.0578
0.4746    0.3556    0.0578
0.5141    0.3462    0.0578
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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>
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<technique_common>
<accessor source="#Reflect_Coordinates" count="  521" stride="3">
<param name="X" type="float" />
<param name="Y" type="float" />
<param name="Z" type="float" />
</accessor>
</technique_common>
</source>
<source id="Reflect_Normals">
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134  732  109  732  135  732
135  733  109  733  110  733
135  734  110  734  136  734
136  735  110  735  111  735
136  736  111  736  137  736
137  737  111  737  112  737
137  738  112  738  138  738
138  739  112  739  113  739
138  740  113  740  139  740
139  741  113  741  114  741
139  742  114  742  140  742
140  743  114  743  115  743
140  744  115  744  141  744
141  745  115  745  116  745
141  746  116  746  142  746
142  747  116  747  117  747
142  748  117  748  143  748
143  749  117  749  118  749
143  750  118  750  144  750
144  751  118  751  119  751
144  752  119  752  145  752
145  753  119  753  120  753
145  754  120  754  146  754
146  755  120  755  121  755
146  756  121  756  147  756
147  757  121  757  122  757
147  758  122  758  148  758
148  759  122  759  123  759
148  760  123  760  149  760
149  761  123  761  124  761
149  762  124  762  150  762
150  763  124  763  125  763
150  764  125  764  151  764
151  765  125  765  126  765
151  766  126  766  152  766
152  767  126  767  127  767
152  768  127  768  153  768
153  769  127  769  128  769
153  770  128  770  154  770
154  771  128  771  129  771
154  772  129  772  155  772
155  773  129  773  130  773
155  774  130  774  156  774
105  775   79  775   80  775
105  776   80  776  106  776
106  777   80  777   81  777
106  778   81  778  107  778
107  779   81  779   82  779
107  780   82  780  108  780
108  781   82  781   83  781
108  782   83  782  109  782
109  783   83  783   84  783
109  784   84  784  110  784
110  785   84  785   85  785
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112  790   87  790  113  790
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114  793   88  793   89  793
114  794   89  794  115  794
115  795   89  795   90  795
115  796   90  796  116  796
116  797   90  797   91  797
116  798   91  798  117  798
117  799   91  799   92  799
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126  817  100  817  101  817
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127  820  102  820  128  820
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129  823  103  823  104  823
129  824  104  824  130  824
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51  973   25  973   26  973
51  974   26  974   52  974
</p>
</polylist>
</mesh>
</geometry>
<!-- EquatorialPlane (begin) -->
<geometry id="EquatorialPlane">
<mesh>
<source id="EquatorialPlane_Positions">
<float_array id="EquatorialPlane_Coordinates" count="48">
-5.5000    -5.5000    0.2000
5.5000    -5.5000    0.2000
5.5000     5.5000    0.2000
-5.5000     5.5000    0.2000
-5.7500    -5.7500    0.2000
5.7500    -5.7500    0.2000
5.7500     5.7500    0.2000
-5.7500     5.7500    0.2000
-5.5000    -5.5000   -0.2000
5.5000    -5.5000   -0.2000
5.5000     5.5000   -0.2000
-5.5000     5.5000   -0.2000
-5.7500    -5.7500   -0.2000
5.7500    -5.7500   -0.2000
5.7500     5.7500   -0.2000
-5.7500     5.7500   -0.2000
</float_array>
<technique_common>
<accessor source="#EquatorialPlane_Coordinates" count="  16" stride="3">
<param name="X" type="float" />
<param name="Y" type="float" />
<param name="Z" type="float" />
</accessor>
</technique_common>
</source>
<source id="EquatorialPlane_Normals">
<float_array id="EquatorialPlane_Normals01" count="18">
0.0000    0.0000     1.0000
0.0000    0.0000    -1.0000
0.0000   -1.0000     0.0000
0.0000    1.0000     0.0000
-1.0000    0.0000     0.0000
1.0000    0.0000     0.0000
</float_array>
<technique_common>
<accessor source="#EquatorialPlane_Normals01" count="6" stride="3">
<param name="X" type="float" />
<param name="Y" type="float" />
<param name="Z" type="float" />
</accessor>
</technique_common>
</source>
<vertices id="EquatorialPlane_Vertices">
<input semantic="POSITION" source="#EquatorialPlane_Positions" />
</vertices>
<polylist count="  12" material="Material2">
<input semantic="VERTEX" source="#EquatorialPlane_Vertices" offset="0" />
<input semantic="NORMAL" source="#EquatorialPlane_Normals" offset="1" />
<vcount>
4 4 4 4
4 4 4 4
4 4 4 4
</vcount>
<p>
4 0  5 0  1 0  0 0
5 0  6 0  2 0  1 0
6 0  7 0  3 0  2 0
7 0  4 0  0 0  3 0
8 1   9 1  13 1  12 1
9 1  10 1  14 1  13 1
10 1  11 1  15 1  14 1
11 1   8 1  12 1  15 1
12 2  13 2   5 2   4 2
14 3  15 3   7 3   6 3
15 4  12 4   4 4   7 4
13 5  14 5   6 5   5 5
</p>
</polylist>
</mesh>
</geometry>
<!-- EquatorialPlane (end)   -->
</library_geometries>
<library_animations>
<animation id="First_rotation_euler_Z">
<!-- for EFE/Ou model b41c385, clockstop = 36.5047 and anglestop = 1800.0 -->
<!-- this means that one 360 degree turn of the ellipsoid takes 7.3009 clock units -->
<source id="First_rotation_euler_Z-input">
<float_array id="First_rotation_euler_Z-input-array" count="31">
0.00
1.22
2.43
3.65
4.87
6.08
7.30
8.52
9.73
10.95
12.17
13.39
14.60
15.82
17.04
18.25
19.47
20.69
21.90
23.12
24.34
25.55
26.77
27.99
29.20
30.42
31.64
32.85
34.07
35.29
36.50
</float_array>
<technique_common>
<accessor source="#First_rotation_euler_Z-input-array" count="31" stride="1">
<param name="TIME" type="float"/>
</accessor>
</technique_common>
</source>
<!-- This sets the spin rate of the "Entire" ellipsoid -->
<source id="First_rotation_euler_Z-output">
<float_array id="First_rotation_euler_Z-output-array" count="31">
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
5.0
</float_array>
<technique_common>
<accessor source="#First_rotation_euler_Z-output-array" count="31" stride="1">
<param name="ANGLE" type="float"/>
</accessor>
</technique_common>
</source>
<!-- This sets the spin rate of the "MidPlane" Frame of reference -->
<source id="Frame_rotation_euler_Z-output">
<float_array id="Frame_rotation_euler_Z-output-array" count="31">
1803.0
1743.0
1683.0
1623.0
1563.0
1503.0
1443.0
1383.0
1323.0
1263.0
1203.0
1143.0
1083.0
1023.0
963.0
903.0
843.0
783.0
723.0
663.0
603.0
543.0
483.0
423.0
363.0
303.0
243.0
183.0
123.0
63.0
3.0
</float_array>
<technique_common>
<accessor source="#Frame_rotation_euler_Z-output-array" count="31" stride="1">
<param name="ANGLE" type="float"/>
</accessor>
</technique_common>
</source>
<sampler id="First_rotation_euler_Z-sampler">
<input semantic="INPUT" source="#First_rotation_euler_Z-input"/>
<input semantic="OUTPUT" source="#First_rotation_euler_Z-output"/>
</sampler>
<sampler id="Frame_rotation_euler_Z-sampler">
<input semantic="INPUT" source="#First_rotation_euler_Z-input"/>
<input semantic="OUTPUT" source="#Frame_rotation_euler_Z-output"/>
</sampler>
