Difference between revisions of "User:Tohline/ThreeDimensionalConfigurations/MeetsCOLLADAandOculusRiftS"

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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:   
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:   
<ol>
[[File:ClockImage01.png|200px|right|Clock Image]]<ol>
<li>
<li>
We use the motion of the hands on the wall-mounted clock to identify the natural oscillation frequency of the physical system, namely, <math>~\Omega_0 \equiv [\pi G \rho]^{1 / 2}</math>.  More specifically, by declaration, one oscillation period of the red "minute" hand &#8212; that is to say, one wall-clock "hour" &#8212; is <math>~P_0 = 2\pi[\pi G \rho]^{-1 / 2} = [4\pi/(G \rho)]^{1 / 2}</math>.  One full cycle of the wall-clock's black "hour" hand is therefore 12P<sub>0</sub>.  For purposes of illustration here, we have equated P<sub>0</sub> with a COLLADA TIME interval of 4.0, which means that in our COLLADA-driven animation, one wall-clock hour passes every (approximately) 4 seconds of real time.</li>
We use the motion of the hands on the wall-mounted clock to identify the natural oscillation frequency of the physical system, namely, <math>~\Omega_0 \equiv [\pi G \rho]^{1 / 2}</math>.  More specifically, by declaration, one oscillation period of the red "minute" hand &#8212; that is to say, one wall-clock "hour" &#8212; is <math>~P_0 = 2\pi[\pi G \rho]^{-1 / 2} = [4\pi/(G \rho)]^{1 / 2}</math>.  One full cycle of the wall-clock's black "hour" hand is therefore 12P<sub>0</sub>.  For purposes of illustration here, we have equated P<sub>0</sub> with a COLLADA TIME interval of 4.0, which means that in our COLLADA-driven animation, one wall-clock hour passes every (approximately) 4 seconds of real time.</li>

Revision as of 14:31, 23 May 2020


Riemann Meets COLLADA & Oculus Rift S

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


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

Key Physical Parameters

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

Figure 1a
EFE Parameter Space

 

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

 

Figure 1b
EFE Model b41c385

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

Direct

 

