2024-06-25 02:37:57 +00:00
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<!DOCTYPE html>
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<html>
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<head>
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<style>
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body {
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background-color: #ffe0f0;
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}
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/* needed to keep Ganja canvas from blowing up */
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canvas {
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min-width: 600px;
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max-width: 600px;
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min-height: 600px;
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max-height: 600px;
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}
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</style>
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<script src="https://unpkg.com/ganja.js"></script>
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</head>
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<body>
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2024-06-25 20:40:40 +00:00
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<p><button onclick="flip()">Flip</button></p>
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2024-06-25 02:37:57 +00:00
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<script>
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2024-06-25 08:54:01 +00:00
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// in the default view, e4 + e5 is the point at infinity
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2024-06-25 09:07:39 +00:00
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let CGA3 = Algebra(4, 1);
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2024-06-26 00:57:16 +00:00
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let elements = [
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2024-06-25 20:40:40 +00:00
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CGA3.inline(() => Math.sqrt(0.5)*( 1e1 + 1e2 + 1e3 + 1e5))(),
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CGA3.inline(() => Math.sqrt(0.5)*( 1e1 - 1e2 - 1e3 + 1e5))(),
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CGA3.inline(() => Math.sqrt(0.5)*(-1e1 + 1e2 - 1e3 + 1e5))(),
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CGA3.inline(() => Math.sqrt(0.5)*(-1e1 - 1e2 + 1e3 + 1e5))(),
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CGA3.inline(() => -Math.sqrt(3)*1e4 + Math.sqrt(2)*1e5)()
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2024-06-25 10:11:50 +00:00
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];
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2024-06-28 04:45:41 +00:00
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/*
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these blocks of commented-out code can be used to confirm that a spacelike
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vector and its Hodge dual represent the same generalized sphere
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*/
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/*let elements = [
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CGA3.inline(() => Math.sqrt(0.5)*!( 1e1 + 1e2 + 1e3 + 1e5))(),
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CGA3.inline(() => Math.sqrt(0.5)*!( 1e1 - 1e2 - 1e3 + 1e5))(),
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CGA3.inline(() => Math.sqrt(0.5)*!(-1e1 + 1e2 - 1e3 + 1e5))(),
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CGA3.inline(() => Math.sqrt(0.5)*!(-1e1 - 1e2 + 1e3 + 1e5))(),
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CGA3.inline(() => !(-Math.sqrt(3)*1e4 + Math.sqrt(2)*1e5))()
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];*/
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/*let elements = [
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CGA3.inline(() => 1e1 + 1e5)(),
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CGA3.inline(() => 1e2 + 1e5)(),
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CGA3.inline(() => 1e3 + 1e5)(),
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CGA3.inline(() => -1e4 + 1e5)(),
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CGA3.inline(() => Math.sqrt(0.5)*(1e1 + 1e2 + 1e3 + 1e5))(),
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CGA3.inline(() => Math.sqrt(0.5)*!(1e1 + 1e2 + 1e3 - 0.01e4 + 1e5))()
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];*/
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2024-06-26 00:57:16 +00:00
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// set up palette
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var colorIndex;
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var palette = [0xff00b0, 0x00ffb0, 0x00b0ff, 0x8040ff, 0xc0c0c0];
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function nextColor() {
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colorIndex = (colorIndex + 1) % palette.length;
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return palette[colorIndex];
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}
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function resetColorCycle() {
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colorIndex = palette.length - 1;
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}
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resetColorCycle();
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2024-06-25 10:11:50 +00:00
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// create scene function
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2024-06-26 00:57:16 +00:00
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function scene() {
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commands = [];
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resetColorCycle();
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elements.forEach((elt) => commands.push(nextColor(), elt));
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return commands;
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}
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// initialize graph
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2024-06-26 00:57:16 +00:00
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let graph = CGA3.graph(
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scene,
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2024-06-25 08:54:01 +00:00
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{
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conformal: true, gl: true, grid: true
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}
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2024-06-25 10:11:50 +00:00
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)
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2024-06-26 00:57:16 +00:00
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document.body.appendChild(graph);
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2024-06-25 10:11:50 +00:00
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2024-06-25 20:40:40 +00:00
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function flip() {
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2024-06-26 00:57:16 +00:00
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let last = elements.length - 1;
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for (let n = 0; n < last; ++n) {
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2024-06-25 20:40:40 +00:00
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// reflect
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2024-06-26 00:57:16 +00:00
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elements[n] = CGA3.Mul(CGA3.Mul(elements[last], elements[n]), elements[last]);
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2024-06-25 20:40:40 +00:00
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// de-noise
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2024-06-26 00:57:16 +00:00
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for (let k = 6; k < elements[n].length; ++k) {
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2024-06-28 04:45:41 +00:00
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/*for (let k = 0; k < 26; ++k) {*/
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2024-06-26 00:57:16 +00:00
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elements[n][k] = 0;
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2024-06-25 20:40:40 +00:00
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}
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}
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2024-06-26 00:57:16 +00:00
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requestAnimationFrame(graph.update.bind(graph, scene));
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2024-06-25 10:11:50 +00:00
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}
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2024-06-25 02:37:57 +00:00
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</script>
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</body>
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</html>
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