Engine prototype #13
@ -17,31 +17,25 @@
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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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<p><button onclick="flipPoint()">Flip point</button></p>
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<p><button onclick="flip()">Flip</button></p>
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<script>
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// in the default view, e4 + e5 is the point at infinity
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let CGA3 = Algebra(4, 1);
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let v = [
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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(() => 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 w = [
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CGA3.inline(() => 1e1 - Math.sqrt(0.2)*1e4 + Math.sqrt(1.2)*1e5)(),
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CGA3.inline(() => 1e2 - Math.sqrt(0.2)*1e4 + Math.sqrt(1.2)*1e5)(),
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CGA3.inline(() => 1e3 - Math.sqrt(0.2)*1e4 + Math.sqrt(1.2)*1e5)()
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];
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let s = CGA3.inline(() => -Math.sqrt(1.2)*1e4 + Math.sqrt(0.2)*1e5);
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// create scene function
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let scene = () => [
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0xff00b0, v[0],
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0x00ffb0, v[1],
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0x00b0ff, v[2],
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0x800040, w[0],
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0x008040, w[1],
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0x004080, w[2],
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0xd0e0f0, s
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0x8040ff, v[3],
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0xc0c0c0, v[4]
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];
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// initialize graph
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@ -53,8 +47,16 @@
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)
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document.body.appendChild(gr);
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function flipPoint() {
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v[0] = CGA3.Dual(CGA3.Mul(s, v[0]));
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function flip() {
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for (let n = 0; n < 4; ++n) {
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// reflect
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v[n] = CGA3.Mul(CGA3.Mul(v[4], v[n]), v[4]);
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// de-noise
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for (let k = 6; k < v[n].length; ++k) {
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v[n][k] = 0;
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}
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}
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requestAnimationFrame(gr.update.bind(gr, scene));
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}
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</script>
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@ -26,33 +26,27 @@ canvas {
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"""
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controls = """
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<p><button id="flip-button">Flip point</button></p>
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<p><button id="flip-button">Flip</button></p>
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"""
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graph_script = """
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// in the default view, e4 + e5 is the point at infinity
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let CGA3 = Algebra(4, 1);
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let v = [
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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(() => 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 w = [
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CGA3.inline(() => 1e1 - Math.sqrt(0.2)*1e4 + Math.sqrt(1.2)*1e5)(),
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CGA3.inline(() => 1e2 - Math.sqrt(0.2)*1e4 + Math.sqrt(1.2)*1e5)(),
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CGA3.inline(() => 1e3 - Math.sqrt(0.2)*1e4 + Math.sqrt(1.2)*1e5)()
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];
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let s = CGA3.inline(() => -Math.sqrt(1.2)*1e4 + Math.sqrt(0.2)*1e5);
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// create scene function
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let scene = () => [
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0xff00b0, v[0],
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0x00ffb0, v[1],
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0x00b0ff, v[2],
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0x800040, w[0],
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0x008040, w[1],
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0x004080, w[2],
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0xd0e0f0, s
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0x8040ff, v[3],
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0xc0c0c0, v[4]
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];
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// initialize graph
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@ -65,11 +59,19 @@ let gr = CGA3.graph(
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document.body.appendChild(gr);
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// connect flip button
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function flipPoint() {
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v[0] = CGA3.Dual(CGA3.Mul(s, v[0]));
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function flip() {
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for (let n = 0; n < 4; ++n) {
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// reflect
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v[n] = CGA3.Mul(CGA3.Mul(v[4], v[n]), v[4]);
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// de-noise
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for (let k = 6; k < v[n].length; ++k) {
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v[n][k] = 0;
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}
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}
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requestAnimationFrame(gr.update.bind(gr, scene));
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}
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document.querySelector('#flip-button').addEventListener('click', flipPoint);
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document.querySelector('#flip-button').addEventListener('click', flip);
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"""
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# === page construction ===
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Loading…
Reference in New Issue
Block a user