Adjoint

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

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

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

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

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

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

The COLLADA Code & Initial 3D Scene

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


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

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

                 <node>        <geometry>       <material>      <effect>
*** firstclock:    ID3     Clock_OuterEdge         ID6            ID5
***           :            Clock_InnerEdge       InnerID6       InnerID5
***   Jetman  :  ArrowID3  Clock_ArrowEdge       ArrowID6       ArrowID5
***  HourHand :  HourID3   Clock_HourEdge        HourID6        HourID5
-->
    </asset>
    <library_effects>
        <effect id="DiffusePurple_00">
            <profile_COMMON>
                <technique sid="COMMON">
                    <phong>
                        <diffuse>
                            <color>0.5 0.0 0.99  1.0</color>
                        </diffuse>
                        <transparency>
               <float sid="transparency">1.0</float>
                        </transparency>
                    </phong>
                </technique>
            </profile_COMMON>
        </effect>
        <effect id="DiffuseRed_EFE">
            <profile_COMMON>
                <technique sid="COMMON">
                    <lambert>
                        <diffuse>
                            <color>1.0 0.0 0.0  1.0</color>
                        </diffuse>
                    </lambert>
                </technique>
            </profile_COMMON>
        </effect>
<!-- effect:  MidPlane Frame -->
        <effect id="MidPlaneID5">
            <profile_COMMON>
                <technique sid="COMMON">
                    <lambert>
                        <diffuse>
                            <color>0.0 0.0 0.6 0.5</color>
                        </diffuse>
                    </lambert>
                </technique>
            </profile_COMMON>
        </effect>
<!-- effect:  Cylindrical Pointer -->
        <effect id="CylID5">
            <profile_COMMON>
                <technique sid="COMMON">
                    <lambert>
                        <diffuse>
                            <color>0.0 0.0 0.0 1.0</color>
                        </diffuse>
                    </lambert>
                </technique>
            </profile_COMMON>
        </effect>
        <effect id="MarkersID5">
          <profile_COMMON>
            <technique sid="COMMON">
              <lambert>
                <diffuse>
                  <color>1 1 0 1</color>
                </diffuse>
              </lambert>
            </technique>
          </profile_COMMON>
        </effect>
<!-- effect:  Letters -->
        <effect id="LettersID5">
            <profile_COMMON>
                <technique sid="COMMON">
                    <lambert>
                        <diffuse>
                            <color>0 0 0 1</color>
                        </diffuse>
                    </lambert>
                </technique>
            </profile_COMMON>
        </effect>
        <effect id="DiagonalID5">
            <profile_COMMON>
                <technique sid="COMMON">
                    <lambert>
                        <diffuse>
                            <color>0 0 1 1</color>
                        </diffuse>
                    </lambert>
                </technique>
            </profile_COMMON>
        </effect>
        <effect id="Black_DiagonalID5">
            <profile_COMMON>
                <technique sid="COMMON">
                    <lambert>
                        <diffuse>
                            <color>0 0 0 1</color>
                        </diffuse>
                    </lambert>
                </technique>
            </profile_COMMON>
        </effect>
<!-- effect:  Four Clock Components -->
        <effect id="ID5">
            <profile_COMMON>
                <technique sid="COMMON">
                    <lambert>
                        <diffuse>
                            <color>0 0 1 1</color>
                        </diffuse>
                    </lambert>
                </technique>
            </profile_COMMON>
        </effect>
        <effect id="InnerID5">
            <profile_COMMON>
                <technique sid="COMMON">
                    <lambert>
                        <diffuse>
                            <color>0.4 0.0 0.7 0.4</color>
                        </diffuse>
                    </lambert>
                </technique>
            </profile_COMMON>
        </effect>
        <effect id="ArrowID5">
            <profile_COMMON>
                <technique sid="COMMON">
                    <lambert>
                        <diffuse>
                            <color>1.0 0.0 0.0 1.0</color>
                        </diffuse>
                    </lambert>
                </technique>
            </profile_COMMON>
        </effect>
        <effect id="HourID5">
            <profile_COMMON>
                <technique sid="COMMON">
                    <lambert>
                        <diffuse>
                            <color>0.0 0.0 0.0 1.0</color>
                        </diffuse>
                    </lambert>
                </technique>
            </profile_COMMON>
        </effect>
    </library_effects>
    <library_materials>
<!-- material:  Four Clock Components -->
        <material id="ID6" name="material">
            <instance_effect url="#ID5" />
        </material>
        <material id="InnerID6" name="Inner_material">
            <instance_effect url="#InnerID5" />
        </material>
        <material id="ArrowID6" name="Arrow_material">
            <instance_effect url="#ArrowID5" />
        </material>
        <material id="HourID6" name="Hour_material">
            <instance_effect url="#HourID5" />
        </material>
        <material id="ID6_EFE" name="material">
            <instance_effect url="#DiffusePurple_00" />
        </material>
<!-- material:  MidPlane Frame -->
        <material id="MidPlaneID6" name="MidPlane_material">
            <instance_effect url="#MidPlaneID5" />
        </material>
<!-- material:  Cylindrical Pointer -->
        <material id="CylID6" name="Cyl_material">
            <instance_effect url="#CylID5" />
        </material>
        <material id="ZupID6" name="Zup_material">
            <instance_effect url="#MidPlaneID5" />
        </material>
        <material id="MarkersID6" name="markers_material">
            <instance_effect url="#MarkersID5" />
        </material>
        <material id="Primary_MarkerID6" name="primary_marker_material">
            <instance_effect url="#DiffuseRed_EFE" />
        </material>
<!-- material:  Letters -->
        <material id="LettersID6" name="material">
            <instance_effect url="#LettersID5" />
        </material>
        <material id="DiagonalID6" name="material">
            <instance_effect url="#DiagonalID5" />
        </material>
        <material id="Black_DiagonalID6" name="material">
            <instance_effect url="#Black_DiagonalID5" />
        </material>
    </library_materials>
    <library_nodes>
<!-- node:  Three clock components -->
        <node id="ID3" name="cube_component">
            <instance_geometry url="#Clock_OuterEdge">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#ID6">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                        </instance_material>
                    </technique_common>
                </bind_material>
            </instance_geometry>
            <instance_geometry url="#Clock_InnerEdge">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#InnerID6">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                        </instance_material>
                    </technique_common>
                </bind_material>
            </instance_geometry>
        </node>
        <node id="ArrowID3" name="cube_component">
            <instance_geometry url="#Clock_ArrowEdge">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#ArrowID6">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                        </instance_material>
                    </technique_common>
                </bind_material>
            </instance_geometry>
        </node>
        <node id="HourID3" name="hour_hand">
            <instance_geometry url="#Clock_HourEdge">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#HourID6">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                        </instance_material>
                    </technique_common>
                </bind_material>
            </instance_geometry>
        </node>
        <node id="ID3_EFE" name="cube_componentEFE">
            <instance_geometry url="#EllipsoidOctant">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#ID6_EFE">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                        </instance_material>
                    </technique_common>
                </bind_material>
            </instance_geometry>
            <instance_geometry url="#ReflectOctant">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#ID6_EFE">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                        </instance_material>
                    </technique_common>
                </bind_material>
            </instance_geometry>
        </node>
<!-- node:  MidPlane Frame -->
        <node id="EqPlane" name="equatorial_plane">
            <instance_geometry url="#EquatorialPlane">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#MidPlaneID6">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                        </instance_material>
                    </technique_common>
                </bind_material>
            </instance_geometry>
        </node>
<!-- node:  Cylindrical Pointer -->
        <node id="CylPointer" name="cylindrical_component">
            <instance_geometry url="#Cylinder">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#CylID6">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                        </instance_material>
                    </technique_common>
                </bind_material>
            </instance_geometry>
        </node>
        <node id="ZupPointer" name="Zup_component">
            <instance_geometry url="#CubeID4">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#ZupID6">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                        </instance_material>
                    </technique_common>
                </bind_material>
            </instance_geometry>
        </node>
        <node id="MarkersID3" name="Lagrange_markers">
          <instance_geometry url="#CubeID4">
            <bind_material>
              <technique_common>
                <instance_material symbol="Material2" target="#MarkersID6">
                  <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                </instance_material>
              </technique_common>
            </bind_material>
          </instance_geometry>
        </node>
        <node id="Primary_MarkerID3" name="Primary_marker">
          <instance_geometry url="#CubeID4">
            <bind_material>
              <technique_common>
                <instance_material symbol="Material2" target="#Primary_MarkerID6">
                  <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                </instance_material>
              </technique_common>
            </bind_material>
          </instance_geometry>
        </node>
<!-- node:  Letters -->
        <node id="LettersID3" name="cube_component">
            <instance_geometry url="#CubeID4">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#LettersID6">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                        </instance_material>
                    </technique_common>
                </bind_material>
            </instance_geometry>
        </node>
        <node id="DiagonalID3" name="diagonal_component">
            <instance_geometry url="#DiagonalID4">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#DiagonalID6">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                        </instance_material>
                    </technique_common>
                </bind_material>
            </instance_geometry>
        </node>
        <node id="Black_DiagonalID3" name="Blackdiagonal_component">
            <instance_geometry url="#DiagonalID4">
                <bind_material>
                    <technique_common>
                        <instance_material symbol="Material2" target="#Black_DiagonalID6">
                            <bind_vertex_input semantic="UVSET0" input_semantic="TEXCOORD" input_set="0" />
                        </instance_material>
                    </technique_common>
                </bind_material>
            </instance_geometry>
        </node>
    </library_nodes>
    <library_geometries>
<!-- geometry:  Four Clock Components -->
        <geometry id="Clock_OuterEdge">
            <mesh>
<!--
            **********************************************
            *
            *  Insert first portion of clock's structure
            *
            **********************************************
-->
                <source id="Clock_Positions">
                  <float_array id="Coordinates01" count="123"> 0.0  1.0  0.2 1.0  1.0  0.2 1.0  0.0  0.2 1.0 -1.0  0.2 0.0 -1.0  0.2 -1.0 -1.0  0.2 -1.0  0.0  0.2 -1.0  1.0  0.2 0.0  1.0 -0.2 1.0  1.0 -0.2 1.0  0.0 -0.2 1.0 -1.0 -0.2 0.0 -1.0 -0.2 -1.0 -1.0 -0.2 -1.0  0.0 -0.2 -1.0  1.0 -0.2 0.9  0.0  0.2 0.779423 0.45 0.2 0.45 0.779423 0.2 0.0  0.9  0.2 -0.45 0.779423 0.2 -0.779423 0.45 0.2 -0.9 0.0 0.2 -0.779423 -0.45 0.2 -0.45 -0.779423 0.2 0.0 -0.9 0.2 0.45 -0.779423 0.2 0.779423 -0.45 0.2 -0.9  0.0  -0.2 -0.779423 0.45 -0.2 -0.45 0.779423 -0.2 -0.0  0.9  -0.2 0.45 0.779423 -0.2 0.779423 0.45 -0.2 0.9 0.0 -0.2 0.779423 -0.45 -0.2 0.45 -0.779423 -0.2 -0.0 -0.9 -0.2 -0.45 -0.779423 -0.2 -0.779423 -0.45 -0.2  0.0 0.0 -0.2</float_array>
                  <technique_common>
                    <accessor source="#Coordinates01" count="41" stride="3">
                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
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                  </technique_common>
                </source>
