Removed fancy colors, standardised polytope generation
Mike Lynch
parent
c0f59edac6
commit
f2c6ba9a1c
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@ -3,8 +3,8 @@ import * as THREE from 'three';
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const HYPERPLANE = 2;
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const NODE_SIZE = 0.02;
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const LINK_SIZE = 0.02;
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const NODE_SIZE = 0.01;
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const LINK_SIZE = 0.01;
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24
main.js
24
main.js
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@ -7,7 +7,7 @@ import { FourDShape } from './fourDShape.js';
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import { GUI } from 'lil-gui';
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const DEFAULT_SHAPE = '120-cell';
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const DEFAULT_SHAPE = '5-cell';
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// hacky stuff for 4d rotations
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@ -107,23 +107,10 @@ document.body.appendChild( renderer.domElement );
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const NODE_OPACITY = 1.0;
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const LINK_OPACITY = 0.7;
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// nodes. links
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// 0 R 0 (0-1) Y
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// 1 G 1 (1-2) C
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// 2 B 2 (0-2) M
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// duals
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// 0 C 0 (0-1) G
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// 1 Y 1 (1-2) R
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// 2 M 2 (0-2) B
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const LINK_OPACITY = 1.0;
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const node_ms = [
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new THREE.MeshStandardMaterial( { color: 0xc0c0ff } ),
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new THREE.MeshStandardMaterial( { color: 0x20dddd } ),
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new THREE.MeshStandardMaterial( { color: 0xdddd20 } ),
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new THREE.MeshStandardMaterial( { color: 0xdd20dd } ),
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new THREE.MeshStandardMaterial( { color: 0x90ebff } )
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];
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for( const node_m of node_ms ) {
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@ -136,10 +123,7 @@ for( const node_m of node_ms ) {
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}
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const link_ms = [
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new THREE.MeshStandardMaterial( { color: 0xc0c0ff } ),
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new THREE.MeshStandardMaterial( { color: 0x20dd20 } ),
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new THREE.MeshStandardMaterial( { color: 0xdd2020 } ),
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new THREE.MeshStandardMaterial( { color: 0x2020dd } ),
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new THREE.MeshStandardMaterial( { color: 0x90ebff } )
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];
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for( const link_m of link_ms ) {
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76
permute.js
76
permute.js
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@ -102,86 +102,14 @@ function expand_sign(a, label) {
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}
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export function coordinates(a, id0=1, even=false) {
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export function coordinates(a, label, even=false) {
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const ps = even ? permutations_even(a) : permutations(a);
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const coords = [];
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for( const p of ps ) {
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const expanded = expand_sign(p, 0);
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const expanded = expand_sign(p, label);
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coords.push(...expanded);
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}
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return coords;
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}
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function scale_and_index(nodes, scale) {
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let i = 1;
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for( const n of nodes ) {
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n["id"] = i;
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i++;
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for( const a of [ 'x', 'y', 'z', 'w' ] ) {
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n[a] = scale * n[a];
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}
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}
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return nodes;
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}
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function make_120cell_vertices() {
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const phi = 0.5 * (1 + Math.sqrt(5));
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const r5 = Math.sqrt(5);
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const phi2 = phi * phi;
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const phiinv = 1 / phi;
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const phi2inv = 1 / phi2;
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const nodes = [
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coordinates([2, 2, 0, 0], 0),
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coordinates([r5, 1, 1, 1], 1),
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coordinates([phi, phi, phi, phi2inv], 2),
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coordinates([phi, phiinv, phiinv, phiinv], 0),
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coordinates([phi2, phi2inv, 1, 0], 1, true),
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coordinates([r5, phiinv, phi, 0], 2, true),
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coordinates([2, 1, phi, phiinv], 0, true),
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].flat();
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return scale_and_index(nodes, 0.5);
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}
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function dist2(n1, n2) {
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return (n1.x - n2.x) ** 2 + (n1.y - n2.y) ** 2 + (n1.z - n2.z) ** 2 + (n1.w - n2.w) ** 2;
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}
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function make_120cell_edges(nodes) {
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const seen = {};
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const nnodes = nodes.length;
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const links = [];
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let id = 1;
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for( let i = 0; i < nnodes - 1; i++ ) {
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const d2 = [];
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for( let j = 0; j < nnodes; j++ ) {
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d2.push({ d2: dist2(nodes[i], nodes[j]), id: j });
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}
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d2.sort((a, b) => b.d2 - a.d2);
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const closest = d2.slice(1, 4);
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for( const e in closest ) {
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const ids = [ nodes[i].id, e.id ];
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ids.sort();
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const fp = ids.join(',');
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if( !seen[fp] ) {
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seen[fp] = true;
