Editing Appendix/Ramblings/RiemannB28C256

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=Another S-type Example b28c256=

This chapter is an extension of the chapter we have titled, "[[ThreeDimensionalConfigurations/MeetsCOLLADAandOculusRiftS|Riemann Meets COLLADA &amp; Oculus Rift S]]."  In that chapter we used as our first example of a Riemann S-type ellipsoid the model with parameters, <b>(b/a, c/a) = (0.41, 0.385)</b>.  Here we construct a model with parameters, <b>(b/a, c/a) = (0.28, 0.256)</b>.  Other closely related chapters are listed below under the heading, "[[#See_Also|See Also]]".

==Key Physical Parameters==

The model that we have chosen to use in our second successful construction of a COLLADA-based, 3D and interactive animation has the following properties; this model has been selected from [[ThreeDimensionalConfigurations/RiemannStype#Table2|Table 2 of our accompanying discussion of Riemann S-type ellipsoids]]:

<table border="0" cellpadding="5" align="center">

<tr>
  <td align="center" rowspan="6">
<b>Figure 1a</b><br />&nbsp;<br />
[[File:B28c256EFEdiagram02.png|325px|EFE Parameter Space]]
  </td>
  <td align="center" rowspan="6" width="2%">
&nbsp;
  </td>
  <td align="center" colspan="3">
<math>~\frac{b}{a} = 0.28</math>
  </td>
  <td align="center" rowspan="6" width="2%">
&nbsp;
  </td>
  <td align="center" rowspan="6" bgcolor="lightgrey">
<b>Figure 1b</b><br />
[[File:COLLADAb28c256OldModel.png|300px|EFE Model b28c256]]
  </td>
</tr>

<tr>
  <td align="center" colspan="3">
<math>~\frac{c}{a} = 0.256</math>
  </td>
</tr>

<tr>
  <td align="center">
''Direct''
  </td>
  <td align="center" width="2%" rowspan="4">
&nbsp;
  </td> 
  <td align="center">
''Adjoint''
  </td>
</tr>

<tr>
  <td align="center">
<math>~\Omega_\mathrm{EFE} =  0.456676</math>
  </td>
  <td align="center">
<math>~\Omega_\mathrm{EFE} = - 0.020692</math>
  </td>
</tr>

<tr>
  <td align="center">
<math>~\lambda_\mathrm{EFE} = 0.020692</math>
  </td>
  <td align="center">
<math>~\lambda_\mathrm{EFE} = - 0.456676</math>
  </td>
</tr>

<tr>
  <td align="center">
<math>~f = - 0.174510</math>
  </td>
  <td align="center">
<math>~f = - 85.0007</math>
  </td>
</tr>
</table>

The subscript "EFE" on &Omega; and &lambda; means that the relevant frequency is given in units that have been adopted in [<b>[[Appendix/References#EFE|<font color="red">EFE</font>]]</b>], that is, in units of <math>~[\pi G\rho]^{1 / 2}</math>.  In Figure 1a, the yellow circular marker, that has been placed where the pair of purple dashed lines cross, identifies the location of this model in the "c/a versus b/a" ''[[ThreeDimensionalConfigurations/RiemannStype#Fig2|EFE Diagram]]'' that appears as Figure 2 on p. 902 of [http://adsabs.harvard.edu/abs/1965ApJ...142..890C S. Chandrasekhar (1965)]; essentially the same diagram appears in &sect;49 (p. 147) of [<b>[[Appendix/References#EFE|<font color="red">EFE</font>]]</b>].

==Coding Steps==
===Part A===

Here we begin with a working model of [[Appendix/Ramblings/RiemannB90C333#Another_S-type_Example_b90c333|b90c333]] and use incremental changes in the COLLADA-based code to construct a working model of b28c256.

