TikZ figure showing collision points on a single ellipsoid

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created: 2022-07-08 13:55:07
modified: 2022-07-08 14:20:53

In TikZ we can draw ellipsoids, like shown in here. Using this and a short JavaScript program, we can place a large amount of red dots on an ellipsoid to illustrate the collision points collectively.

The LaTeX source code for this figure is:

\begin{tikzpicture}
    \def \rotatangle {90}
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    \shade[rotate=\rotatangle,ball color = blue!90, opacity = 0.4] (0,0) ellipse (2 cm and 1 cm);
    \draw[rotate=\rotatangle,black] (0,0) ellipse (2 cm and 1 cm);
    \draw[rotate=\rotatangle,black,dashed] (-2,0) arc (180:360:2 and 0.45);
    \draw[rotate=\rotatangle-90,black,dashed] (1,0) arc (0:180:1 and 0.3);
    \node at (0,0) {\Cross};

    % this is where the putput of the JavaScript program goes
    \node at (0.23056130599988545,1.4432262851413828) [circle,fill=red,inner sep=0.7pt]{};\node at (0.9614647186573674,-0.14159292517943373) [circle,fill=red!65,inner sep=0.6pt]{};
    % ..... many more nodes here
    \node at (-0.6803843426552629,0.9240404061286351) [circle,fill=red!65,inner sep=0.6pt]{};\node at (-0.788481335628056,-0.04170110654372987) [circle,fill=red,inner sep=0.7pt]{};\node at (-0.11942406039602257,1.870007025781883) [circle,fill=red,inner sep=0.7pt]{};
    % it ends here

    \draw[rotate=\rotatangle,black] (2,0) arc (0:180:2 and 0.45);
    \draw[rotate=\rotatangle-90,black] (-1,0) arc (180:360:1 and 0.3);
\end{tikzpicture}

And the source code for the JavaScript program:

let str = "";
for (let i = 0; i < 300; i++) {
    let r1 = Math.random();
    let r2 = Math.random();
    let x = Math.sqrt(r1) * Math.cos(2 * 3.14159265 * r2) * 1;
    let y = Math.sqrt(r1) * Math.sin(2 * 3.14159265 * r2) * 2;
    let color = "red";
    let size = "0.7";
    let r3 = Math.random();
    if (r3 > 0.5) {
        color = "red!80";
        size = "0.65";
    }
    if (r3 > 0.7) {
        color = "red!65";
        size = "0.6";
    }
    str += (`\\node at (<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.439ex;" xmlns="http://www.w3.org/2000/svg" width="1.923ex" height="1.439ex" role="img" focusable="false" viewBox="0 -442 850 636" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-5583-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-5583-TEX-N-2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD"><g data-mml-node="mi"><use data-c="1D465" xlink:href="#MJX-5583-TEX-I-1D465"></use></g></g><g data-mml-node="mo" transform="translate(572,0)"><use data-c="2C" xlink:href="#MJX-5583-TEX-N-2C"></use></g></g></g></svg></mjx-container>{y}) [circle,fill=<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.439ex;" xmlns="http://www.w3.org/2000/svg" width="17.087ex" height="2.009ex" role="img" focusable="false" viewBox="0 -694 7552.4 888" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-5584-TEX-I-1D450" d="M34 159Q34 268 120 355T306 442Q362 442 394 418T427 355Q427 326 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