<channel source="#First_rotation_euler_Z-sampler" target="EntireEllipsoid/rotationZ.ANGLE"/>
<channel source="#Frame_rotation_euler_Z-sampler" target="Inertial/rotationZ.ANGLE"/>
</animation>
<!-- FLUID ELEMENT 1 -->
<animation id="FluidElement1_location">
<source id="Lagrange1_location_X-input">
<float_array id="Lagrange1_location_X-input-array" count="   37">
0.0000
1.0014
2.0029
3.0043
4.0057
5.0071
6.0086
7.0100
8.0114
9.0129
10.0143
11.0157
12.0171
13.0186
14.0200
15.0214
16.0229
17.0243
18.0257
19.0271
20.0286
21.0300
22.0314
23.0329
24.0343
25.0357
26.0371
27.0386
28.0400
29.0414
30.0429
31.0443
32.0457
33.0472
34.0486
35.0500
36.0514
</float_array>
<technique_common>
<accessor source="#Lagrange1_location_X-input-array" count="   37" stride="1">
<param name="TIME" type="float"/>
</accessor>
</technique_common>
</source>
<source id="Lagrange1_location_X-output">
<float_array id="Lagrange1_location_X-output-array" count="   37">
1.0000
0.9921
0.9686
0.9298
0.8763
0.8090
0.7290
0.6374
0.5358
0.4258
0.3090
0.1874
0.0628
-0.0628
-0.1874
-0.3090
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-1.0000
-0.9921
-0.9686
-0.9298
-0.8763
-0.8090
-0.7290
-0.6374
-0.5358
-0.4258
-0.3090
-0.1874
</float_array>
<technique_common>
<accessor source="#Lagrange1_location_X-output-array" count="   37" stride="1">
<param name="X" type="float"/>
</accessor>
</technique_common>
</source>
<sampler id="Lagrange1_location_X-sampler">
<input semantic="INPUT" source="#Lagrange1_location_X-input"/>
<input semantic="OUTPUT" source="#Lagrange1_location_X-output"/>
</sampler>
<source id="Lagrange1_location_Y-output">
<float_array id="Lagrange1_location_Y-output-array" count="   37">
-0.0000
-0.0514
-0.1020
-0.1509
-0.1975
-0.2410
-0.2807
-0.3159
-0.3462
-0.3710
-0.3899
-0.4027
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-0.4092
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-0.3899
-0.3710
-0.3462
-0.3159
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-0.1509
-0.1020
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0.0000
0.0514
0.1020
0.1509
0.1975
0.2410
0.2807
0.3159
0.3462
0.3710
0.3899
0.4027
</float_array>
<technique_common>
<accessor source="#Lagrange1_location_Y-output-array" count="   37" stride="1">
<param name="Y" type="float"/>
</accessor>
</technique_common>
</source>
<sampler id="Lagrange1_location_Y-sampler">
<input semantic="INPUT" source="#Lagrange1_location_X-input"/>
<input semantic="OUTPUT" source="#Lagrange1_location_Y-output"/>
</sampler>
<channel source="#Lagrange1_location_X-sampler" target="Lagrange01/location.X"/>
<channel source="#Lagrange1_location_Y-sampler" target="Lagrange01/location.Y"/>
<channel source="#Lagrange1_location_X-sampler" target="Lagrange02/location.X"/>
<channel source="#Lagrange1_location_Y-sampler" target="Lagrange02/location.Y"/>
<channel source="#Lagrange1_location_X-sampler" target="Lagrange03/location.X"/>
<channel source="#Lagrange1_location_Y-sampler" target="Lagrange03/location.Y"/>
</animation>
<!-- CLOCK (clockstop = 36.5047)
One spin of ellipsoid (or frame) is 1.8252 EFE sqrt(pi * G * rho) units;
Want 1 EFE unit to take 4.0 seconds of TIME;
Hence, one spin of ellipsoid (360 degrees) is 7.3009 seconds of TIME;
and 5 ellipsoid spins is 36.5047 seconds of TIME.
Divide one spin (360) into 12 pieces
==> 30 degrees = 1 timestep = 4 x 0.1521 = 0.6084 seconds of TIME.
-->
<animation id="Cube_quaternion_Z">
<source id="Cube_quaternion_Z-input">
<float_array id="Cube_quaternion_Z-input-array" count=" 147">
0.00  0.25  0.50  0.75  1.00  1.25  1.50  1.75  2.00  2.25  2.50  2.75  3.00  3.25  3.50  3.75
4.00  4.25  4.50  4.75  5.00  5.25  5.50  5.75  6.00  6.25  6.50  6.75  7.00  7.25  7.50  7.75
8.00  8.25  8.50  8.75  9.00  9.25  9.50  9.75 10.00 10.25 10.50 10.75 11.00 11.25 11.50 11.75
12.00 12.25 12.50 12.75 13.00 13.25 13.50 13.75 14.00 14.25 14.50 14.75 15.00 15.25 15.50 15.75
16.00 16.25 16.50 16.75 17.00 17.25 17.50 17.75 18.00 18.25 18.50 18.75 19.00 19.25 19.50 19.75
20.00 20.25 20.50 20.75 21.00 21.25 21.50 21.75 22.00 22.25 22.50 22.75 23.00 23.25 23.50 23.75
24.00 24.25 24.50 24.75 25.00 25.25 25.50 25.75 26.00 26.25 26.50 26.75 27.00 27.25 27.50 27.75
28.00 28.25 28.50 28.75 29.00 29.25 29.50 29.75 30.00 30.25 30.50 30.75 31.00 31.25 31.50 31.75
32.00 32.25 32.50 32.75 33.00 33.25 33.50 33.75 34.00 34.25 34.50 34.75 35.00 35.25 35.50 35.75
36.00 36.25 36.50
</float_array>
<technique_common>
<accessor source="#Cube_quaternion_Z-input-array" count="   147" stride="1">
<param name="TIME" type="float"/>
</accessor>
</technique_common>
</source>
<source id="Cube_quaternion_Z-output">
<float_array id="Cube_quaternion_Z-output-array" count="2352">
0.000  0.000 -1.00  0.00  -1.0000  0.0000  0.000  0.000   0.0000  1.0000  0.000  0.00   0.000  0.000  0.000  1.000
0.000  0.000 -1.00  0.00  -0.9239 -0.3827  0.000  0.000  -0.3827  0.9239  0.000  0.00   0.000  0.000  0.000  1.000
0.000  0.000 -1.00  0.00  -0.7071 -0.7071  0.000  0.000  -0.7071  0.7071  0.000  0.00   0.000  0.000  0.000  1.000
0.000  0.000 -1.00  0.00  -0.3827 -0.9239  0.000  0.000  -0.9239  0.3827  0.000  0.00   0.000  0.000  0.000  1.000
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0.000  0.000 -1.00  0.00   0.7071  0.7071  0.000  0.000   0.7071 -0.7071  0.000  0.00   0.000  0.000  0.000  1.000
0.000  0.000 -1.00  0.00   0.3827  0.9239  0.000  0.000   0.9239 -0.3827  0.000  0.00   0.000  0.000  0.000  1.000
0.000  0.000 -1.00  0.00   0.0000  1.0000  0.000  0.000   1.0000  0.0000  0.000  0.00   0.000  0.000  0.000  1.000
0.000  0.000 -1.00  0.00  -0.3827  0.9239  0.000  0.000   0.9239  0.3827  0.000  0.00   0.000  0.000  0.000  1.000
0.000  0.000 -1.00  0.00  -0.7071  0.7071  0.000  0.000   0.7071  0.7071  0.000  0.00   0.000  0.000  0.000  1.000
0.000  0.000 -1.00  0.00  -0.9239  0.3827  0.000  0.000   0.3827  0.9239  0.000  0.00   0.000  0.000  0.000  1.000
0.000  0.000 -1.00  0.00  -1.0000  0.0000  0.000  0.000   0.0000  1.0000  0.000  0.00   0.000  0.000  0.000  1.000
0.000  0.000 -1.00  0.00  -0.9239 -0.3827  0.000  0.000  -0.3827  0.9239  0.000  0.00   0.000  0.000  0.000  1.000
0.000  0.000 -1.00  0.00  -0.7071 -0.7071  0.000  0.000  -0.7071  0.7071  0.000  0.00   0.000  0.000  0.000  1.000
0.000  0.000 -1.00  0.00  -0.3827 -0.9239  0.000  0.000  -0.9239  0.3827  0.000  0.00   0.000  0.000  0.000  1.000
0.000  0.000 -1.00  0.00   0.0000 -1.0000  0.000  0.000  -1.0000  0.0000  0.000  0.00   0.000  0.000  0.000  1.000
0.000  0.000 -1.00  0.00   0.3827 -0.9239  0.000  0.000  -0.9239 -0.3827  0.000  0.00   0.000  0.000  0.000  1.000
0.000  0.000 -1.00  0.00   0.7071 -0.7071  0.000  0.000  -0.7071 -0.7071  0.000  0.00   0.000  0.000  0.000  1.000
0.000  0.000 -1.00  0.00   0.9239 -0.3827  0.000  0.000  -0.3827 -0.9239  0.000  0.00   0.000  0.000  0.000  1.000
0.000  0.000 -1.00  0.00   1.0000  0.0000  0.000  0.000   0.0000 -1.0000  0.000  0.00   0.000  0.000  0.000  1.000
0.000  0.000 -1.00  0.00   0.9239  0.3827  0.000  0.000   0.3827 -0.9239  0.000  0.00   0.000  0.000  0.000  1.000