                <source id="Clock_Normals">
                  <float_array id="InnerNormals01" count="18">
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-1.0  0.0  0.0
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                    <technique_common>
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                            <param name="X" type="float" />
                            <param name="Y" type="float" />
                            <param name="Z" type="float" />
                        </accessor>
                    </technique_common>
                </source>
                <vertices id="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
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<technique_common>
  <accessor source="#Ellipsoid_Coordinates" count="  521" stride="3">
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        <param name="Y" type="float" />
        <param name="Z" type="float" />
  </accessor>
</technique_common>
</source>
<source id="Ellipsoid_Normals">
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<technique_common>
  <accessor source="#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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    0.5068   -0.8611    0.0401
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    0.7528   -0.6562    0.0519
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</float_array>
<technique_common>
  <accessor source="#Reflect_Normals01" count="  975" stride="3">
        <param name="X" type="float" />
        <param name="Y" type="float" />
        <param name="Z" type="float" />
  </accessor>
</technique_common>
</source>
<vertices id="Reflect_Vertices">
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</vertices>
<polylist count="  975" material="Material2">
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  <input semantic="NORMAL" source="#Reflect_Normals" offset="1" />
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3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
</vcount>
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   51  973   25  973   26  973
   51  974   26  974   52  974
</p>
</polylist>
  </mesh>
</geometry>
<!-- EquatorialPlane (begin) -->
<geometry id="EquatorialPlane">
  <mesh>
<source id="EquatorialPlane_Positions">
<float_array id="EquatorialPlane_Coordinates" count="48">
   -5.5000    -5.5000    0.2000
    5.5000    -5.5000    0.2000
    5.5000     5.5000    0.2000
   -5.5000     5.5000    0.2000
   -5.7500    -5.7500    0.2000
    5.7500    -5.7500    0.2000
    5.7500     5.7500    0.2000
   -5.7500     5.7500    0.2000
   -5.5000    -5.5000   -0.2000
    5.5000    -5.5000   -0.2000
    5.5000     5.5000   -0.2000
   -5.5000     5.5000   -0.2000
   -5.7500    -5.7500   -0.2000
    5.7500    -5.7500   -0.2000
    5.7500     5.7500   -0.2000
   -5.7500     5.7500   -0.2000
</float_array>
<technique_common>
  <accessor source="#EquatorialPlane_Coordinates" count="  16" stride="3">
        <param name="X" type="float" />
        <param name="Y" type="float" />
        <param name="Z" type="float" />
  </accessor>
</technique_common>
</source>
<source id="EquatorialPlane_Normals">
<float_array id="EquatorialPlane_Normals01" count="18">
    0.0000    0.0000     1.0000
    0.0000    0.0000    -1.0000
    0.0000   -1.0000     0.0000
    0.0000    1.0000     0.0000
   -1.0000    0.0000     0.0000
    1.0000    0.0000     0.0000
</float_array>
<technique_common>
  <accessor source="#EquatorialPlane_Normals01" count="6" stride="3">
        <param name="X" type="float" />
        <param name="Y" type="float" />
        <param name="Z" type="float" />
  </accessor>
</technique_common>
</source>
<vertices id="EquatorialPlane_Vertices">
  <input semantic="POSITION" source="#EquatorialPlane_Positions" />
</vertices>
<polylist count="  12" material="Material2">
  <input semantic="VERTEX" source="#EquatorialPlane_Vertices" offset="0" />
  <input semantic="NORMAL" source="#EquatorialPlane_Normals" offset="1" />
<vcount>
4 4 4 4
4 4 4 4
4 4 4 4
</vcount>
<p>
 4 0  5 0  1 0  0 0
 5 0  6 0  2 0  1 0
 6 0  7 0  3 0  2 0
 7 0  4 0  0 0  3 0
 8 1   9 1  13 1  12 1
 9 1  10 1  14 1  13 1
10 1  11 1  15 1  14 1
11 1   8 1  12 1  15 1
12 2  13 2   5 2   4 2
14 3  15 3   7 3   6 3
15 4  12 4   4 4   7 4
13 5  14 5   6 5   5 5
</p>
</polylist>
  </mesh>
</geometry>
<!-- EquatorialPlane (end)   -->
    </library_geometries>
    <library_animations>
  <animation id="First_rotation_euler_Z">
<!-- for EFE/Ou model b41c385, clockstop = 36.5047 and anglestop = 1800.0 -->
<!-- this means that one 360 degree turn of the ellipsoid takes 7.3009 clock units -->
    <source id="First_rotation_euler_Z-input">
      <float_array id="First_rotation_euler_Z-input-array" count="31">
   0.00
   1.22
   2.43
   3.65
   4.87
   6.08
   7.30
   8.52
   9.73
  10.95
  12.17
  13.39
  14.60
  15.82
  17.04
  18.25
  19.47
  20.69
  21.90
  23.12
  24.34
  25.55
  26.77
  27.99
  29.20
  30.42
  31.64
  32.85
  34.07
  35.29
  36.50
      </float_array>
      <technique_common>
          <accessor source="#First_rotation_euler_Z-input-array" count="31" stride="1">
            <param name="TIME" type="float"/>
          </accessor>
      </technique_common>
    </source>
<!-- This sets the spin rate of the "Entire" ellipsoid -->
    <source id="First_rotation_euler_Z-output">
      <float_array id="First_rotation_euler_Z-output-array" count="31">
     3.0
    63.0
   123.0
   183.0
   243.0
   303.0
   363.0
   423.0
   483.0
   543.0
   603.0
   663.0
   723.0
   783.0
   843.0
   903.0
   963.0
  1023.0
  1083.0
  1143.0
  1203.0
  1263.0
  1323.0
  1383.0
  1443.0
  1503.0
  1563.0
  1623.0
  1683.0
  1743.0
  1803.0
      </float_array>
      <technique_common>
          <accessor source="#First_rotation_euler_Z-output-array" count="31" stride="1">
            <param name="ANGLE" type="float"/>
          </accessor>
      </technique_common>
    </source>
<!-- This sets the spin rate of the "MidPlane" Frame of reference -->
    <source id="Frame_rotation_euler_Z-output">
      <float_array id="Frame_rotation_euler_Z-output-array" count="31">
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
      </float_array>
      <technique_common>
          <accessor source="#Frame_rotation_euler_Z-output-array" count="31" stride="1">
            <param name="ANGLE" type="float"/>
          </accessor>
      </technique_common>
    </source>
    <sampler id="First_rotation_euler_Z-sampler">
      <input semantic="INPUT" source="#First_rotation_euler_Z-input"/>
      <input semantic="OUTPUT" source="#First_rotation_euler_Z-output"/>
    </sampler>
    <sampler id="Frame_rotation_euler_Z-sampler">
      <input semantic="INPUT" source="#First_rotation_euler_Z-input"/>
      <input semantic="OUTPUT" source="#Frame_rotation_euler_Z-output"/>
    </sampler>
    <channel source="#First_rotation_euler_Z-sampler" target="EntireEllipsoid/rotationZ.ANGLE"/>
    <channel source="#Frame_rotation_euler_Z-sampler" target="Inertial/rotationZ.ANGLE"/>
  </animation>
<!-- FLUID ELEMENT 1 -->
  <animation id="FluidElement1_location">
    <source id="Lagrange1_location_X-input">
      <float_array id="Lagrange1_location_X-input-array" count="   37">
  0.0000
  1.0014
  2.0029
  3.0043
  4.0057
  5.0071
  6.0086
  7.0100
  8.0114
  9.0129
 10.0143
 11.0157
 12.0171
 13.0186
 14.0200
 15.0214
 16.0229
 17.0243
 18.0257
 19.0271
 20.0286
 21.0300
 22.0314
 23.0329
 24.0343
 25.0357
 26.0371
 27.0386
 28.0400
 29.0414
 30.0429
 31.0443
 32.0457
 33.0472
 34.0486
 35.0500
 36.0514
      </float_array>
      <technique_common>
          <accessor source="#Lagrange1_location_X-input-array" count="   37" stride="1">
            <param name="TIME" type="float"/>
          </accessor>
      </technique_common>
    </source>
    <source id="Lagrange1_location_X-output">
      <float_array id="Lagrange1_location_X-output-array" count="   37">
  1.0000
  0.9921
  0.9686
  0.9298
  0.8763
  0.8090
  0.7290
  0.6374
  0.5358
  0.4258
  0.3090
  0.1874
  0.0628
 -0.0628
 -0.1874
 -0.3090
 -0.4258
 -0.5358
 -0.6374
 -0.7290
 -0.8090
 -0.8763
 -0.9298
 -0.9686
 -0.9921
 -1.0000
 -0.9921
 -0.9686
 -0.9298
 -0.8763
 -0.8090
 -0.7290
 -0.6374
 -0.5358
 -0.4258
 -0.3090
 -0.1874
      </float_array>
      <technique_common>
          <accessor source="#Lagrange1_location_X-output-array" count="   37" stride="1">
            <param name="X" type="float"/>
          </accessor>
      </technique_common>
    </source>
    <sampler id="Lagrange1_location_X-sampler">
      <input semantic="INPUT" source="#Lagrange1_location_X-input"/>
      <input semantic="OUTPUT" source="#Lagrange1_location_X-output"/>
    </sampler>
    <source id="Lagrange1_location_Y-output">
      <float_array id="Lagrange1_location_Y-output-array" count="   37">
 -0.0000
 -0.0514
 -0.1020
 -0.1509
 -0.1975
 -0.2410
 -0.2807
 -0.3159
 -0.3462
 -0.3710
 -0.3899
 -0.4027
 -0.4092
 -0.4092
 -0.4027
 -0.3899
 -0.3710
 -0.3462
 -0.3159
 -0.2807
 -0.2410
 -0.1975
 -0.1509
 -0.1020
 -0.0514
  0.0000
  0.0514
  0.1020
  0.1509
  0.1975
  0.2410
  0.2807
  0.3159
  0.3462
  0.3710
  0.3899
  0.4027
      </float_array>
      <technique_common>
          <accessor source="#Lagrange1_location_Y-output-array" count="   37" stride="1">
            <param name="Y" type="float"/>
          </accessor>
      </technique_common>
    </source>
    <sampler id="Lagrange1_location_Y-sampler">
      <input semantic="INPUT" source="#Lagrange1_location_X-input"/>
      <input semantic="OUTPUT" source="#Lagrange1_location_Y-output"/>
    </sampler>
    <channel source="#Lagrange1_location_X-sampler" target="Lagrange01/location.X"/>
    <channel source="#Lagrange1_location_Y-sampler" target="Lagrange01/location.Y"/>
</animation>
<!-- CLOCK (clockstop = 36.5047) 
     One spin of ellipsoid (or frame) is 1.8252 EFE sqrt(pi * G * rho) units;
     Want 1 EFE unit to take 4.0 seconds of TIME;
     Hence, one spin of ellipsoid (360 degrees) is 7.3009 seconds of TIME;
            and 5 ellipsoid spins is 36.5047 seconds of TIME.
     Divide one spin (360) into 12 pieces 
     ==> 30 degrees = 1 timestep = 4 x 0.1521 = 0.6084 seconds of TIME.
-->
  <animation id="Cube_quaternion_Z">
    <source id="Cube_quaternion_Z-input">
      <float_array id="Cube_quaternion_Z-input-array" count=" 147">
     0.00  0.25  0.50  0.75  1.00  1.25  1.50  1.75  2.00  2.25  2.50  2.75  3.00  3.25  3.50  3.75
     4.00  4.25  4.50  4.75  5.00  5.25  5.50  5.75  6.00  6.25  6.50  6.75  7.00  7.25  7.50  7.75
     8.00  8.25  8.50  8.75  9.00  9.25  9.50  9.75 10.00 10.25 10.50 10.75 11.00 11.25 11.50 11.75
    12.00 12.25 12.50 12.75 13.00 13.25 13.50 13.75 14.00 14.25 14.50 14.75 15.00 15.25 15.50 15.75
    16.00 16.25 16.50 16.75 17.00 17.25 17.50 17.75 18.00 18.25 18.50 18.75 19.00 19.25 19.50 19.75
    20.00 20.25 20.50 20.75 21.00 21.25 21.50 21.75 22.00 22.25 22.50 22.75 23.00 23.25 23.50 23.75
    24.00 24.25 24.50 24.75 25.00 25.25 25.50 25.75 26.00 26.25 26.50 26.75 27.00 27.25 27.50 27.75
    28.00 28.25 28.50 28.75 29.00 29.25 29.50 29.75 30.00 30.25 30.50 30.75 31.00 31.25 31.50 31.75
    32.00 32.25 32.50 32.75 33.00 33.25 33.50 33.75 34.00 34.25 34.50 34.75 35.00 35.25 35.50 35.75
    36.00 36.25 36.50 
      </float_array>
      <technique_common>
          <accessor source="#Cube_quaternion_Z-input-array" count="   147" stride="1">
            <param name="TIME" type="float"/>
          </accessor>
      </technique_common>
    </source>
    <source id="Cube_quaternion_Z-output">
      <float_array id="Cube_quaternion_Z-output-array" count="2352">
   0.000  0.000 -1.00  0.00  -1.0000  0.0000  0.000  0.000   0.0000  1.0000  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.9239 -0.3827  0.000  0.000  -0.3827  0.9239  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.7071 -0.7071  0.000  0.000  -0.7071  0.7071  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.3827 -0.9239  0.000  0.000  -0.9239  0.3827  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.0000 -1.0000  0.000  0.000  -1.0000  0.0000  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.3827 -0.9239  0.000  0.000  -0.9239 -0.3827  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.7071 -0.7071  0.000  0.000  -0.7071 -0.7071  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.9239 -0.3827  0.000  0.000  -0.3827 -0.9239  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   1.0000  0.0000  0.000  0.000   0.0000 -1.0000  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.9239  0.3827  0.000  0.000   0.3827 -0.9239  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.7071  0.7071  0.000  0.000   0.7071 -0.7071  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.3827  0.9239  0.000  0.000   0.9239 -0.3827  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.0000  1.0000  0.000  0.000   1.0000  0.0000  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.3827  0.9239  0.000  0.000   0.9239  0.3827  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.7071  0.7071  0.000  0.000   0.7071  0.7071  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.9239  0.3827  0.000  0.000   0.3827  0.9239  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -1.0000  0.0000  0.000  0.000   0.0000  1.0000  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.9239 -0.3827  0.000  0.000  -0.3827  0.9239  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.7071 -0.7071  0.000  0.000  -0.7071  0.7071  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.3827 -0.9239  0.000  0.000  -0.9239  0.3827  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.0000 -1.0000  0.000  0.000  -1.0000  0.0000  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.3827 -0.9239  0.000  0.000  -0.9239 -0.3827  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.7071 -0.7071  0.000  0.000  -0.7071 -0.7071  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.9239 -0.3827  0.000  0.000  -0.3827 -0.9239  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   1.0000  0.0000  0.000  0.000   0.0000 -1.0000  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.9239  0.3827  0.000  0.000   0.3827 -0.9239  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.7071  0.7071  0.000  0.000   0.7071 -0.7071  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.3827  0.9239  0.000  0.000   0.9239 -0.3827  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.0000  1.0000  0.000  0.000   1.0000  0.0000  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.3827  0.9239  0.000  0.000   0.9239  0.3827  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.7071  0.7071  0.000  0.000   0.7071  0.7071  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.9239  0.3827  0.000  0.000   0.3827  0.9239  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -1.0000  0.0000  0.000  0.000   0.0000  1.0000  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.9239 -0.3827  0.000  0.000  -0.3827  0.9239  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.7071 -0.7071  0.000  0.000  -0.7071  0.7071  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.3827 -0.9239  0.000  0.000  -0.9239  0.3827  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.0000 -1.0000  0.000  0.000  -1.0000  0.0000  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.3827 -0.9239  0.000  0.000  -0.9239 -0.3827  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.7071 -0.7071  0.000  0.000  -0.7071 -0.7071  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.9239 -0.3827  0.000  0.000  -0.3827 -0.9239  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   1.0000  0.0000  0.000  0.000   0.0000 -1.0000  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.9239  0.3827  0.000  0.000   0.3827 -0.9239  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.7071  0.7071  0.000  0.000   0.7071 -0.7071  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.3827  0.9239  0.000  0.000   0.9239 -0.3827  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.0000  1.0000  0.000  0.000   1.0000  0.0000  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.3827  0.9239  0.000  0.000   0.9239  0.3827  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.7071  0.7071  0.000  0.000   0.7071  0.7071  0.000  0.00   0.000  0.000  0.000  1.000