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links.push({ id: id, label: 0, source: nodes[i].id, target: e.id });
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id++;
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}
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}
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}
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return links;
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}
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const nodes = make_120cell_vertices();
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const links = make_120cell_edges(nodes);
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console.log(links);
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283
polytopes.js
283
polytopes.js
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@ -13,6 +13,37 @@ function scale_and_index(nodes, scale) {
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return nodes;
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}
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function dist2(n1, n2) {
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return (n1.x - n2.x) ** 2 + (n1.y - n2.y) ** 2 + (n1.z - n2.z) ** 2 + (n1.w - n2.w) ** 2;
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}
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function auto_detect_edges(nodes, neighbours) {
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const seen = {};
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const nnodes = nodes.length;
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const links = [];
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let id = 1;
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for( const n1 of nodes ) {
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const d2 = [];
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for( const n2 of nodes ) {
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d2.push({ d2: dist2(n1, n2), id: n2.id });
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}
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d2.sort((a, b) => a.d2 - b.d2);
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const closest = d2.slice(1, neighbours + 1);
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for( const e of closest ) {
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const ids = [ n1.id, e.id ];
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ids.sort();
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const fp = ids.join(',');
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if( !seen[fp] ) {
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seen[fp] = true;
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links.push({ id: id, label: 0, source: n1.id, target: e.id });
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id++;
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}
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}
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}
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return links;
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}
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// too small and simple to calculate
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export const cell5 = () => {
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const r5 = Math.sqrt(5);
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@ -42,200 +73,24 @@ export const cell5 = () => {
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export const cell16 = () => {
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const s2 = Math.sqrt(2) * 0.5;
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let nodes = PERMUTE.coordinates([1, 1, 1, 1], 0);
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nodes = nodes.filter((n) => n.x * n.y * n.z * n.w > 0);
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scale_and_index(nodes, 0.75);
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console.log('cell16 auto_detect_edges');
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console.log(nodes);
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const links = auto_detect_edges(nodes, 8);
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return {
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nodes: [
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{ id: 1, x: -s2, y: -s2, z: -s2, w: -s2 },
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{ id: 2, x: s2, y: s2, z: -s2, w: -s2 },
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{ id: 3, x: s2, y: -s2, z: s2, w: -s2 },
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{ id: 4, x: -s2, y: s2, z: s2, w: -s2 },
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{ id: 5, x: s2, y: -s2, z: -s2, w: s2 },
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{ id: 6, x: -s2, y: s2, z: -s2, w: s2 },
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{ id: 7, x: -s2, y: -s2, z: s2, w: s2 },
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{ id: 8, x: s2, y: s2, z: s2, w: s2 },
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],
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// opposite pairs: 1 - 8
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// 2 - 7
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// 3 - 6
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// 4 - 5 .. these don't have edges
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// label 1 links: 1 / 3 / 8 / 6
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// label 1 links: 2 / 4 / 7 / 5
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// label 2 links: 1 / 4 / 8 / 5
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// label 2 links: 2 / 3 / 7 / 6 (??)
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links: [
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{ id: 1, source: 1, target: 2, label: 1 },
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{ id: 2, source: 1, target: 3, label: 2 },
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{ id: 3, source: 1, target: 4, label: 3 },
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{ id: 4, source: 2, target: 3, label: 3 },
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{ id: 5, source: 2, target: 4, label: 2 },
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{ id: 6, source: 3, target: 4, label: 1 },
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{ id: 7, source: 5, target: 6, label: 1 },
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{ id: 8, source: 5, target: 7, label: 2 },
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{ id: 9, source: 5, target: 8, label: 3 },
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{ id: 10, source: 6, target: 7, label: 3 },
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{ id: 11, source: 6, target: 8, label: 2 },
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{ id: 12, source: 7, target: 8, label: 1 },
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{ id: 13, source: 1, target: 5, label: 3 },
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{ id: 14, source: 1, target: 6, label: 2 },
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{ id: 15, source: 1, target: 7, label: 1 },
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{ id: 16, source: 2, target: 5, label: 2 },
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{ id: 17, source: 2, target: 6, label: 3 },
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{ id: 18, source: 2, target: 8, label: 1 },
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{ id: 19, source: 3, target: 5, label: 1 },
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{ id: 20, source: 3, target: 7, label: 3 },
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{ id: 21, source: 3, target: 8, label: 2 },
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{ id: 22, source: 4, target: 6, label: 1 },
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{ id: 23, source: 4, target: 7, label: 2 },
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{ id: 24, source: 4, target: 8, label: 3 },
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]
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}
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nodes: nodes,
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links: links
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};
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};
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export const tesseract = () => {
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const s2 = Math.sqrt(2) * 0.5;
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return {