0.000  0.000 -1.00  0.00   0.7071  0.7071  0.000  0.000   0.7071 -0.7071  0.000  0.00   0.000  0.000  0.000  1.000
0.000  0.000 -1.00  0.00   0.3827  0.9239  0.000  0.000   0.9239 -0.3827  0.000  0.00   0.000  0.000  0.000  1.000
0.000  0.000 -1.00  0.00   0.0000  1.0000  0.000  0.000   1.0000  0.0000  0.000  0.00   0.000  0.000  0.000  1.000
0.000  0.000 -1.00  0.00  -0.3827  0.9239  0.000  0.000   0.9239  0.3827  0.000  0.00   0.000  0.000  0.000  1.000
0.000  0.000 -1.00  0.00  -0.7071  0.7071  0.000  0.000   0.7071  0.7071  0.000  0.00   0.000  0.000  0.000  1.000
0.000  0.000 -1.00  0.00  -0.9239  0.3827  0.000  0.000   0.3827  0.9239  0.000  0.00   0.000  0.000  0.000  1.000
0.000  0.000 -1.00  0.00  -1.0000  0.0000  0.000  0.000   0.0000  1.0000  0.000  0.00   0.000  0.000  0.000  1.000
0.000  0.000 -1.00  0.00  -0.9239 -0.3827  0.000  0.000  -0.3827  0.9239  0.000  0.00   0.000  0.000  0.000  1.000
0.000  0.000 -1.00  0.00  -0.7071 -0.7071  0.000  0.000  -0.7071  0.7071  0.000  0.00   0.000  0.000  0.000  1.000
</float_array>
<technique_common>
<accessor source="#Cube_quaternion_Z-output-array" count="  147" stride="16">
<param name="TRANSFORM" type="float4x4"/>
</accessor>
</technique_common>
</source>
<sampler id="Cube_quaternion_Z-sampler">
<input semantic="INPUT" source="#Cube_quaternion_Z-input"/>
<input semantic="OUTPUT" source="#Cube_quaternion_Z-output"/>
</sampler>
<channel source="#Cube_quaternion_Z-sampler" target="Jetman/transformation"/>
</animation>
<!-- HOURHAND (clockstop =    36.5047) -->
<animation id="HourHand_euler_Z">
<source id="HourHand_euler_Z-input">
<float_array id="HourHand_euler_Z-input-array" count="  147">
0.00  0.25  0.50  0.75  1.00  1.25  1.50  1.75  2.00  2.25  2.50  2.75  3.00  3.25  3.50  3.75
4.00  4.25  4.50  4.75  5.00  5.25  5.50  5.75  6.00  6.25  6.50  6.75  7.00  7.25  7.50  7.75
8.00  8.25  8.50  8.75  9.00  9.25  9.50  9.75 10.00 10.25 10.50 10.75 11.00 11.25 11.50 11.75
12.00 12.25 12.50 12.75 13.00 13.25 13.50 13.75 14.00 14.25 14.50 14.75 15.00 15.25 15.50 15.75
16.00 16.25 16.50 16.75 17.00 17.25 17.50 17.75 18.00 18.25 18.50 18.75 19.00 19.25 19.50 19.75
20.00 20.25 20.50 20.75 21.00 21.25 21.50 21.75 22.00 22.25 22.50 22.75 23.00 23.25 23.50 23.75
24.00 24.25 24.50 24.75 25.00 25.25 25.50 25.75 26.00 26.25 26.50 26.75 27.00 27.25 27.50 27.75
28.00 28.25 28.50 28.75 29.00 29.25 29.50 29.75 30.00 30.25 30.50 30.75 31.00 31.25 31.50 31.75
32.00 32.25 32.50 32.75 33.00 33.25 33.50 33.75 34.00 34.25 34.50 34.75 35.00 35.25 35.50 35.75
36.00 36.25 36.50
</float_array>
<technique_common>
<accessor source="#HourHand_euler_Z-input-array" count="  147" stride="1">
<param name="TIME" type="float"/>
</accessor>
</technique_common>
</source>
<source id="HourHand_euler_Z-output">
<float_array id="HourHand_euler_Z-output-array" count="  147">
270.0
268.125
266.25
264.375
262.5
260.625
258.75
256.875
255.0
253.125
251.25
249.375
247.5
245.625
243.75
241.875
240.0
238.125
236.25
234.375
232.5
230.625
228.75
226.875
225.0
223.125
221.25
219.375
217.5
215.625
213.75
211.875
210.0
208.125
206.25
204.375
202.5
200.625
198.75
196.875
195.0
193.125
191.25
189.375
187.5
185.625
183.75
181.875
180.0
178.125
176.25
174.375
172.5
170.625
168.75
166.875
165.0
163.125
161.25
159.375
157.5
155.625
153.75
151.875
150.0
148.125
146.25
144.375
142.5
140.625
138.75
136.875
135.0
133.125
131.25
129.375
127.5
125.625
123.75
121.875
120.0
118.125
116.25
114.375
112.5
110.625
108.75
106.875
105.0
103.125
101.25
99.375
97.5
95.625
93.75
91.875
90.0
88.125
86.25
84.375
82.5
80.625
78.75
76.875
75.0
73.125
71.25
69.375
67.5
65.625
63.75
61.875
60.0
58.125
56.25
54.375
52.5
50.625
48.75
46.875
45.0
43.125
41.25
39.375
37.5
35.625
33.75
31.875
30.0
28.125
26.25
24.375
22.5
20.625
18.75
16.875
15.0
13.125
11.25
9.375
7.5
5.625
3.75
1.875
0.0
-1.875
-3.75
</float_array>
<technique_common>
<accessor source="#HourHand_euler_Z-output-array" count="   147" stride="1">
<param name="ANGLE" type="float"/>
</accessor>
</technique_common>
</source>
<sampler id="HourHand_euler_Z-sampler">
<input semantic="INPUT" source="#HourHand_euler_Z-input"/>
<input semantic="OUTPUT" source="#HourHand_euler_Z-output"/>
</sampler>
<channel source="#HourHand_euler_Z-sampler" target="HourHand/rotationZ.ANGLE"/>
</animation>
</library_animations>
<library_controllers/>
<library_visual_scenes>
<visual_scene id="ID1">
<node id="EntireEllipsoid" name="OculusRift_EFE">
<translate>0.0 0.0 0.0</translate>
<rotate sid="rotationX">1.0 0.0 0.0  0.0</rotate>
<rotate sid="rotationY">0.0 1.0 0.0  0.0</rotate>
<rotate sid="rotationZ">0.0 0.0 1.0  5.0</rotate>
<scale sid="scale">5.0 5.0 5.0</scale>
<node id="First" name="First_instance_EFE">
<translate>0.0 0.0 0.0</translate>
<rotate sid="rotationX">1.0 0.0 0.0  0.0</rotate>
<rotate sid="rotationY">0.0 1.0 0.0  0.0</rotate>
<rotate sid="rotationZ">0.0 0.0 1.0  0.0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<instance_node url="#ID3_EFE" />
</node>
<node id="Second" name="Second_instance_EFE">
<translate>0.0 0.0 0.0</translate>
<rotate sid="rotationX">1.0 0.0 0.0  180.0</rotate>
<rotate sid="rotationY">0.0 1.0 0.0    0.0</rotate>
<rotate sid="rotationZ">0.0 0.0 1.0    0.0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<instance_node url="#ID3_EFE" />
</node>
<node id="Third" name="Third_instance_EFE">
<translate>0.0 0.0 0.0</translate>
<rotate sid="rotationX">1.0 0.0 0.0    0.0</rotate>
<rotate sid="rotationY">0.0 1.0 0.0  180.0</rotate>
<rotate sid="rotationZ">0.0 0.0 1.0    0.0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<instance_node url="#ID3_EFE" />
</node>
<node id="Fourth" name="Fourth_instance_EFE">
<translate>0.0 0.0 0.0</translate>
<rotate sid="rotationX">1.0 0.0 0.0  180.0</rotate>
<rotate sid="rotationY">0.0 1.0 0.0  180.0</rotate>
<rotate sid="rotationZ">0.0 0.0 1.0    0.0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<instance_node url="#ID3_EFE" />
</node>
<!-- instance:  Cylindrical Pointer -->
<node id="CylinderPointer" name="instance_cylinder">
<translate sid="location">-1.0 0.0 0.0</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 180</rotate>
<scale sid="scale">0.05 0.025 0.025</scale>
<instance_node url="#CylPointer" />
</node>
<!-- Begin LAGRANGE markers -->
<node id="Lagrange01" name="instance_Lagrange01">
<translate sid="location">1.0000 0.0000 0.0</translate>
<rotate sid="rotationX">1.0 0.0 0.0  0.0</rotate>
<rotate sid="rotationY">0.0 1.0 0.0  0.0</rotate>
<rotate sid="rotationZ">0.0 0.0 1.0  0.0</rotate>
<scale sid="scale">0.06 0.06 0.06</scale>
<instance_node url="#Primary_MarkerID3" />
</node>
<node id="Shrink02" name="instance_Shrink02">
<scale sid="scale">0.8 0.8 0.8</scale>
<node id="Lagrange02" name="instance_Lagrange02">
<translate sid="location">1.0000 0.0000 0.0</translate>
<rotate sid="rotationX">1.0 0.0 0.0  0.0</rotate>
<rotate sid="rotationY">0.0 1.0 0.0  0.0</rotate>
<rotate sid="rotationZ">0.0 0.0 1.0  0.0</rotate>
<scale sid="scale">0.075 0.075 0.075</scale>
