# COLLADA-based Models of Riemann S-Type Ellipsoids

(Initially posted January 2021)

## Instructions

Table 1 provides links to a variety of COLLADA-based animated 3D models that have been developed for use with the Oculus Rift S (virtual-reality) system; models with a .glb filetype (this is a binary filetype) can be imported directly into the Oculus Rift's home environment. Models with a .glb filetype also can be viewed using the 3D Viewer that usually is installed on Windows PCs. Models with a .dae filetype (this is an ascii filetype) can be viewed using the Preview app that is usually installed on a Mac desktop or laptop.

Each model depicts the structure and fluid-flow that is associated with a specific equilibrium Riemann S-Type ellipsoid, as labeled. In each animated scene, the wall-mounted clock cycle is calibrated by the characteristic frequency, ${\displaystyle [\pi G\rho ]^{1/2}}$; see also NOTE #4, below. For additional technical information about the structure of each model, see our accompanying discussion of "Example 3D Interactive Animations".

## Table of Accessible COLLADA Models

 Table 1 Riemann S-type EllipsoidProperties Linked files are to be used as input to ... MacintoshPreview(ascii filetype .dae)Hold down option key to download;and make sure filetype remains .dae Microsoft PC3D ViewerorOculus Rift S(binary filetype .glb)right-click to download & save INERTIAL frame ROTATING frame INERTIAL frame ROTATING frame b/a = 0.28 c/a = 0.256 DIRECT b28c256DirInertial.dae b28c256DirRotating.dae b28c256DirInertial.glb b28c256DirRotating.glb ADJOINT n/a n/a n/a n/a b/a = 0.41 c/a = 0.385 DIRECT b41c385DirInertial.dae b41c385DirRotating.dae b41c385DirInertial.glb b41c385DirRotating.glb ADJOINT b41c385AdjInertial.dae b41c385AdjRotating.dae n/a n/a b/a = 0.90 c/a = 0.333 DIRECT b90c333DirInertial.dae b90c333DirRotating.dae b90c333DirInertial.glb b90c333DirRotating.glb ADJOINT b90c333AdjInertial.dae b90c333AdjRotating.dae n/a n/a b/a = 0.74 c/a = 0.692 DIRECT b74c692DirInertial.dae b74c692DirRotating.dae b74c692DirInertial.glb b74c692DirRotating.glb ADJOINT b74c692AdjInertial.dae b74c692AdjRotating.dae n/a n/a

## Notes

1. The XML-based COLLADA language/instruction-set has been used to generate each animated 3D scene; in each case, the raw set of instructions was written from scratch and can be viewed by opening the relevant ".dae" (ascii filetype) file in a plain-text editor.
2. The steps that have been followed (on our Mac Desktop) in order to convert each ".dae" (ascii) filetype to a ".glb" (binary) filetype are enumerated in an accompanying discussion.
3. To control the 3D/animated scene:
1. When the Mac Preview application is used to view a 3D configuration, the displayed configuration is, by default, static. The play/pause button becomes visible if the cursor is simply placed near the bottom of the Preview's display window; the animation will start (on a continuous loop) when the play button is clicked.
2. To view the 3D model from different angles, place the mouse cursor anywhere near the center of the viewing window, then click and drag the cursor in different directions.
3. Resize the image by (on the Mac) holding down the "shift" key while sliding your finger up/down on the mouse (without clicking); or (on the PC) by simply sliding your finger up/down on the mouse (without clicking)
4. Three different characteristic times are incorporated with quantitative accuracy within each animated 3D scene: the wall-mounted clock cycle, the spin frequency of the ellipsoidal figure, and the orbital frequency of Lagrangian fluid elements as viewed from the rotating frame of reference. These times are explained in an accompanying discussion. (The example values used in this referenced discussion come from the "b41c385" model.)