<ul>
  <li>This pair of starting models has been copied from the successful modeling of Riemann S-type ellipsoids that have (b/a, c/a) = (0.90, 0.333)</li>
  <ul>
  <li>Inertial Frame:  <font color="lightgreen">[KEEP]</font> FastInertial80.dae [04 June 2020]</li>
  <li>Rotating Frame:  <font color="lightgreen">[KEEP]</font> FastRot79.dae [04 June 2020]</li>
  </ul>
  <li><font color="darkgreen"><b>Pencil90.dae</b></font>
<br />Identical to <b>FastRot79.dae</b> except wall-mounted labeling has been changed to reflect new values of b/a and c/a.  <font color="red">This works in both visualization venues</font>.
  </li>
  <li><font color="darkgreen"><b>Pencil91.dae</b></font>
<br />Inserted correct surface geometry of this rapidly rotating Riemann ellipsoid.    <font color="red">This works in both visualization venues</font>.
  </li>
  <li><font color="darkgreen"><b>Pencil92.dae</b></font>
<br />Inserted the correct ''animated'' depiction of the 9 Lagrangian fluid elements.
  </li>
  <li><font color="darkgreen"><b>Pencil93.dae</b></font>
<br />Placed 51 yellow, equatorial-plane markers.    <font color="red">This works in both visualization venues</font>
  </li>
  <li><font color="darkgreen"><b>Pencil94.dae</b></font>
<br />Finished specifying correct behavior of clock, which gives the final, fully functional model.    <font color="red">This works in both visualization venues</font>
  </li>
  <li><font color="darkgreen"><b>PencilInertial95.dae</b></font>
<br />Flipped from rotating- to inertial-frame of reference.    <font color="red">This works in both visualization venues</font>
  </li>
  <li><font color="darkgreen"><b>PencilInertial96.dae</b></font>
<br />Enlarged red "Lagrange01" marker from 0.03 to 0.075; and changed transparency of ellipsoid surface to (totally opaque) 1.0.    <font color="red">This works in both visualization venues</font>
  </li>
</ul>


===Best b28c256 Models===

The example models created for display in the Oculus Rift S are the following:
<ol>
  <li>Inertial Frame:   <font color="lightgreen">[KEEP]</font> PencilInertial96.dae [04 June 2020]  </li>
  <li>Rotating Frame:   <font color="lightgreen">[KEEP]</font> Pencil94.dae [04 June 2020] </li>
</ol>

==COLLADA Model Files==

===''Direct'' Configurations===


<div align="center" id="Scroll1">
<b>b28c256DI.dae</b> [''Direct'' Inertial Frame]&nbsp; &nbsp; &hellip; &nbsp; &nbsp; a COLLADA code containing nnnn lines of <xml>-formatted ASCII text
<br />Original filename used above: xxx.dae
</div>

<div style="height: 250px; width: 100%; overflow: scroll;">
<pre>
<?xml version="1.0" encoding="UTF-8" standalone="no" ?>
</pre>
</div>


<div align="center" id="Scroll2">
<b>b28c256DRot.dae</b> [''Direct'' Rotating Frame]&nbsp; &nbsp; &hellip; &nbsp; &nbsp; a COLLADA code containing nnnn lines of <xml>-formatted ASCII text
<br />Original filename used above: xxx.dae
</div>

<div style="height: 250px; width: 100%; overflow: scroll;">
<pre>
<?xml version="1.0" encoding="UTF-8" standalone="no" ?>
</pre>
</div>

=See Also=

* Discussion of [[ThreeDimensionalConfigurations/RiemannStype|Ou's Riemann-Like Ellipsoids]]

* [[ThreeDimensionalConfigurations/MeetsCOLLADAandOculusRiftS|Riemann Meets COLLADA &amp; Oculus Rift S]]: Example <b>(b/a, c/a) = (0.41, 0.385)</b>
** [[Appendix/Ramblings/VirtualReality#Virtual_Reality_and_3D_Printing|Virtual Reality and 3D Printing]]
** [[Appendix/Ramblings/OculusRiftS|Success Importing Animated Scene into Oculus Rift S]]
** [[Appendix/Ramblings/RiemannMeetsOculus|Carefully (Re)Build Riemann Type S Ellipsoids Inside Oculus Rift Environment]]
** Other Example S-type Riemann Ellipsoids:
*** <b>[[Appendix/Ramblings/RiemannB90C333|(b/a, c/a) = (0.90, 0.333)]]</b>
*** <b>[[Appendix/Ramblings/RiemannB74C692|(b/a, c/a) = (0.74, 0.692)]]</b>
*** <b>[[Appendix/Ramblings/RiemannB28C256|(b/a, c/a) = (0.28, 0.256)]]</b>


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