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   0.000  0.000 -1.00  0.00  -1.0000  0.0000  0.000  0.000   0.0000  1.0000  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.9239 -0.3827  0.000  0.000  -0.3827  0.9239  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.7071 -0.7071  0.000  0.000  -0.7071  0.7071  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.3827 -0.9239  0.000  0.000  -0.9239  0.3827  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.0000 -1.0000  0.000  0.000  -1.0000  0.0000  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.3827 -0.9239  0.000  0.000  -0.9239 -0.3827  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.7071 -0.7071  0.000  0.000  -0.7071 -0.7071  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.9239 -0.3827  0.000  0.000  -0.3827 -0.9239  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   1.0000  0.0000  0.000  0.000   0.0000 -1.0000  0.000  0.00   0.000  0.000  0.000  1.000
   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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             <translate>0.0 0.0 0.0</translate>
             <rotate sid="rotationX">1.0 0.0 0.0  0.0</rotate>
             <rotate sid="rotationY">0.0 1.0 0.0  0.0</rotate>
             <rotate sid="rotationZ">0.0 0.0 1.0  3.0</rotate>
             <scale sid="scale">5.0 5.0 5.0</scale>
                <node id="First" name="First_instance_EFE">
                  <translate>0.0 0.0 0.0</translate>
                  <rotate sid="rotationX">1.0 0.0 0.0  0.0</rotate>
                  <rotate sid="rotationY">0.0 1.0 0.0  0.0</rotate>
                  <rotate sid="rotationZ">0.0 0.0 1.0  0.0</rotate>
                  <scale sid="scale">1.0 1.0 1.0</scale>
                  <instance_node url="#ID3_EFE" />
                </node>
                <node id="Second" name="Second_instance_EFE">
                  <translate>0.0 0.0 0.0</translate>
                  <rotate sid="rotationX">1.0 0.0 0.0  180.0</rotate>
                  <rotate sid="rotationY">0.0 1.0 0.0    0.0</rotate>
                  <rotate sid="rotationZ">0.0 0.0 1.0    0.0</rotate>
                  <scale sid="scale">1.0 1.0 1.0</scale>
                  <instance_node url="#ID3_EFE" />
                </node>
                <node id="Third" name="Third_instance_EFE">
                  <translate>0.0 0.0 0.0</translate>
                  <rotate sid="rotationX">1.0 0.0 0.0    0.0</rotate>
                  <rotate sid="rotationY">0.0 1.0 0.0  180.0</rotate>
                  <rotate sid="rotationZ">0.0 0.0 1.0    0.0</rotate>
                  <scale sid="scale">1.0 1.0 1.0</scale>
                  <instance_node url="#ID3_EFE" />
                </node>
                <node id="Fourth" name="Fourth_instance_EFE">
                  <translate>0.0 0.0 0.0</translate>
                  <rotate sid="rotationX">1.0 0.0 0.0  180.0</rotate>
                  <rotate sid="rotationY">0.0 1.0 0.0  180.0</rotate>
                  <rotate sid="rotationZ">0.0 0.0 1.0    0.0</rotate>
                  <scale sid="scale">1.0 1.0 1.0</scale>
                  <instance_node url="#ID3_EFE" />
                </node>
<!-- instance:  Cylindrical Pointer -->
                <node id="CylinderPointer" name="instance_cylinder">  
                  <translate sid="location">-1.0 0.0 0.0</translate>
                    <rotate sid="rotationX">1 0 0 0</rotate>
                    <rotate sid="rotationY">0 1 0 0</rotate>
                    <rotate sid="rotationZ">0 0 1 180</rotate>
                  <scale sid="scale">0.05 0.025 0.025</scale>
                  <instance_node url="#CylPointer" />
                </node>                                         
<!-- Begin LAGRANGE markers -->
              <node id="Lagrange01" name="instance_Lagrange01">
                  <translate sid="location">1.0000 0.0000 0.0</translate>
                  <rotate sid="rotationX">1.0 0.0 0.0  0.0</rotate>
                  <rotate sid="rotationY">0.0 1.0 0.0  0.0</rotate>
                  <rotate sid="rotationZ">0.0 0.0 1.0  0.0</rotate>
                  <scale sid="scale">0.075 0.075 0.075</scale>
                <instance_node url="#Primary_MarkerID3" />
              </node>
              <node id="Marker01" name="instance_marker01">
                <matrix>0.025 0.0 0.0 1.0000  0.0 0.025 0.0 -0.0000  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker02" name="instance_marker02">
                <matrix>0.025 0.0 0.0 0.9921  0.0 0.025 0.0 -0.0514  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker03" name="instance_marker03">
                <matrix>0.025 0.0 0.0 0.9686  0.0 0.025 0.0 -0.1020  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker04" name="instance_marker04">
                <matrix>0.025 0.0 0.0 0.9298  0.0 0.025 0.0 -0.1509  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker05" name="instance_marker05">
                <matrix>0.025 0.0 0.0 0.8763  0.0 0.025 0.0 -0.1975  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker06" name="instance_marker06">
                <matrix>0.025 0.0 0.0 0.8090  0.0 0.025 0.0 -0.2410  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker07" name="instance_marker07">
                <matrix>0.025 0.0 0.0 0.7290  0.0 0.025 0.0 -0.2807  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker08" name="instance_marker08">
                <matrix>0.025 0.0 0.0 0.6374  0.0 0.025 0.0 -0.3159  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker09" name="instance_marker09">
                <matrix>0.025 0.0 0.0 0.5358  0.0 0.025 0.0 -0.3462  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker10" name="instance_marker10">
                <matrix>0.025 0.0 0.0 0.4258  0.0 0.025 0.0 -0.3710  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker11" name="instance_marker11">
                <matrix>0.025 0.0 0.0 0.3090  0.0 0.025 0.0 -0.3899  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker12" name="instance_marker12">
                <matrix>0.025 0.0 0.0 0.1874  0.0 0.025 0.0 -0.4027  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker13" name="instance_marker13">
                <matrix>0.025 0.0 0.0 0.0628  0.0 0.025 0.0 -0.4092  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker14" name="instance_marker14">
                <matrix>0.025 0.0 0.0 -0.0628  0.0 0.025 0.0 -0.4092  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker15" name="instance_marker15">
                <matrix>0.025 0.0 0.0 -0.1874  0.0 0.025 0.0 -0.4027  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker16" name="instance_marker16">
                <matrix>0.025 0.0 0.0 -0.3090  0.0 0.025 0.0 -0.3899  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker17" name="instance_marker17">
                <matrix>0.025 0.0 0.0 -0.4258  0.0 0.025 0.0 -0.3710  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker18" name="instance_marker18">
                <matrix>0.025 0.0 0.0 -0.5358  0.0 0.025 0.0 -0.3462  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker19" name="instance_marker19">
                <matrix>0.025 0.0 0.0 -0.6374  0.0 0.025 0.0 -0.3159  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker20" name="instance_marker20">
                <matrix>0.025 0.0 0.0 -0.7290  0.0 0.025 0.0 -0.2807  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker21" name="instance_marker21">
                <matrix>0.025 0.0 0.0 -0.8090  0.0 0.025 0.0 -0.2410  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker22" name="instance_marker22">
                <matrix>0.025 0.0 0.0 -0.8763  0.0 0.025 0.0 -0.1975  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker23" name="instance_marker23">
                <matrix>0.025 0.0 0.0 -0.9298  0.0 0.025 0.0 -0.1509  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker24" name="instance_marker24">
                <matrix>0.025 0.0 0.0 -0.9686  0.0 0.025 0.0 -0.1020  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker25" name="instance_marker25">
                <matrix>0.025 0.0 0.0 -0.9921  0.0 0.025 0.0 -0.0514  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker26" name="instance_marker26">
                <matrix>0.025 0.0 0.0 -1.0000  0.0 0.025 0.0 -0.0000  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
<!-- Second Half -->
              <node id="Marker28" name="instance_marker28">
                <matrix>0.025 0.0 0.0 -0.9921  0.0 0.025 0.0 0.0514  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker29" name="instance_marker29">
                <matrix>0.025 0.0 0.0 -0.9686  0.0 0.025 0.0 0.1020  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker30" name="instance_marker30">
                <matrix>0.025 0.0 0.0 -0.9298  0.0 0.025 0.0 0.1509  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker31" name="instance_marker31">
                <matrix>0.025 0.0 0.0 -0.8763  0.0 0.025 0.0 0.1975  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker32" name="instance_marker32">
                <matrix>0.025 0.0 0.0 -0.8090  0.0 0.025 0.0 0.2410  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker33" name="instance_marker33">
                <matrix>0.025 0.0 0.0 -0.7290  0.0 0.025 0.0 0.2807  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker34" name="instance_marker34">
                <matrix>0.025 0.0 0.0 -0.6374  0.0 0.025 0.0 0.3159  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker35" name="instance_marker35">
                <matrix>0.025 0.0 0.0 -0.5358  0.0 0.025 0.0 0.3462  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker36" name="instance_marker36">
                <matrix>0.025 0.0 0.0 -0.4258  0.0 0.025 0.0 0.3710  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker37" name="instance_marker37">
                <matrix>0.025 0.0 0.0 -0.3090  0.0 0.025 0.0 0.3899  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker38" name="instance_marker38">
                <matrix>0.025 0.0 0.0 -0.1874  0.0 0.025 0.0 0.4027  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker39" name="instance_marker39">
                <matrix>0.025 0.0 0.0 -0.0628  0.0 0.025 0.0 0.4092  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker40" name="instance_marker40">
                <matrix>0.025 0.0 0.0 0.0628  0.0 0.025 0.0 0.4092  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker41" name="instance_marker41">
                <matrix>0.025 0.0 0.0 0.1874  0.0 0.025 0.0 0.4027  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker42" name="instance_marker42">
                <matrix>0.025 0.0 0.0 0.3090  0.0 0.025 0.0 0.3899  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker43" name="instance_marker43">
                <matrix>0.025 0.0 0.0 0.4258  0.0 0.025 0.0 0.3710  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker44" name="instance_marker44">
                <matrix>0.025 0.0 0.0 0.5358  0.0 0.025 0.0 0.3462  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker45" name="instance_marker45">
                <matrix>0.025 0.0 0.0 0.6374  0.0 0.025 0.0 0.3159  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker46" name="instance_marker46">
                <matrix>0.025 0.0 0.0 0.7290  0.0 0.025 0.0 0.2807  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker47" name="instance_marker47">
                <matrix>0.025 0.0 0.0 0.8090  0.0 0.025 0.0 0.2410  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker48" name="instance_marker48">
                <matrix>0.025 0.0 0.0 0.8763  0.0 0.025 0.0 0.1975  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker49" name="instance_marker49">
                <matrix>0.025 0.0 0.0 0.9298  0.0 0.025 0.0 0.1509  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker50" name="instance_marker50">
                <matrix>0.025 0.0 0.0 0.9686  0.0 0.025 0.0 0.1020  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
              <node id="Marker51" name="instance_marker51">
                <matrix>0.025 0.0 0.0 0.9921  0.0 0.025 0.0 0.0514  0.0 0.0 0.025 0.0000 0.0 0.0 0.0 1.0</matrix>
                <instance_node url="#MarkersID3" />
              </node>
<!-- End LAGRANGE markers -->
            </node>                           <!-- END EntireEllipsoid -->
          <node id="Inertial" name="instance_inertial">  <!-- Start Inertial Grouping of Objects -->
            <translate>0.0 0.0 0.0</translate>
            <rotate sid="rotationX">1.0 0.0 0.0  0.0</rotate>
            <rotate sid="rotationY">0.0 1.0 0.0  0.0</rotate>
            <rotate sid="rotationZ">0.0 0.0 1.0  3.0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
            <node id="Zup_Pointer" name="instance_zupPointer">  
              <translate>0.0 0.0 5.0</translate>
                <rotate sid="rotationX">1 0 0  0.0</rotate>
                <rotate sid="rotationY">0 1 0  0.0</rotate>