<instance_node url="#Primary_MarkerID3" />
</node>
</node>
<node id="Shrink03" name="instance_Shrink03">
<scale sid="scale">0.6 0.6 0.6</scale>
<node id="Lagrange03" name="instance_Lagrange03">
<translate sid="location">1.0000 0.0000 0.0</translate>
<rotate sid="rotationX">1.0 0.0 0.0  0.0</rotate>
<rotate sid="rotationY">0.0 1.0 0.0  0.0</rotate>
<rotate sid="rotationZ">0.0 0.0 1.0  0.0</rotate>
<scale sid="scale">0.1 0.1 0.1</scale>
<instance_node url="#Primary_MarkerID3" />
</node>
</node>
<node id="Marker01" name="instance_marker01">
<matrix>0.025 0.0 0.0 1.0000  0.0 0.025 0.0 -0.0000  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker02" name="instance_marker02">
<matrix>0.025 0.0 0.0 0.9921  0.0 0.025 0.0 -0.0514  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker03" name="instance_marker03">
<matrix>0.025 0.0 0.0 0.9686  0.0 0.025 0.0 -0.1020  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker04" name="instance_marker04">
<matrix>0.025 0.0 0.0 0.9298  0.0 0.025 0.0 -0.1509  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker05" name="instance_marker05">
<matrix>0.025 0.0 0.0 0.8763  0.0 0.025 0.0 -0.1975  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker06" name="instance_marker06">
<matrix>0.025 0.0 0.0 0.8090  0.0 0.025 0.0 -0.2410  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker07" name="instance_marker07">
<matrix>0.025 0.0 0.0 0.7290  0.0 0.025 0.0 -0.2807  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker08" name="instance_marker08">
<matrix>0.025 0.0 0.0 0.6374  0.0 0.025 0.0 -0.3159  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker09" name="instance_marker09">
<matrix>0.025 0.0 0.0 0.5358  0.0 0.025 0.0 -0.3462  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker10" name="instance_marker10">
<matrix>0.025 0.0 0.0 0.4258  0.0 0.025 0.0 -0.3710  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker11" name="instance_marker11">
<matrix>0.025 0.0 0.0 0.3090  0.0 0.025 0.0 -0.3899  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker12" name="instance_marker12">
<matrix>0.025 0.0 0.0 0.1874  0.0 0.025 0.0 -0.4027  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker13" name="instance_marker13">
<matrix>0.025 0.0 0.0 0.0628  0.0 0.025 0.0 -0.4092  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker14" name="instance_marker14">
<matrix>0.025 0.0 0.0 -0.0628  0.0 0.025 0.0 -0.4092  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker15" name="instance_marker15">
<matrix>0.025 0.0 0.0 -0.1874  0.0 0.025 0.0 -0.4027  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker16" name="instance_marker16">
<matrix>0.025 0.0 0.0 -0.3090  0.0 0.025 0.0 -0.3899  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker17" name="instance_marker17">
<matrix>0.025 0.0 0.0 -0.4258  0.0 0.025 0.0 -0.3710  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker18" name="instance_marker18">
<matrix>0.025 0.0 0.0 -0.5358  0.0 0.025 0.0 -0.3462  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker19" name="instance_marker19">
<matrix>0.025 0.0 0.0 -0.6374  0.0 0.025 0.0 -0.3159  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker20" name="instance_marker20">
<matrix>0.025 0.0 0.0 -0.7290  0.0 0.025 0.0 -0.2807  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker21" name="instance_marker21">
<matrix>0.025 0.0 0.0 -0.8090  0.0 0.025 0.0 -0.2410  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker22" name="instance_marker22">
<matrix>0.025 0.0 0.0 -0.8763  0.0 0.025 0.0 -0.1975  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker23" name="instance_marker23">
<matrix>0.025 0.0 0.0 -0.9298  0.0 0.025 0.0 -0.1509  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker24" name="instance_marker24">
<matrix>0.025 0.0 0.0 -0.9686  0.0 0.025 0.0 -0.1020  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker25" name="instance_marker25">
<matrix>0.025 0.0 0.0 -0.9921  0.0 0.025 0.0 -0.0514  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker26" name="instance_marker26">
<matrix>0.025 0.0 0.0 -1.0000  0.0 0.025 0.0 -0.0000  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<!-- Second Half -->
<node id="Marker28" name="instance_marker28">
<matrix>0.025 0.0 0.0 -0.9921  0.0 0.025 0.0 0.0514  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker29" name="instance_marker29">
<matrix>0.025 0.0 0.0 -0.9686  0.0 0.025 0.0 0.1020  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker30" name="instance_marker30">
<matrix>0.025 0.0 0.0 -0.9298  0.0 0.025 0.0 0.1509  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker31" name="instance_marker31">
<matrix>0.025 0.0 0.0 -0.8763  0.0 0.025 0.0 0.1975  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker32" name="instance_marker32">
<matrix>0.025 0.0 0.0 -0.8090  0.0 0.025 0.0 0.2410  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker33" name="instance_marker33">
<matrix>0.025 0.0 0.0 -0.7290  0.0 0.025 0.0 0.2807  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker34" name="instance_marker34">
<matrix>0.025 0.0 0.0 -0.6374  0.0 0.025 0.0 0.3159  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker35" name="instance_marker35">
<matrix>0.025 0.0 0.0 -0.5358  0.0 0.025 0.0 0.3462  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker36" name="instance_marker36">
<matrix>0.025 0.0 0.0 -0.4258  0.0 0.025 0.0 0.3710  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker37" name="instance_marker37">
<matrix>0.025 0.0 0.0 -0.3090  0.0 0.025 0.0 0.3899  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker38" name="instance_marker38">
<matrix>0.025 0.0 0.0 -0.1874  0.0 0.025 0.0 0.4027  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker39" name="instance_marker39">
<matrix>0.025 0.0 0.0 -0.0628  0.0 0.025 0.0 0.4092  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker40" name="instance_marker40">
<matrix>0.025 0.0 0.0 0.0628  0.0 0.025 0.0 0.4092  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker41" name="instance_marker41">
<matrix>0.025 0.0 0.0 0.1874  0.0 0.025 0.0 0.4027  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker42" name="instance_marker42">
<matrix>0.025 0.0 0.0 0.3090  0.0 0.025 0.0 0.3899  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker43" name="instance_marker43">
<matrix>0.025 0.0 0.0 0.4258  0.0 0.025 0.0 0.3710  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker44" name="instance_marker44">
<matrix>0.025 0.0 0.0 0.5358  0.0 0.025 0.0 0.3462  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker45" name="instance_marker45">
<matrix>0.025 0.0 0.0 0.6374  0.0 0.025 0.0 0.3159  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker46" name="instance_marker46">
<matrix>0.025 0.0 0.0 0.7290  0.0 0.025 0.0 0.2807  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker47" name="instance_marker47">
<matrix>0.025 0.0 0.0 0.8090  0.0 0.025 0.0 0.2410  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker48" name="instance_marker48">
