User:Tohline/Appendix/Ramblings/RiemannMeetsOculus

Rebuild Riemann S-Type Ellipsoid Inside Oculus Rift S Environment

Preamble

In an accompanying discussion, we have illustrated how an animated, interactive 3D scene can be largely defined via the xml-formatted language named COLLADA. In the last major subsection of that discussion, we have outlined the steps that can be followed to specifically generate any of a variety of Riemann S-Type ellipsoids. These steps were identified within the context of our effort to construct 3D VR/AR models that could be faithfully rendered using the Mac's Preview app.

In a separate but closely connected discussion, we have demonstrated that most of our COLLADA-based models can be imported into the 3D virtual-reality environment of the Oculus Rift S. Toward the end of this separate discussion, we provide the full COLLADA code — in a plain text format — along with a summary description of a model that has been assigned the name, FullLast45X.dae.

Intially, we discovered that most of the Riemann S-Type ellipsoids that we developed while relying on the Mac's Preview app did not display properly within the Oculus Rift S environment. What we propose to do, here, is methodically re-construct a variety of our earlier models that were viewable in the "Preview" app in such a way that they are all viewable with the Oculus Rift S. We begin with this "… 45X" model — renaming it, RiemannBuild00.dae. Step by step we will insert components of one of our previously constructed COLLADA-based models of an S-Type Riemann ellipsoid into a <visual_scene> that can be properly executed within the Oculus Rift S.

Assemble Components

• RiemannBuild00.dae:
  • This model, with <up_axis>Z_UP></up_axis>, contains a set of purple cubes that lie in the Y₀-Z₀ plane, and along the inertial frame's X₀ axis from -5.0 inches to +5.0 inches; the last purple "cube" (at X₀ = +5) is actually a rectangular box whose longest axis is parallel to the Z₀ axis.
  • The scene also includes a red ellipsoid with axis ratios b/a = 0.41 and c/a = 0.385. The "EntireEllipsoid" has been scaled such that its longest ( c ) axis has a length of 4 inches; and it has been translated in the Y₀-Z₀ plane to a location along the Y₀ axis where the center of the ellipsoid is 8.0 inches from the origin of the inertial coordinate system. The ellipsoid's "First" quadrant node was, in addition, scaled by (1.1, 1.1, 1.1) in order for it to stick out a bit from the other quadrants to help the viewer decipher its rotational behavior.
  • The default orientation of the "EntireEllipsoid" is <math>~(a, b, c) \Leftrightarrow ~ (X_0, Y_0, Z_0)</math>. But for this model, before the animation starts, the "EntireEllipsoid" is reoriented by turning it 90° in Y, then 90° in Z, then 90° in X; this resulted in an alignment of <math>~(a, b, c) \Leftrightarrow ~ (Y_0, X_0, -Z_0)</math>.

              <node id="EntireEllipsoid" name="OculusRift_EFE">
                 <translate>0.0 8.0 0.0</translate>
                 <rotate sid="rotationY">0.0 1.0 0.0  90.0</rotate>
                 <rotate sid="rotationZ">0.0 0.0 1.0  90.0</rotate>
                 <rotate sid="rotationX">1.0 0.0 0.0  90.0</rotate>
                 <scale sid="scale">4.0 4.0 4.0</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">1.1 1.1 1.1</scale>
                      <instance_node url="#ID3_EFE" />
                    </node>
                    ...
    

See Also

• Tohline, J. E., (2008) Computing in Science & Engineering, vol. 10, no. 4, pp. 84-85 — Where is My Digital Holographic Display? [ PDF ]

© 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