                <rotate sid="rotationZ">0 0 1  0.0</rotate>
              <scale sid="scale">0.125 0.5 1.5</scale>
              <instance_node url="#ZupPointer" />
            </node>                                         
<!-- instance:  MidPlane Frame (MidPlane flips with rotationX = 180 for clockwise spin)-->
            <node id="MidPlane" name="instance_MidPlane">  
              <translate>0.0 0.0 0.0</translate>
                  <rotate sid="rotationX">1.0 0.0 0.0  0.0</rotate>
                  <rotate sid="rotationY">0.0 1.0 0.0  0.0</rotate>
                  <rotate sid="rotationZ">0.0 0.0 1.0  0.0</rotate>
              <scale sid="scale">1.25 1.25 1.25</scale>
              <instance_node url="#EqPlane" />
            </node> 
<!-- BEGIN LABELING HERE -->
          <node name="Labels">
          <translate>7.0 -2.0 5.0</translate>
          <rotate sid="rotationX">1 0 0 0.0</rotate>
          <rotate sid="rotationY">0 1 0 0</rotate>
          <rotate sid="rotationZ">0 0 1 180</rotate>
          <scale sid="scale">0.1 0.1 0.1</scale>
<!--  Equals sign #1  -->
            <node name="Equals1">
            <translate>0.0 15.0 1.0</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
                <node id="IDd51" name="instance_51">
                    <matrix>0.25  0 0 0.0   0 1  0 0.0  0 0 1 2.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDd52" name="instance_52">
                    <matrix>0.25  0 0 0.0   0 1  0 1.1  0 0 1 2.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDd53" name="instance_53">
                    <matrix>0.25  0 0 0.0   0 1  0 2.2  0 0 1 2.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDd55" name="instance_55">
                    <matrix>0.25  0 0 0.0   0 1  0 0.0  0 0 1 4.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDd56" name="instance_56">
                    <matrix>0.25  0 0 0.0   0 1  0 1.1  0 0 1 4.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDd57" name="instance_57">
                    <matrix>0.25  0 0 0.0   0 1  0 2.2  0 0 1 4.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
            </node>
<!--  Equals sign #2  -->
            <node name="Equals2">
            <translate>0.0 15.0 -8.5</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
                <node id="IDd51" name="instance_51">
                    <matrix>0.25  0 0 0.0   0 1  0 0.0  0 0 1 2.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDd52" name="instance_52">
                    <matrix>0.25  0 0 0.0   0 1  0 1.1  0 0 1 2.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDd53" name="instance_53">
                    <matrix>0.25  0 0 0.0   0 1  0 2.2  0 0 1 2.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDd55" name="instance_55">
                    <matrix>0.25  0 0 0.0   0 1  0 0.0  0 0 1 4.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDd56" name="instance_56">
                    <matrix>0.25  0 0 0.0   0 1  0 1.1  0 0 1 4.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDd57" name="instance_57">
                    <matrix>0.25  0 0 0.0   0 1  0 2.2  0 0 1 4.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
          </node>
<!--  Division sign #1  -->
            <node name="Divide1">
            <translate>0.0 4.4 1.0</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 0.75 1.0</scale>
                <node id="IDd21" name="instance_21">
                    <matrix>0.25  0 0 0.0   0 1  0 0.0  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
                <node id="IDd22" name="instance_22">
                    <matrix>0.25  0 0 0.0   0 -1  0 1.1  0 0 -1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
                <node id="IDd23" name="instance_23">
                    <matrix>0.25  0 0 0.0   0 1  0 1.1  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
                <node id="IDd24" name="instance_24">
                    <matrix>0.25  0 0 0.0   0 -1  0 2.2  0 0 -1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
                <node id="IDd25" name="instance_25">
                    <matrix>0.25  0 0 0.0   0 1  0 2.2  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
                <node id="IDd26" name="instance_26">
                    <matrix>0.25  0 0 0.0   0 -1  0 3.3  0 0 -1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
                <node id="IDd27" name="instance_27">
                    <matrix>0.25  0 0 0.0   0 1  0 3.3  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
            </node>
<!--  Division sign #2  -->
            <node name="Divide2">
            <translate>0.0 4.4 -8.5</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 0.75 1.0</scale>
                <node id="IDd21" name="instance_21">
                    <matrix>0.25  0 0 0.0   0 1  0 0.0  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
                <node id="IDd22" name="instance_22">
                    <matrix>0.25  0 0 0.0   0 -1  0 1.1  0 0 -1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
                <node id="IDd23" name="instance_23">
                    <matrix>0.25  0 0 0.0   0 1  0 1.1  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
                <node id="IDd24" name="instance_24">
                    <matrix>0.25  0 0 0.0   0 -1  0 2.2  0 0 -1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
                <node id="IDd25" name="instance_25">
                    <matrix>0.25  0 0 0.0   0 1  0 2.2  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
                <node id="IDd26" name="instance_26">
                    <matrix>0.25  0 0 0.0   0 -1  0 3.3  0 0 -1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
                <node id="IDd27" name="instance_27">
                    <matrix>0.25  0 0 0.0   0 1  0 3.3  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#Black_DiagonalID3" />
                </node>
            </node>
<!--  Letter "a" #1  -->
            <node name="Letter_a1">
            <translate>0.0 8.0 1.0</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
                <node id="IDa01" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa06" name="instance_6">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa07" name="instance_7">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa10" name="instance_10">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa11" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa18" name="instance_18">
                    <matrix>0.25  0 0 0.0  0 1 0 0.0  0 0  1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDa19" name="instance_19">
                    <matrix>0.25  0 0 0.0  0 0 1 4.4  0 -1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDa19" name="instance_19">
                    <matrix>0.25  0 0 0.0  0 0 -1 3.3  0 1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDa11" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa31" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa20" name="instance_20">
                    <matrix>0.25  0 0 0.0   0 0 1 3.3  0 -1 0 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDa21" name="instance_21">
                    <matrix>0.25  0 0 0.0   0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
            </node>
<!--  Letter "a" #2  -->
            <node name="Letter_a2">
            <translate>0.0 8.0 -8.5</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
                <node id="IDa01" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa06" name="instance_6">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa07" name="instance_7">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa10" name="instance_10">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa11" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa18" name="instance_18">
                    <matrix>0.25  0 0 0.0  0 1 0 0.0  0 0  1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDa19" name="instance_19">
                    <matrix>0.25  0 0 0.0  0 0 1 4.4  0 -1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDa19" name="instance_19">
                    <matrix>0.25  0 0 0.0  0 0 -1 3.3  0 1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDa11" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa31" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa20" name="instance_20">
                    <matrix>0.25  0 0 0.0   0 0 1 3.3  0 -1 0 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDa21" name="instance_21">
                    <matrix>0.25  0 0 0.0   0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
            </node>
<!--  Letter "a" #2  -->
            <node name="Letter_a2">
            <translate>0.0 8.0 -8.5</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
                <node id="IDa01" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa06" name="instance_6">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa07" name="instance_7">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa10" name="instance_10">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa11" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa18" name="instance_18">
                    <matrix>0.25  0 0 0.0  0 1 0 0.0  0 0  1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDa19" name="instance_19">
                    <matrix>0.25  0 0 0.0  0 0 1 4.4  0 -1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDa19" name="instance_19">
                    <matrix>0.25  0 0 0.0  0 0 -1 3.3  0 1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDa11" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa31" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDa20" name="instance_20">
                    <matrix>0.25  0 0 0.0   0 0 1 3.3  0 -1 0 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDa21" name="instance_21">
                    <matrix>0.25  0 0 0.0   0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
            </node>
<!--  Letter "c"  -->
            <node name="Letter_c">
            <translate>0.0 0.0 -8.5</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
                <node id="ID001" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID002" name="instance_2">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID006" name="instance_6">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID007" name="instance_7">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID010" name="instance_10">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID011" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID018" name="instance_18">
                    <matrix>0.25  0 0 0.0  0 1 0 0.0  0 0  1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="ID019" name="instance_19">
                    <matrix>0.25  0 0 0.0  0 -1 0 3.3  0 0  -1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="ID020" name="instance_20">
                    <matrix>0.25  0 0 0.0   0 0 1 3.3  0 -1 0 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="ID021" name="instance_21">
                    <matrix>0.25  0 0 0.0   0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
            </node>
<!--  Letter "b"  ... has 8 + (4 x 15) = 68 lines -->
            <node name="Letter_b">
            <translate>0.0 0.0 1.0</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
                <node id="IDb01" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb02" name="instance_2">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb03" name="instance_3">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb04" name="instance_4">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 4.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb05" name="instance_5">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 5.5  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb12" name="instance_12">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb06" name="instance_6">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb07" name="instance_7">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb08" name="instance_8">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb09" name="instance_9">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb10" name="instance_10">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb11" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb19" name="instance_19">
                    <matrix>0.25  0 0 0.0  0 -1 0 3.3  0 0  -1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDb20" name="instance_20">
                    <matrix>0.25  0 0 0.0   0 0 1 3.3  0 -1 0 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDb21" name="instance_21">
                    <matrix>0.25  0 0 0.0   0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
            </node>
<!-- DECIMAL POINTS -->
                <node id="IDD01" name="Decimal_1">
                    <matrix>0.25 0 0 0.0  0 1 0 25.0  0 0 1 1.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDD02" name="Decimal_2">
                    <matrix>0.25 0 0 0.0  0 1 0 25.0  0 0 1 -8.5  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
<!--  Number "0" #1  ... has 8 + (4 x 18) = 80 lines -->
            <node name="Number_0">
            <translate>0.0 20.0 1.0</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
                <node id="IDb01" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb02" name="instance_2">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb03" name="instance_3">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb04" name="instance_4">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 4.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb05" name="instance_5">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 5.5  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDz19" name="instance_z19">
                    <matrix>0.25  0 0 0.0  0 1 0 0.0  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDb06" name="instance_6">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb07" name="instance_7">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb08" name="instance_8">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb09" name="instance_9">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb10" name="instance_10">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb11" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb19" name="instance_19">
                    <matrix>0.25  0 0 0.0  0 -1 0 3.3  0 0  -1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDb20" name="instance_20">
                    <matrix>0.25  0 0 0.0   0 0 1 3.3  0 -1 0 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDb21" name="instance_21">