<matrix>0.025 0.0 0.0 0.8763  0.0 0.025 0.0 0.1975  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker49" name="instance_marker49">
<matrix>0.025 0.0 0.0 0.9298  0.0 0.025 0.0 0.1509  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker50" name="instance_marker50">
<matrix>0.025 0.0 0.0 0.9686  0.0 0.025 0.0 0.1020  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<node id="Marker51" name="instance_marker51">
<matrix>0.025 0.0 0.0 0.9921  0.0 0.025 0.0 0.0514  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
<instance_node url="#MarkersID3" />
</node>
<!-- End LAGRANGE markers -->
</node>                           <!-- END EntireEllipsoid -->
<node id="Inertial" name="instance_inertial">  <!-- Start Inertial Grouping of Objects -->
<translate>0.0 0.0 0.0</translate>
<rotate sid="rotationX">1.0 0.0 0.0  0.0</rotate>
<rotate sid="rotationY">0.0 1.0 0.0  0.0</rotate>
<rotate sid="rotationZ">0.0 0.0 1.0  1803.0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<node id="Zup_Pointer" name="instance_zupPointer">
<translate>0.0 0.0 5.0</translate>
<rotate sid="rotationX">1 0 0  0.0</rotate>
<rotate sid="rotationY">0 1 0  0.0</rotate>
<rotate sid="rotationZ">0 0 1  0.0</rotate>
<scale sid="scale">0.125 0.5 1.5</scale>
<instance_node url="#ZupPointer" />
</node>
<!-- instance:  MidPlane Frame (MidPlane flips with rotationX = 180 for clockwise spin)-->
<node id="MidPlane" name="instance_MidPlane">
<translate>0.0 0.0 0.0</translate>
<rotate sid="rotationX">1.0 0.0 0.0  0.0</rotate>
<rotate sid="rotationY">0.0 1.0 0.0  0.0</rotate>
<rotate sid="rotationZ">0.0 0.0 1.0  0.0</rotate>
<scale sid="scale">1.25 1.25 1.25</scale>
<instance_node url="#EqPlane" />
</node>
<!-- BEGIN LABELING HERE -->
<node name="Labels">
<translate>7.0 -2.0 5.0</translate>
<rotate sid="rotationX">1 0 0 0.0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 180</rotate>
<scale sid="scale">0.1 0.1 0.1</scale>
<!--  Equals sign #1  -->
<node name="Equals1">
<translate>0.0 15.0 1.0</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<node id="IDd51" name="instance_51">
<matrix>0.25  0 0 0.0   0 1  0 0.0  0 0 1 2.4  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDd52" name="instance_52">
<matrix>0.25  0 0 0.0   0 1  0 1.1  0 0 1 2.4  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDd53" name="instance_53">
<matrix>0.25  0 0 0.0   0 1  0 2.2  0 0 1 2.4  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDd55" name="instance_55">
<matrix>0.25  0 0 0.0   0 1  0 0.0  0 0 1 4.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDd56" name="instance_56">
<matrix>0.25  0 0 0.0   0 1  0 1.1  0 0 1 4.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDd57" name="instance_57">
<matrix>0.25  0 0 0.0   0 1  0 2.2  0 0 1 4.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
</node>
<!--  Equals sign #2  -->
<node name="Equals2">
<translate>0.0 15.0 -8.5</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<node id="IDd51" name="instance_51">
<matrix>0.25  0 0 0.0   0 1  0 0.0  0 0 1 2.4  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDd52" name="instance_52">
<matrix>0.25  0 0 0.0   0 1  0 1.1  0 0 1 2.4  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDd53" name="instance_53">
<matrix>0.25  0 0 0.0   0 1  0 2.2  0 0 1 2.4  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDd55" name="instance_55">
<matrix>0.25  0 0 0.0   0 1  0 0.0  0 0 1 4.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDd56" name="instance_56">
<matrix>0.25  0 0 0.0   0 1  0 1.1  0 0 1 4.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDd57" name="instance_57">
<matrix>0.25  0 0 0.0   0 1  0 2.2  0 0 1 4.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
</node>
<!--  Division sign #1  -->
<node name="Divide1">
<translate>0.0 4.4 1.0</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 0.75 1.0</scale>
<node id="IDd21" name="instance_21">
<matrix>0.25  0 0 0.0   0 1  0 0.0  0 0 1 0.0  0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
<node id="IDd22" name="instance_22">
<matrix>0.25  0 0 0.0   0 -1  0 1.1  0 0 -1 0.0  0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
<node id="IDd23" name="instance_23">
<matrix>0.25  0 0 0.0   0 1  0 1.1  0 0 1 1.1  0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
<node id="IDd24" name="instance_24">
<matrix>0.25  0 0 0.0   0 -1  0 2.2  0 0 -1 1.1  0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
<node id="IDd25" name="instance_25">
<matrix>0.25  0 0 0.0   0 1  0 2.2  0 0 1 2.2  0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
<node id="IDd26" name="instance_26">
<matrix>0.25  0 0 0.0   0 -1  0 3.3  0 0 -1 2.2  0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
<node id="IDd27" name="instance_27">
<matrix>0.25  0 0 0.0   0 1  0 3.3  0 0 1 3.3  0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
</node>
<!--  Division sign #2  -->
<node name="Divide2">
<translate>0.0 4.4 -8.5</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 0.75 1.0</scale>
<node id="IDd21" name="instance_21">
<matrix>0.25  0 0 0.0   0 1  0 0.0  0 0 1 0.0  0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
<node id="IDd22" name="instance_22">
<matrix>0.25  0 0 0.0   0 -1  0 1.1  0 0 -1 0.0  0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
<node id="IDd23" name="instance_23">
<matrix>0.25  0 0 0.0   0 1  0 1.1  0 0 1 1.1  0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
<node id="IDd24" name="instance_24">
<matrix>0.25  0 0 0.0   0 -1  0 2.2  0 0 -1 1.1  0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
<node id="IDd25" name="instance_25">
<matrix>0.25  0 0 0.0   0 1  0 2.2  0 0 1 2.2  0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
<node id="IDd26" name="instance_26">
<matrix>0.25  0 0 0.0   0 -1  0 3.3  0 0 -1 2.2  0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
<node id="IDd27" name="instance_27">
<matrix>0.25  0 0 0.0   0 1  0 3.3  0 0 1 3.3  0 0 0 1.0</matrix>
<instance_node url="#Black_DiagonalID3" />
</node>
</node>
<!--  Letter "a" #1  -->
<node name="Letter_a1">
<translate>0.0 8.0 1.0</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<node id="IDa01" name="instance_1">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa06" name="instance_6">
<matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 2.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa07" name="instance_7">
<matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 2.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa10" name="instance_10">
<matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa11" name="instance_11">
<matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa18" name="instance_18">
<matrix>0.25  0 0 0.0  0 1 0 0.0  0 0  1 2.2  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDa19" name="instance_19">
<matrix>0.25  0 0 0.0  0 0 1 4.4  0 -1 0 0.0  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDa19" name="instance_19">
