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f79a90e0d9
...
1ec7955861
12
gui.js
12
gui.js
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@ -2,8 +2,8 @@ import { GUI } from 'lil-gui';
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const DEFAULTS = {
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thickness: 0.5,
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nodesize: 1.5,
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thickness: 1.0,
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nodesize: 2.0,
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linkopacity: 0.5,
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link2opacity: 0.5,
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shape: '120-cell',
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@ -13,10 +13,10 @@ const DEFAULTS = {
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inscribe_all: false,
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color: 0x3293a9,
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background: 0xd4d4d4,
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hyperplane: 0.93,
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hyperplane: 1.5,
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zoom: 1,
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xRotate: 'YW',
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yRotate: 'XW',
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yRotate: 'XZ',
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dtheta: 0,
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dpsi: 0,
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}
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@ -65,9 +65,9 @@ class FourDGUI {
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options_ctrl = this.gui.add(this.params, 'option').options(options).onChange((option) => {
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setVisibility(option)
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});
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this.gui.add(this.params, 'hyperplane', 0.5, 1 / 0.8);
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this.gui.add(this.params, 'hyperplane', 1.4, 2.0);
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this.gui.add(this.params, 'zoom', 0.1, 2.0);
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this.gui.add(this.params, 'thickness', 0, 1);
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this.gui.add(this.params, 'thickness', 0, 2);
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this.gui.add(this.params, 'linkopacity', 0, 1).onChange(
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(v) => setLinkOpacity(v, true)
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);
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6
main.js
6
main.js
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@ -9,7 +9,7 @@ import { FourDShape } from './fourDShape.js';
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import { get_colours } from './colours.js';
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const FACE_OPACITY = 0.3;
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const CAMERA_K = 5;
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const CAMERA_K = 10;
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// scene, lights and camera
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@ -213,8 +213,8 @@ function animate() {
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rotfn[gui.params.xRotate](theta),
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rotfn[gui.params.yRotate](psi)
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];
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shape.hyperplane = 1 / gui.params.hyperplane;
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camera.position.set(0, 0, gui.params.zoom * CAMERA_K * gui.params.hyperplane);
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shape.hyperplane = gui.params.hyperplane;
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camera.position.set(0, 0, gui.params.zoom * CAMERA_K / gui.params.hyperplane);
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shape.link_scale = gui.params.thickness;
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shape.node_scale = gui.params.nodesize;
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174
polytopes.js
174
polytopes.js
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@ -58,15 +58,16 @@ export function auto_detect_edges(nodes, neighbours, debug=false) {
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// too small and simple to calculate
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export const cell5 = () => {
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const c1 = Math.sqrt(5) / 4;
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const r5 = Math.sqrt(5);
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const r2 = Math.sqrt(2) / 2;
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return {
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name: '5-cell',
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nodes: [
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{id:1, label: 1, x: c1, y: c1, z: c1, w: -0.25 },
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{id:2, label: 2, x: c1, y: -c1, z: -c1, w: -0.25 },
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{id:3, label: 3, x: -c1, y: c1, z: -c1, w: -0.25 },
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{id:4, label: 4, x: -c1, y: -c1, z: c1, w: -0.25 },
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{id:5, label: 5, x: 0, y: 0, z: 0, w: 1 },
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{id:1, label: 1, x: r2, y: r2, z: r2, w: -r2 / r5 },
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{id:2, label: 2, x: r2, y: -r2, z: -r2, w: -r2 / r5 },
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{id:3, label: 3, x: -r2, y: r2, z: -r2, w: -r2 / r5 },
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{id:4, label: 4, x: -r2, y: -r2, z: r2, w: -r2 / r5 },
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{id:5, label: 5, x: 0, y: 0, z: 0, w: 4 * r2 / r5 },
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],
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links: [
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{ id:1, source:1, target: 2},
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@ -108,7 +109,7 @@ export const cell16 = () => {
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nodes[1].label = 4;
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index_nodes(nodes);
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scale_nodes(nodes, 0.5);
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scale_nodes(nodes, 0.75);
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const links = auto_detect_edges(nodes, 6);
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return {
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@ -141,7 +142,7 @@ export const tesseract = () => {
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}
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}