                    <matrix>0.25  0 0 0.0   0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDz11" name="instance_z11">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDz12" name="instance_z12">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 4.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDz13" name="instance_z13">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 5.5  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
            </node>
<!--  Number "0" #2  ... has 8 + (4 x 18) = 80 lines -->
            <node name="Number_0b">
            <translate>0.0 20.0 -8.5</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
                <node id="IDb01" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb02" name="instance_2">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb03" name="instance_3">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb04" name="instance_4">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 4.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb05" name="instance_5">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 5.5  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDz19" name="instance_z19">
                    <matrix>0.25  0 0 0.0  0 1 0 0.0  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDb06" name="instance_6">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb07" name="instance_7">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb08" name="instance_8">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb09" name="instance_9">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb10" name="instance_10">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb11" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb19" name="instance_19">
                    <matrix>0.25  0 0 0.0  0 -1 0 3.3  0 0  -1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDb20" name="instance_20">
                    <matrix>0.25  0 0 0.0   0 0 1 3.3  0 -1 0 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDb21" name="instance_21">
                    <matrix>0.25  0 0 0.0   0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDz11" name="instance_z11">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDz12" name="instance_z12">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 4.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDz13" name="instance_z13">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 5.5  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
            </node>
<!--  Number "1" ... has 8 + (4 x 8) = 40 lines -->
<!--  Number "2" #1 ... has 8 + (4 x 17) = 76 lines -->
<!--  Number "2" #2 ... has 8 + (4 x 17) = 76 lines -->
<!--  Number "3"  ... has 8 + (4 x 18) = 80 lines -->
<!--  Number "4" ... has 8 + (4 x 13) = 60 lines -->
<!--  Number "5"  ... has 8 + (4 x 17) = 76 lines -->
<!--  Number "6" ... has 8 + (4 x 18) = 80 lines -->
<!--  Number "7" ... has 8 + (4 x 14) = 64 lines -->
<!--  Number "8" ... has 8 + (4 x 22) = 96 lines -->
<!--  Number "9"  ... has 8 + (4 x 15) = 68 lines -->
<!-- bovera_Digit1 is "4" -->
            <node name="bovera_Digit1">
            <translate>0.0 26.8 1.0</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
<!--  Number "4" ... has 8 + (4 x 13) = 60 lines -->
                <node id="IDe01" name="instance_e01">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDe02" name="instance_e02">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDe02" name="instance_e02">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb04" name="instance_4">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 4.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb05" name="instance_5">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 5.5  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb06" name="instance_6">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb08" name="instance_8">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb09" name="instance_9">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDn09" name="instance_9">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDf12" name="instance_n12">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDn12" name="instance_n12">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDz12" name="instance_z12">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 4.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDz13" name="instance_z13">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 5.5  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
            </node>
<!-- bovera_Digit2 is "1" -->
            <node name="bovera_Digit2">
            <translate>0.0 31.8 1.0</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
<!--  Number "1" ... has 8 + (4 x 8) = 40 lines -->
                <node id="ID101" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID102" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID103" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID104" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID105" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 4.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID106" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 5.5  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID107" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID109" name="instance_z19">
                    <matrix>0.25  0 0 0.0  0 1 0 1.1  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
            </node>
<!-- covera_Digit1 is "3" -->
            <node name="covera_Digit1">
            <translate>0.0 26.8 -8.5</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
<!--  Number "3"  ... has 8 + (4 x 18) = 80 lines -->
                <node id="ID301" name="instance_e01">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID302" name="instance_e02">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID303" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID304" name="instance_5">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 5.5  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID305" name="instance_z19">
                    <matrix>0.25  0 0 0.0  0 1 0 0.0  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="ID306" name="instance_6">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID307" name="instance_7">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID308" name="instance_8">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID309" name="instance_9">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID310" name="instance_10">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID311" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID312" name="instance_19">
                    <matrix>0.25  0 0 0.0  0 -1 0 3.3  0 0  -1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="ID313" name="instance_20">
                    <matrix>0.25  0 0 0.0   0 0 1 3.3  0 -1 0 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="ID314" name="instance_21">
                    <matrix>0.25  0 0 0.0   0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="ID315" name="instance_e19">
                    <matrix>0.25  0 0 0.0  0 -1 0 3.3  0 0  -1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="ID316" name="instance_e20">
                    <matrix>0.25  0 0 0.0   0 0 1 3.3  0 -1 0 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="ID317" name="instance_z12">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 4.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="ID318" name="instance_z13">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 5.5  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
            </node>
<!-- covera_Digit2 is "8" -->
            <node name="covera_Digit2">
            <translate>0.0 31.8 -8.5</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
<!--  Number "8" ... has 8 + (4 x 22) = 96 lines -->
                <node id="IDe01" name="instance_e01">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDe02" name="instance_e02">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb01" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb02" name="instance_2">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDe19" name="instance_e19">
                    <matrix>0.25  0 0 0.0  0 1 0 0.0  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDe21" name="instance_e21">
                    <matrix>0.25  0 0 0.0   0 0 -1 0.0  0 1 0 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDb04" name="instance_4">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 4.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb05" name="instance_5">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 5.5  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDz19" name="instance_z19">
                    <matrix>0.25  0 0 0.0  0 1 0 0.0  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDb06" name="instance_6">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb07" name="instance_7">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb08" name="instance_8">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb09" name="instance_9">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb10" name="instance_10">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb11" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb19" name="instance_19">
                    <matrix>0.25  0 0 0.0  0 -1 0 3.3  0 0  -1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDb20" name="instance_20">
                    <matrix>0.25  0 0 0.0   0 0 1 3.3  0 -1 0 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDb21" name="instance_21">
                    <matrix>0.25  0 0 0.0   0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDe19" name="instance_e19">
                    <matrix>0.25  0 0 0.0  0 -1 0 3.3  0 0  -1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDe20" name="instance_e20">
                    <matrix>0.25  0 0 0.0   0 0 1 3.3  0 -1 0 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDz12" name="instance_z12">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 4.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDz13" name="instance_z13">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 5.5  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
            </node>
<!-- covera_Digit3 is "5" -->
            <node name="covera_Digit3">
            <translate>0.0 37.1 -8.5</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
<!--  Number "5"  ... has 8 + (4 x 17) = 76 lines -->
                <node id="IDb01" name="instance_1">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb04" name="instance_4">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 4.4  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb05" name="instance_5">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 5.5  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDf06" name="instance_f6">
                    <matrix>0.25 0 0 0.0  0 1 0 0.0  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb06" name="instance_6">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb07" name="instance_7">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb08" name="instance_8">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 2.2  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb09" name="instance_9">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 1.1  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb10" name="instance_10">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb11" name="instance_11">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb19" name="instance_19">
                    <matrix>0.25  0 0 0.0  0 -1 0 3.3  0 0  -1 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDb20" name="instance_20">
                    <matrix>0.25  0 0 0.0   0 0 1 3.3  0 -1 0 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDf11" name="instance_f11">
                    <matrix>0.25 0 0 0.0  0 1 0 3.3  0 0 1 6.6  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDb21" name="instance_21">
                    <matrix>0.25  0 0 0.0   0 0 -1 0.0  0 1 0 0.0  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDf21" name="instance_f21">
                    <matrix>0.25  0 0 0.0   0 0 -1 0.0  0 1 0 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#DiagonalID3" />
                </node>
                <node id="IDz12" name="instance_z12">
                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="IDz13" name="instance_z13">
                    <matrix>0.25 0 0 0.0  0 1 0 2.2  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
            </node>
<!-- END LABELING HERE -->
            </node>
<!-- BEGIN CLOCK -->
          <node id="EntireClock" name="instance_Clock">
            <translate>7.0 0.0 5.0</translate>
            <rotate sid="rotationX">1.0 0.0 0.0 0.0</rotate>
            <rotate sid="rotationY">0.0 1.0 0.0 0.0</rotate>
            <rotate sid="rotationZ">0.0 0.0 1.0 0.0</rotate>
            <scale sid="scale">1.00 1.00 1.00</scale>
            <node id="firstclock" name="instance_1">        <!-- TWO -->
              <translate>0.0 0.0 0.0</translate>
              <rotate sid="rotationX">1.0 0.0 0.0 0.0</rotate>
              <rotate sid="rotationY">0.0 1.0 0.0 -90.0</rotate>
              <rotate sid="rotationZ">0.0 0.0 1.0 0.0</rotate>
              <scale sid="scale">1.00 1.00 1.00</scale>
              <instance_node url="#ID3" />
            </node>                                         <!-- /TWO -->
            <node id="Jetman" name="instance_Arrow">        <!-- TWO -->
              <matrix sid="transformation"> 0.000  0.000 -1.00  0.00  -1.0000  0.0000  0.000  0.000   0.0000  1.0000  0.000  0.00   0.000  0.000  0.000  1.000</matrix>
              <instance_node url="#ArrowID3" />
            </node>                                         <!-- /TWO -->
            <node id="HourHand" name="instance_Hour">       <!-- TWO -->
              <translate>0.0 0.0 0.0</translate>
              <rotate sid="rotationX">1.0 0.0 0.0 0.0</rotate>
              <rotate sid="rotationY">0.0 1.0 0.0 -90.0</rotate>
              <rotate sid="rotationZ">0.0 0.0 1 270.0</rotate>
              <scale sid="scale">0.75 0.75 0.75</scale>
              <instance_node url="#HourID3" />
            </node>                                         <!-- /TWO -->
          </node>
<!-- END CLOCK   -->
          </node> <!-- End Inertial Grouping of Objects -->
        </visual_scene>
    </library_visual_scenes>
    <scene>
        <instance_visual_scene url="#ID1" />
    </scene>
</COLLADA>