<matrix>0.25  0 0 0.0  0 0 -1 3.3  0 1 0 0.0  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDa11" name="instance_11">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa31" name="instance_11">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa20" name="instance_20">
<matrix>0.25  0 0 0.0   0 0 1 3.3  0 -1 0 3.3  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDa21" name="instance_21">
<matrix>0.25  0 0 0.0   0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
</node>
<!--  Letter "a" #2  -->
<node name="Letter_a2">
<translate>0.0 8.0 -8.5</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<node id="IDa01" name="instance_1">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa06" name="instance_6">
<matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 2.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa07" name="instance_7">
<matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 2.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa10" name="instance_10">
<matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa11" name="instance_11">
<matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa18" name="instance_18">
<matrix>0.25  0 0 0.0  0 1 0 0.0  0 0  1 2.2  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDa19" name="instance_19">
<matrix>0.25  0 0 0.0  0 0 1 4.4  0 -1 0 0.0  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDa19" name="instance_19">
<matrix>0.25  0 0 0.0  0 0 -1 3.3  0 1 0 0.0  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDa11" name="instance_11">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa31" name="instance_11">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa20" name="instance_20">
<matrix>0.25  0 0 0.0   0 0 1 3.3  0 -1 0 3.3  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDa21" name="instance_21">
<matrix>0.25  0 0 0.0   0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
</node>
<!--  Letter "a" #2  -->
<node name="Letter_a2">
<translate>0.0 8.0 -8.5</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<node id="IDa01" name="instance_1">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa06" name="instance_6">
<matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 2.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa07" name="instance_7">
<matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 2.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa10" name="instance_10">
<matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa11" name="instance_11">
<matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa18" name="instance_18">
<matrix>0.25  0 0 0.0  0 1 0 0.0  0 0  1 2.2  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDa19" name="instance_19">
<matrix>0.25  0 0 0.0  0 0 1 4.4  0 -1 0 0.0  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDa19" name="instance_19">
<matrix>0.25  0 0 0.0  0 0 -1 3.3  0 1 0 0.0  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDa11" name="instance_11">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa31" name="instance_11">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDa20" name="instance_20">
<matrix>0.25  0 0 0.0   0 0 1 3.3  0 -1 0 3.3  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDa21" name="instance_21">
<matrix>0.25  0 0 0.0   0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
</node>
<!--  Letter "c"  -->
<node name="Letter_c">
<translate>0.0 0.0 -8.5</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<node id="ID001" name="instance_1">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID002" name="instance_2">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 2.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID006" name="instance_6">
<matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 3.3  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID007" name="instance_7">
<matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 3.3  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID010" name="instance_10">
<matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID011" name="instance_11">
<matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="ID018" name="instance_18">
<matrix>0.25  0 0 0.0  0 1 0 0.0  0 0  1 3.3  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="ID019" name="instance_19">
<matrix>0.25  0 0 0.0  0 -1 0 3.3  0 0  -1 0.0  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="ID020" name="instance_20">
<matrix>0.25  0 0 0.0   0 0 1 3.3  0 -1 0 3.3  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="ID021" name="instance_21">
<matrix>0.25  0 0 0.0   0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
</node>
<!--  Letter "b"  ... has 8 + (4 x 15) = 68 lines -->
<node name="Letter_b">
<translate>0.0 0.0 1.0</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<node id="IDb01" name="instance_1">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb02" name="instance_2">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 2.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb03" name="instance_3">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 3.3  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb04" name="instance_4">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 4.4  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb05" name="instance_5">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 5.5  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb12" name="instance_12">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 6.6  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb06" name="instance_6">
<matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 3.3  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb07" name="instance_7">
<matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 3.3  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb08" name="instance_8">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb09" name="instance_9">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb10" name="instance_10">
<matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb11" name="instance_11">
<matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb19" name="instance_19">
<matrix>0.25  0 0 0.0  0 -1 0 3.3  0 0  -1 0.0  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDb20" name="instance_20">
<matrix>0.25  0 0 0.0   0 0 1 3.3  0 -1 0 3.3  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDb21" name="instance_21">
<matrix>0.25  0 0 0.0   0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
</node>
<!-- DECIMAL POINTS -->
<node id="IDD01" name="Decimal_1">
<matrix>0.25 0 0 0.0  0 1 0 25.0  0 0 1 1.0  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDD02" name="Decimal_2">
<matrix>0.25 0 0 0.0  0 1 0 25.0  0 0 1 -8.5  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<!--  Number "0" #1  ... has 8 + (4 x 18) = 80 lines -->
<node name="Number_0">