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scale_nodes(nodes, 0.5);
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scale_nodes(nodes, Math.sqrt(2) / 2);
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const links = auto_detect_edges(nodes, 4);
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links.map((l) => { l.label = 0 });
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@ -197,7 +198,6 @@ export const cell24 = () => {
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n.label = CELL24_INDEXING[axes[0]][axes[1]];
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}
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scale_nodes(nodes, Math.sqrt(2) / 2);
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index_nodes(nodes);
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const links = auto_detect_edges(nodes, 8);
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links.map((l) => l.label = 0);
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@ -338,7 +338,7 @@ export function make_120cell_vertices() {
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PERMUTE.coordinates([2, 1, phi, phiinv], 0, true),
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].flat();
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index_nodes(nodes);
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scale_nodes(nodes, 0.25 * Math.sqrt(2));
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scale_nodes(nodes, 0.5);
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return nodes;
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}
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@ -540,7 +540,7 @@ export function make_600cell_vertices() {
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index_nodes(nodes);
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scale_nodes(nodes, 0.5);
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scale_nodes(nodes, 0.75);
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return nodes;
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}
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@ -715,7 +715,6 @@ function make_dodecahedron_vertices() {
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{ x: -phi, y: phiinv, z:0, w: 0 , label: 4},
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{ x: -phi, y: -phiinv, z:0, w: 0 , label: 2},
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];
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scale_nodes(nodes, 1 / Math.sqrt(3));
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index_nodes(nodes);
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return nodes;
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}
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@ -755,155 +754,8 @@ export const dodecahedron = () => {
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}
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export const tetrahedron = () => {
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const r2 = Math.sqrt(2);
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const r3 = Math.sqrt(3);
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return {
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name: 'Tetrahedron',
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nodes: [
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{id:1, label: 1, x: 2 * r2 / 3, y: 0, z: -1/3, w: 0 },
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{id:2, label: 2, x: -r2 / 3, y: r2 / r3, z: -1/3, w: 0 },
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{id:3, label: 3, x: -r2 / 3, y: -r2 / r3, z: -1/3, w: 0 },
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{id:4, label: 4, x: 0, y: 0, z: 1, w: 0 },
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],
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links: [
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{ id:1, source:1, target: 2},
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{ id:2, source:1, target: 3},
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{ id:3, source:1, target: 4},
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{ id:4, source:2, target: 3},
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{ id:5, source:2, target: 4},
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{ id:6, source:3, target: 4},
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],
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geometry: {
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node_size: 0.02,
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link_size: 0.02
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},
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options: [ { name: '--' }],
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description: `The simplest three-dimensional polytope, consisting of four triangles joined at six edges. The 5-cell is its four-dimensional analogue.`,
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};
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};
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export const octahedron = () => {
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const nodes = [
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{id: 1, label: 1, x: 1, y: 0, z: 0, w: 0},
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{id: 2, label: 1, x: -1, y: 0, z: 0, w: 0},
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{id: 3, label: 2, x: 0, y: 1, z: 0, w: 0},
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{id: 4, label: 2, x: 0, y: -1, z: 0, w: 0},
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{id: 5, label: 3, x: 0, y: 0, z: 1, w: 0},
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{id: 6, label: 3, x: 0, y: 0, z: -1, w: 0},
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];
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const links = [
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{id:1, source: 1, target: 3},
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{id:2, source: 1, target: 4},
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{id:3, source: 1, target: 5},
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{id:4, source: 1, target: 6},
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{id:5, source: 2, target: 3},
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{id:6, source: 2, target: 4},
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{id:7, source: 2, target: 5},
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{id:8, source: 2, target: 6},
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{id:9, source: 3, target: 5},
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{id:10, source: 3, target: 6},
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{id:11, source: 4, target: 5},
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{id:12, source: 4, target: 6},
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]
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links.map((l) => { l.label = 0 });
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return {
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name: 'Octahedron',