Instructions for Viewing the Example Model on a Mac†:

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

†I have not yet figured out how to similarly (at no cost) view COLLADA-based 3D scenes on a PC.


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

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

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

Animation

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

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

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

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


Figure 2a Figure 2b

EFE Model b41c385

EFE Model b41c385


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

Rotating Reference Frame

 
Figure 3

Rotating Frame at TIME zero

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

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

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


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

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

                 <node>        <geometry>       <material>      <effect>
*** firstclock:    ID3     Clock_OuterEdge         ID6            ID5
***           :            Clock_InnerEdge       InnerID6       InnerID5
***   Jetman  :  ArrowID3  Clock_ArrowEdge       ArrowID6       ArrowID5
***  HourHand :  HourID3   Clock_HourEdge        HourID6        HourID5
-->
    </asset>
    <library_effects>
        <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
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    0.2397    0.3975    0.0192
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    0.3995    0.3753    0.0192
    0.4394    0.3677    0.0192
    0.4794    0.3592    0.0192
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    0.5593    0.3393    0.0192
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    0.6791    0.3002    0.0192
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<technique_common>
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        <param name="Y" type="float" />
        <param name="Z" type="float" />
  </accessor>
</technique_common>
</source>
<source id="Ellipsoid_Normals">
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    0.4552    0.8896    0.0379
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    0.5068    0.8611    0.0401
    0.5691    0.8212    0.0429
    0.5691    0.8212    0.0429
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    0.6475    0.7606    0.0466
    0.7528    0.6562    0.0519
    0.7528    0.6562    0.0519
    0.9425    0.3284    0.0612
    0.9425    0.3284    0.0612
</float_array>
<technique_common>
  <accessor source="#Ellipsoid_Normals01" count="  975" stride="3">
        <param name="X" type="float" />
        <param name="Y" type="float" />
        <param name="Z" type="float" />
  </accessor>
</technique_common>
</source>
<vertices id="Ellipsoid_Vertices">
  <input semantic="POSITION" source="#Ellipsoid_Positions" />
</vertices>
<polylist count="  975" material="Material2">
  <input semantic="VERTEX" source="#Ellipsoid_Vertices" offset="0" />
  <input semantic="NORMAL" source="#Ellipsoid_Normals" offset="1" />
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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
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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
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3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3  3 3 3 3 3
</vcount>
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    0   15  511   15  510   15
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    0   18  514   18  513   18
    0   19  515   19  514   19
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    0   21  517   21  516   21
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</float_array>
<technique_common>
  <accessor source="#Reflect_Coordinates" count="  521" stride="3">
        <param name="X" type="float" />
        <param name="Y" type="float" />
        <param name="Z" type="float" />
  </accessor>
</technique_common>
</source>
<source id="Reflect_Normals">
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</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
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   72  914   47  914   73  914
   73  915   47  915   48  915
   73  916   48  916   74  916
   74  917   48  917   49  917
   74  918   49  918   75  918
   75  919   49  919   50  919
   75  920   50  920   76  920
   76  921   50  921   51  921
   76  922   51  922   77  922
   77  923   51  923   52  923
   77  924   52  924   78  924
   27  925    1  925    2  925
   27  926    2  926   28  926
   28  927    2  927    3  927
   28  928    3  928   29  928
   29  929    3  929    4  929
   29  930    4  930   30  930
   30  931    4  931    5  931
   30  932    5  932   31  932
   31  933    5  933    6  933
   31  934    6  934   32  934
   32  935    6  935    7  935
   32  936    7  936   33  936
   33  937    7  937    8  937
   33  938    8  938   34  938
   34  939    8  939    9  939
   34  940    9  940   35  940
   35  941    9  941   10  941
   35  942   10  942   36  942
   36  943   10  943   11  943
   36  944   11  944   37  944
   37  945   11  945   12  945
   37  946   12  946   38  946
   38  947   12  947   13  947
   38  948   13  948   39  948
   39  949   13  949   14  949
   39  950   14  950   40  950
   40  951   14  951   15  951
   40  952   15  952   41  952
   41  953   15  953   16  953
   41  954   16  954   42  954
   42  955   16  955   17  955
   42  956   17  956   43  956
   43  957   17  957   18  957
   43  958   18  958   44  958
   44  959   18  959   19  959
   44  960   19  960   45  960
   45  961   19  961   20  961
   45  962   20  962   46  962
   46  963   20  963   21  963
   46  964   21  964   47  964
   47  965   21  965   22  965
   47  966   22  966   48  966
   48  967   22  967   23  967
   48  968   23  968   49  968
   49  969   23  969   24  969
   49  970   24  970   50  970
   50  971   24  971   25  971
   50  972   25  972   51  972
   51  973   25  973   26  973
   51  974   26  974   52  974
</p>
</polylist>
  </mesh>
</geometry>
<!-- EquatorialPlane (begin) -->
<geometry id="EquatorialPlane">
  <mesh>
<source id="EquatorialPlane_Positions">
<float_array id="EquatorialPlane_Coordinates" count="48">
   -5.5000    -5.5000    0.2000
    5.5000    -5.5000    0.2000
    5.5000     5.5000    0.2000
   -5.5000     5.5000    0.2000
   -5.7500    -5.7500    0.2000
    5.7500    -5.7500    0.2000
    5.7500     5.7500    0.2000
   -5.7500     5.7500    0.2000
   -5.5000    -5.5000   -0.2000
    5.5000    -5.5000   -0.2000
    5.5000     5.5000   -0.2000
   -5.5000     5.5000   -0.2000
   -5.7500    -5.7500   -0.2000
    5.7500    -5.7500   -0.2000
    5.7500     5.7500   -0.2000
   -5.7500     5.7500   -0.2000
</float_array>
<technique_common>
  <accessor source="#EquatorialPlane_Coordinates" count="  16" stride="3">
        <param name="X" type="float" />
        <param name="Y" type="float" />
        <param name="Z" type="float" />
  </accessor>
</technique_common>
</source>
<source id="EquatorialPlane_Normals">
<float_array id="EquatorialPlane_Normals01" count="18">
    0.0000    0.0000     1.0000
    0.0000    0.0000    -1.0000
    0.0000   -1.0000     0.0000
    0.0000    1.0000     0.0000
   -1.0000    0.0000     0.0000
    1.0000    0.0000     0.0000
</float_array>
<technique_common>
  <accessor source="#EquatorialPlane_Normals01" count="6" stride="3">
        <param name="X" type="float" />
        <param name="Y" type="float" />
        <param name="Z" type="float" />
  </accessor>
</technique_common>
</source>
<vertices id="EquatorialPlane_Vertices">
  <input semantic="POSITION" source="#EquatorialPlane_Positions" />
</vertices>
<polylist count="  12" material="Material2">
  <input semantic="VERTEX" source="#EquatorialPlane_Vertices" offset="0" />
  <input semantic="NORMAL" source="#EquatorialPlane_Normals" offset="1" />
<vcount>
4 4 4 4
4 4 4 4
4 4 4 4
</vcount>
<p>
 4 0  5 0  1 0  0 0
 5 0  6 0  2 0  1 0
 6 0  7 0  3 0  2 0
 7 0  4 0  0 0  3 0
 8 1   9 1  13 1  12 1
 9 1  10 1  14 1  13 1
10 1  11 1  15 1  14 1
11 1   8 1  12 1  15 1
12 2  13 2   5 2   4 2
14 3  15 3   7 3   6 3
15 4  12 4   4 4   7 4
13 5  14 5   6 5   5 5
</p>
</polylist>
  </mesh>
</geometry>
<!-- EquatorialPlane (end)   -->
    </library_geometries>
    <library_animations>
  <animation id="First_rotation_euler_Z">
<!-- for EFE/Ou model b41c385, clockstop = 36.5047 and anglestop = 1800.0 -->
<!-- this means that one 360 degree turn of the ellipsoid takes 7.3009 clock units -->
    <source id="First_rotation_euler_Z-input">
      <float_array id="First_rotation_euler_Z-input-array" count="31">
   0.00
   1.22
   2.43
   3.65
   4.87
   6.08
   7.30
   8.52
   9.73
  10.95
  12.17
  13.39
  14.60
  15.82
  17.04
  18.25
  19.47
  20.69
  21.90
  23.12
  24.34
  25.55
  26.77
  27.99
  29.20
  30.42
  31.64
  32.85
  34.07
  35.29
  36.50
      </float_array>
      <technique_common>
          <accessor source="#First_rotation_euler_Z-input-array" count="31" stride="1">
            <param name="TIME" type="float"/>
          </accessor>
      </technique_common>
    </source>
<!-- This sets the spin rate of the "Entire" ellipsoid -->
    <source id="First_rotation_euler_Z-output">
      <float_array id="First_rotation_euler_Z-output-array" count="31">
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
     5.0
      </float_array>
      <technique_common>
          <accessor source="#First_rotation_euler_Z-output-array" count="31" stride="1">
            <param name="ANGLE" type="float"/>
          </accessor>
      </technique_common>
    </source>
<!-- This sets the spin rate of the "MidPlane" Frame of reference -->
    <source id="Frame_rotation_euler_Z-output">
      <float_array id="Frame_rotation_euler_Z-output-array" count="31">
  1803.0
  1743.0
  1683.0
  1623.0
  1563.0
  1503.0
  1443.0
  1383.0
  1323.0
  1263.0
  1203.0
  1143.0
  1083.0
  1023.0
   963.0
   903.0
   843.0
   783.0
   723.0
   663.0
   603.0
   543.0
   483.0
   423.0
   363.0
   303.0
   243.0
   183.0
   123.0
    63.0
     3.0
      </float_array>
      <technique_common>
          <accessor source="#Frame_rotation_euler_Z-output-array" count="31" stride="1">
            <param name="ANGLE" type="float"/>
          </accessor>
      </technique_common>
    </source>
    <sampler id="First_rotation_euler_Z-sampler">
      <input semantic="INPUT" source="#First_rotation_euler_Z-input"/>
      <input semantic="OUTPUT" source="#First_rotation_euler_Z-output"/>
    </sampler>
    <sampler id="Frame_rotation_euler_Z-sampler">
      <input semantic="INPUT" source="#First_rotation_euler_Z-input"/>
      <input semantic="OUTPUT" source="#Frame_rotation_euler_Z-output"/>
    </sampler>
    <channel source="#First_rotation_euler_Z-sampler" target="EntireEllipsoid/rotationZ.ANGLE"/>
    <channel source="#Frame_rotation_euler_Z-sampler" target="Inertial/rotationZ.ANGLE"/>
  </animation>
<!-- FLUID ELEMENT 1 -->
  <animation id="FluidElement1_location">
    <source id="Lagrange1_location_X-input">
      <float_array id="Lagrange1_location_X-input-array" count="   37">
  0.0000
  1.0014
  2.0029
  3.0043
  4.0057
  5.0071
  6.0086
  7.0100
  8.0114
  9.0129
 10.0143
 11.0157
 12.0171
 13.0186
 14.0200
 15.0214
 16.0229
 17.0243
 18.0257
 19.0271
 20.0286
 21.0300
 22.0314
 23.0329
 24.0343
 25.0357
 26.0371
 27.0386
 28.0400
 29.0414
 30.0429
 31.0443
 32.0457
 33.0472
 34.0486
 35.0500
 36.0514
      </float_array>
      <technique_common>
          <accessor source="#Lagrange1_location_X-input-array" count="   37" stride="1">
            <param name="TIME" type="float"/>
          </accessor>
      </technique_common>
    </source>
    <source id="Lagrange1_location_X-output">
      <float_array id="Lagrange1_location_X-output-array" count="   37">
  1.0000
  0.9921
  0.9686
  0.9298
  0.8763
  0.8090
  0.7290
  0.6374
  0.5358
  0.4258
  0.3090
  0.1874
  0.0628
 -0.0628
 -0.1874
 -0.3090
 -0.4258
 -0.5358
 -0.6374
 -0.7290
 -0.8090
 -0.8763
 -0.9298
 -0.9686
 -0.9921
 -1.0000
 -0.9921
 -0.9686
 -0.9298
 -0.8763
 -0.8090
 -0.7290
 -0.6374
 -0.5358
 -0.4258
 -0.3090
 -0.1874
      </float_array>
      <technique_common>
          <accessor source="#Lagrange1_location_X-output-array" count="   37" stride="1">
            <param name="X" type="float"/>
          </accessor>
      </technique_common>
    </source>
    <sampler id="Lagrange1_location_X-sampler">
      <input semantic="INPUT" source="#Lagrange1_location_X-input"/>
      <input semantic="OUTPUT" source="#Lagrange1_location_X-output"/>
    </sampler>
    <source id="Lagrange1_location_Y-output">
      <float_array id="Lagrange1_location_Y-output-array" count="   37">
 -0.0000
 -0.0514
 -0.1020
 -0.1509
 -0.1975
 -0.2410
 -0.2807
 -0.3159
 -0.3462
 -0.3710
 -0.3899
 -0.4027
 -0.4092
 -0.4092
 -0.4027
 -0.3899
 -0.3710
 -0.3462
 -0.3159
 -0.2807
 -0.2410
 -0.1975
 -0.1509
 -0.1020
 -0.0514
  0.0000
  0.0514
  0.1020
  0.1509
  0.1975
  0.2410
  0.2807
  0.3159
  0.3462
  0.3710
  0.3899
  0.4027
      </float_array>
      <technique_common>
          <accessor source="#Lagrange1_location_Y-output-array" count="   37" stride="1">
            <param name="Y" type="float"/>
          </accessor>
      </technique_common>
    </source>
    <sampler id="Lagrange1_location_Y-sampler">
      <input semantic="INPUT" source="#Lagrange1_location_X-input"/>
      <input semantic="OUTPUT" source="#Lagrange1_location_Y-output"/>
    </sampler>
    <channel source="#Lagrange1_location_X-sampler" target="Lagrange01/location.X"/>
    <channel source="#Lagrange1_location_Y-sampler" target="Lagrange01/location.Y"/>
    <channel source="#Lagrange1_location_X-sampler" target="Lagrange02/location.X"/>
    <channel source="#Lagrange1_location_Y-sampler" target="Lagrange02/location.Y"/>
    <channel source="#Lagrange1_location_X-sampler" target="Lagrange03/location.X"/>
    <channel source="#Lagrange1_location_Y-sampler" target="Lagrange03/location.Y"/>
</animation>
<!-- CLOCK (clockstop = 36.5047) 
     One spin of ellipsoid (or frame) is 1.8252 EFE sqrt(pi * G * rho) units;
     Want 1 EFE unit to take 4.0 seconds of TIME;
     Hence, one spin of ellipsoid (360 degrees) is 7.3009 seconds of TIME;
            and 5 ellipsoid spins is 36.5047 seconds of TIME.
     Divide one spin (360) into 12 pieces 
     ==> 30 degrees = 1 timestep = 4 x 0.1521 = 0.6084 seconds of TIME.
-->
  <animation id="Cube_quaternion_Z">
    <source id="Cube_quaternion_Z-input">
      <float_array id="Cube_quaternion_Z-input-array" count=" 147">
     0.00  0.25  0.50  0.75  1.00  1.25  1.50  1.75  2.00  2.25  2.50  2.75  3.00  3.25  3.50  3.75
     4.00  4.25  4.50  4.75  5.00  5.25  5.50  5.75  6.00  6.25  6.50  6.75  7.00  7.25  7.50  7.75
     8.00  8.25  8.50  8.75  9.00  9.25  9.50  9.75 10.00 10.25 10.50 10.75 11.00 11.25 11.50 11.75
    12.00 12.25 12.50 12.75 13.00 13.25 13.50 13.75 14.00 14.25 14.50 14.75 15.00 15.25 15.50 15.75
    16.00 16.25 16.50 16.75 17.00 17.25 17.50 17.75 18.00 18.25 18.50 18.75 19.00 19.25 19.50 19.75
    20.00 20.25 20.50 20.75 21.00 21.25 21.50 21.75 22.00 22.25 22.50 22.75 23.00 23.25 23.50 23.75
    24.00 24.25 24.50 24.75 25.00 25.25 25.50 25.75 26.00 26.25 26.50 26.75 27.00 27.25 27.50 27.75
    28.00 28.25 28.50 28.75 29.00 29.25 29.50 29.75 30.00 30.25 30.50 30.75 31.00 31.25 31.50 31.75
    32.00 32.25 32.50 32.75 33.00 33.25 33.50 33.75 34.00 34.25 34.50 34.75 35.00 35.25 35.50 35.75
    36.00 36.25 36.50 
      </float_array>
      <technique_common>
          <accessor source="#Cube_quaternion_Z-input-array" count="   147" stride="1">
            <param name="TIME" type="float"/>
          </accessor>
      </technique_common>
    </source>
    <source id="Cube_quaternion_Z-output">
      <float_array id="Cube_quaternion_Z-output-array" count="2352">
   0.000  0.000 -1.00  0.00  -1.0000  0.0000  0.000  0.000   0.0000  1.0000  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.9239 -0.3827  0.000  0.000  -0.3827  0.9239  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.7071 -0.7071  0.000  0.000  -0.7071  0.7071  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.3827 -0.9239  0.000  0.000  -0.9239  0.3827  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.0000 -1.0000  0.000  0.000  -1.0000  0.0000  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.3827 -0.9239  0.000  0.000  -0.9239 -0.3827  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.7071 -0.7071  0.000  0.000  -0.7071 -0.7071  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.9239 -0.3827  0.000  0.000  -0.3827 -0.9239  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   1.0000  0.0000  0.000  0.000   0.0000 -1.0000  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.9239  0.3827  0.000  0.000   0.3827 -0.9239  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.7071  0.7071  0.000  0.000   0.7071 -0.7071  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.3827  0.9239  0.000  0.000   0.9239 -0.3827  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00   0.0000  1.0000  0.000  0.000   1.0000  0.0000  0.000  0.00   0.000  0.000  0.000  1.000
   0.000  0.000 -1.00  0.00  -0.3827  0.9239  0.000  0.000   0.9239  0.3827  0.000  0.00   0.000  0.000  0.000  1.000
   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
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<!-- HOURHAND (clockstop =    36.5047) -->
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      <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" -->
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            <translate>0.0 31.8 -8.5</translate>
            <rotate sid="rotationX">1 0 0 0</rotate>
            <rotate sid="rotationY">0 1 0 0</rotate>
            <rotate sid="rotationZ">0 0 1 0</rotate>
            <scale sid="scale">1.0 1.0 1.0</scale>
<!--  Number "8" ... has 8 + (4 x 22) = 96 lines -->
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                    <matrix>0.25 0 0 0.0  0 1 0 1.1  0 0 1 3.3  0 0 0 1.0</matrix>
                    <instance_node url="#LettersID3" />
                </node>
                <node id="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>
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            </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>
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            <scale sid="scale">1.00 1.00 1.00</scale>
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              <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>
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              <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>
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              <scale sid="scale">0.75 0.75 0.75</scale>
              <instance_node url="#HourID3" />
            </node>                                         <!-- /TWO -->
          </node>
<!-- END CLOCK   -->
          </node> <!-- End Inertial Grouping of Objects -->
        </visual_scene>
    </library_visual_scenes>
    <scene>
        <instance_visual_scene url="#ID1" />
    </scene>
</COLLADA>