<translate>0.0 20.0 1.0</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<node id="IDb01" name="instance_1">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb02" name="instance_2">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 2.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb03" name="instance_3">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 3.3  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb04" name="instance_4">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 4.4  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb05" name="instance_5">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 5.5  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDz19" name="instance_z19">
<matrix>0.25  0 0 0.0  0 1 0 0.0  0 0 1 6.6  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDb06" name="instance_6">
<matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 6.6  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb07" name="instance_7">
<matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 6.6  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb08" name="instance_8">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb09" name="instance_9">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb10" name="instance_10">
<matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb11" name="instance_11">
<matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb19" name="instance_19">
<matrix>0.25  0 0 0.0  0 -1 0 3.3  0 0  -1 0.0  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDb20" name="instance_20">
<matrix>0.25  0 0 0.0   0 0 1 3.3  0 -1 0 6.6  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDb21" name="instance_21">
<matrix>0.25  0 0 0.0   0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDz11" name="instance_z11">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 3.3  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDz12" name="instance_z12">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 4.4  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDz13" name="instance_z13">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 5.5  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
</node>
<!--  Number "0" #2  ... has 8 + (4 x 18) = 80 lines -->
<node name="Number_0b">
<translate>0.0 20.0 -8.5</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<node id="IDb01" name="instance_1">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb02" name="instance_2">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 2.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb03" name="instance_3">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 3.3  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb04" name="instance_4">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 4.4  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb05" name="instance_5">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 5.5  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDz19" name="instance_z19">
<matrix>0.25  0 0 0.0  0 1 0 0.0  0 0 1 6.6  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDb06" name="instance_6">
<matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 6.6  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb07" name="instance_7">
<matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 6.6  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb08" name="instance_8">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb09" name="instance_9">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb10" name="instance_10">
<matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb11" name="instance_11">
<matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb19" name="instance_19">
<matrix>0.25  0 0 0.0  0 -1 0 3.3  0 0  -1 0.0  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDb20" name="instance_20">
<matrix>0.25  0 0 0.0   0 0 1 3.3  0 -1 0 6.6  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDb21" name="instance_21">
<matrix>0.25  0 0 0.0   0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
<instance_node url="#DiagonalID3" />
</node>
<node id="IDz11" name="instance_z11">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 3.3  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDz12" name="instance_z12">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 4.4  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDz13" name="instance_z13">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 5.5  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
</node>
<!--  Number "1" ... has 8 + (4 x 8) = 40 lines -->
<!--  Number "2" #1 ... has 8 + (4 x 17) = 76 lines -->
<!--  Number "2" #2 ... has 8 + (4 x 17) = 76 lines -->
<!--  Number "3"  ... has 8 + (4 x 18) = 80 lines -->
<!--  Number "4" ... has 8 + (4 x 13) = 60 lines -->
<!--  Number "5"  ... has 8 + (4 x 17) = 76 lines -->
<!--  Number "6" ... has 8 + (4 x 18) = 80 lines -->
<!--  Number "7" ... has 8 + (4 x 14) = 64 lines -->
<!--  Number "8" ... has 8 + (4 x 22) = 96 lines -->
<!--  Number "9"  ... has 8 + (4 x 15) = 68 lines -->
<!-- bovera_Digit1 is "4" -->
<node name="bovera_Digit1">
<translate>0.0 26.8 1.0</translate>
<rotate sid="rotationX">1 0 0 0</rotate>
<rotate sid="rotationY">0 1 0 0</rotate>
<rotate sid="rotationZ">0 0 1 0</rotate>
<scale sid="scale">1.0 1.0 1.0</scale>
<!--  Number "4" ... has 8 + (4 x 13) = 60 lines -->
<node id="IDe01" name="instance_e01">
<matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 3.3  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDe02" name="instance_e02">
<matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 3.3  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDe02" name="instance_e02">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 3.3  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb04" name="instance_4">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 4.4  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb05" name="instance_5">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 5.5  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb06" name="instance_6">
<matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 6.6  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb08" name="instance_8">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDb09" name="instance_9">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDn09" name="instance_9">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 0.0  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDf12" name="instance_n12">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 6.6  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDn12" name="instance_n12">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 3.3  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDz12" name="instance_z12">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 4.4  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
<node id="IDz13" name="instance_z13">
<matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 5.5  0 0 0 1.0</matrix>
<instance_node url="#LettersID3" />
</node>
</node>
<!-- 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>
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## Inside the Oculus Rift S Environment