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nodes: nodes,
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links: links,
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geometry: {
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node_size: 0.02,
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link_size: 0.02
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},
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options: [ { name: '--' }],
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description: `The three-dimensional cross-polytope, the 16-cell is its four-dimensional analogue.`,
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};
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}
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export const cube = () => {
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const nodes = [
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{id: 1, label: 1, x: 1, y: 1, z: 1, w: 0},
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{id: 2, label: 2, x: -1, y: 1, z: 1, w: 0},
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{id: 3, label: 2, x: 1, y: -1, z: 1, w: 0},
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{id: 4, label: 1, x: -1, y: -1, z: 1, w: 0},
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{id: 5, label: 2, x: 1, y: 1, z: -1, w: 0},
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{id: 6, label: 1, x: -1, y: 1, z: -1, w: 0},
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{id: 7, label: 1, x: 1, y: -1, z: -1, w: 0},
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{id: 8, label: 2, x: -1, y: -1, z: -1, w: 0},
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];
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scale_nodes(nodes, 1/Math.sqrt(3));
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const links = auto_detect_edges(nodes, 3);
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links.map((l) => { l.label = 0 });
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return {
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name: 'Cube',
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nodes: nodes,
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links: links,
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geometry: {
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node_size: 0.02,
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link_size: 0.02
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},
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options: [ { name: '--' }],
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description: `The three-dimensional measure polytope, the tesseract is its four-dimensional analogue.`,
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};
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}
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function make_icosahedron_vertices() {
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const phi = 0.5 * (1 + Math.sqrt(5));
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const nodes = [
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{ x: 0, y: 1, z: phi, w: 0, label: 1 },
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{ x: 0, y: -1, z: phi, w: 0, label: 1 },
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{ x: 0, y: 1, z: -phi, w: 0, label: 1 },
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{ x: 0, y: -1, z: -phi, w: 0, label: 1 },
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{ x: 1, y: phi, z: 0, w: 0, label: 2 },
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{ x: -1, y: phi, z: 0, w: 0, label: 2 },
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{ x: 1, y: -phi, z: 0, w: 0, label: 2 },
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{ x: -1, y: -phi, z: 0, w: 0, label: 2 },
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{ x: phi, y: 0, z: 1, w: 0, label: 3},
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{ x: phi, y: 0, z: -1, w: 0, label: 3},
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{ x: -phi, y: 0, z: 1, w: 0, label: 3},
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{ x: -phi, y: 0, z: -1, w: 0, label: 3},
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];
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scale_nodes(nodes, 1/Math.sqrt((5 + Math.sqrt(5)) / 2));
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index_nodes(nodes);
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return nodes;
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}
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export const icosahedron = () => {
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const nodes = make_icosahedron_vertices();
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const links = auto_detect_edges(nodes, 5);
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links.map((l) => l.label = 0);
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return {
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name: 'Icosahedron',
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nodes: nodes,
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links: links,
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geometry: {
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node_size: 0.02,
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link_size: 0.02
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},
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options: [
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{ name: "--"},
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],
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description: `The icosahedron is a twenty-sided polyhedron and is dual to the dodecahedron. Its four-dimensional analogue is the 600-cell.`
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}
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}
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export const build_all = () => {
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return [
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tetrahedron(),
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octahedron(),
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cube(),
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icosahedron(),
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dodecahedron(),
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cell5(),
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cell16(),
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@ -916,7 +768,3 @@ export const build_all = () => {
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cell120_layered()
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];
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}
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export const radii = (shape) => {
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return shape.nodes.map(n => Math.sqrt(n.x * n.x + n.y * n.y + n.z * n.z + n.w * n.w))
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}
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