Inside the Oculus Rift S Environment

The steps that were required in order for us to be able to import one of our COLLADA (.dae) models into the Oculus Rift S were few and deceptively simple. The Oculus system prefers to import files that are in a ".glb" format, which is the binary version of a glTF file. Hence, we looked for a community routine that could translate COLLADA into glTF (or glb).

  • We located the Khronos Group's "COLLADA to glTF" conversion tool under the group's name on GitHub.
  • We downloaded and installed version 2 of this 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
  • The COLLADA-to-glb conversion of both of our example COLLADA model files was accomplished as follows:  Inside the Mac's "Terminal" application, we changed directories until we were sitting in the above-specified Mac (Dropbox) directory. Then we typed …
    • ./COLLADA2GLTF-bin -i Inertial17.dae -b
    • ./COLLADA2GLTF-bin -i MultiLagrange18.dae -b

    which generated, respectively …

    • …/output/Inertial17.glb
    • …/output/MultiLagrange18.glb


Third Oculus Rift Selfie Second Oculus Rift Selfie
Third Oculus Rift Selfie

Two of our COLLADA-driven animated models can be identified in each of the three frames of this image montage: In all three cases, the one on the right is model Inertial17.dae and the one on the left is model MultiLagrange18.dae. 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.

See Also


Whitworth's (1981) Isothermal Free-Energy Surface

© 2014 - 2021 by Joel E. Tohline
|   H_Book Home   |   YouTube   |
Appendices: | Equations | Variables | References | Ramblings | Images | myphys.lsu | ADS |
Recommended citation:   Tohline, Joel E. (2021), The Structure, Stability, & Dynamics of Self-Gravitating Fluids, a (MediaWiki-based) Vistrails.org publication, https://www.vistrails.org/index.php/User:Tohline/citation

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