### Introduction

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

Here are a few discoveries I made along the way:

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

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

 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 

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

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

• Click the "Inventory" menu item.

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

• Click the "My Imports" menu item.

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

NOTE:

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

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

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

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

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

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

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

Additional Photos from Inside the Oculus Rift S Home Environment

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

## Footnotes

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

 ${\displaystyle ~{\bar {\rho }}_{\mathrm {WD} }}$ ${\displaystyle ~\equiv }$ ${\displaystyle ~{\frac {3M_{\mathrm {Ch} }}{4\pi \ell _{1}^{3}}}=\mu _{e}\cdot 5.93972\times 10^{6}~\mathrm {g} ~{\mathrm {cm} }^{-3}\,.}$

Drawing from our above discussion of timescales that arise in the context of our COLLADA-driven animations, we therefore appreciate that the characteristic oscillation period associated with a white dwarf whose molecular weight of electrons is ${\displaystyle ~\mu _{e}=2}$, proves to be,

 ${\displaystyle ~[P_{0}]_{\mathrm {WD} }}$ ${\displaystyle ~=}$ ${\displaystyle ~{\biggl [}{\frac {4\pi }{G{\bar {\rho }}_{\mathrm {WD} }}}{\biggr ]}^{1/2}=3.98~\mathrm {s} \,.}$

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