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nodes: [
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{ id: 1, label: 1, x: -s2, y: -s2, z: -s2, w: -s2 },
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{ id: 2, label: 2, x: s2, y: -s2, z: -s2, w: -s2 },
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{ id: 3, label: 2, x: -s2, y: s2, z: -s2, w: -s2 },
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{ id: 4, label: 1, x: s2, y: s2, z: -s2, w: -s2 },
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{ id: 5, label: 2, x: -s2, y: -s2, z: s2, w: -s2 },
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{ id: 6, label: 1, x: s2, y: -s2, z: s2, w: -s2 },
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{ id: 7, label: 1, x: -s2, y: s2, z: s2, w: -s2 },
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{ id: 8, label: 2, x: s2, y: s2, z: s2, w: -s2 },
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{ id: 9, label: 2, x: -s2, y: -s2, z: -s2, w: s2 },
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{ id: 10, label: 1, x: s2, y: -s2, z: -s2, w: s2 },
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{ id: 11, label: 1, x: -s2, y: s2, z: -s2, w: s2 },
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{ id: 12, label: 2, x: s2, y: s2, z: -s2, w: s2 },
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{ id: 13, label: 1, x: -s2, y: -s2, z: s2, w: s2 },
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{ id: 14, label: 2, x: s2, y: -s2, z: s2, w: s2 },
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{ id: 15, label: 2, x: -s2, y: s2, z: s2, w: s2 },
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{ id: 16, label: 1, x: s2, y: s2, z: s2, w: s2 },
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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: 2, target: 4 },
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{ id: 3, source: 4, target: 3 },
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{ id: 4, source: 3, target: 1 },
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{ id: 5, source: 5, target: 6 },
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{ id: 6, source: 6, target: 8 },
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{ id: 7, source: 8, target: 7 },
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{ id: 8, source: 7, target: 5 },
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{ id: 9, source: 1, target: 5 },
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{ id: 10, source: 2, target: 6 },
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{ id: 11, source: 3, target: 7 },
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{ id: 12, source: 4, target: 8 },
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{ id: 13, source: 9, target: 10 },
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{ id: 14, source: 10, target: 12 },
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{ id: 15, source: 12, target: 11 },
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{ id: 16, source: 11, target: 9 },
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{ id: 17, source: 13, target: 14 },
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{ id: 18, source: 14, target: 16 },
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{ id: 19, source: 16, target: 15 },
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{ id: 20, source: 15, target: 13 },
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{ id: 21, source: 9, target: 13 },
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{ id: 22, source: 10, target: 14 },
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{ id: 23, source: 11, target: 15 },
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{ id: 24, source: 12, target: 16 },
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{ id: 25, source: 1, target: 9 },
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{ id: 26, source: 2, target: 10 },
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{ id: 27, source: 3, target: 11 },
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{ id: 28, source: 4, target: 12 },
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{ id: 29, source: 5, target: 13 },
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{ id: 30, source: 6, target: 14 },
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{ id: 31, source: 7, target: 15 },
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{ id: 32, source: 8, target: 16 },
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]
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}
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};
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// this was done manually and I'm not sure if it's right
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const CELL24_INDEXING = {
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x: { y: 1, z: 3, w: 2 },
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y: { z: 2, w: 3 },
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z: { w: 1 },
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};
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// note that this depends on the colour mapping in main.js, yuck
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const CELL24_LINK_INDEXING = {
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1: { 2: 1, 3: 3 },
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2: { 1: 1, 3: 2 },
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3: { 1: 3, 2: 2 },
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}
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function make_24cell_vertices() {
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const axes = [ 'x', 'y', 'z', 'w' ];
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const nodes = [];
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let i = 1;
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for ( let p = 0; p < 3; p++ ) {
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for ( let q = p + 1; q < 4; q++ ) {
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const a1 = axes[p];
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const a2 = axes[q];
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const label = CELL24_INDEXING[a1][a2];
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for ( const v1 of [ -1, 1 ] ) {
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for ( const v2 of [ -1, 1 ] ) {
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const node = {
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id: i,
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x: 0, y: 0, z: 0, w:0,
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label: label
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};
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node[a1] = v1;
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node[a2] = v2;
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nodes.push(node);
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i++;
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}
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}
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}
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}
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return nodes;
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}
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function node_axes(n1) {
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return [ 'x', 'y', 'z', 'w' ].filter((a) => n1[a] !== 0 );
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}
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function make_24cell_edges(nodes) {
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const seen = {};
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const links = [];
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let id = 1;
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for( const n1 of nodes ) {
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const axes = node_axes(n1);
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const axeq = nodes.filter((n) => n[axes[0]] === n1[axes[0]] && n[axes[1]] === 0);
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const axeq2 = nodes.filter((n) => n[axes[1]] === n1[axes[1]] && n[axes[0]] === 0);
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for( const n2 of axeq.concat(axeq2) ) {
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const ids = [ n1.id, n2.id ];
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ids.sort();
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const fp = ids.join(',');
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if( !seen[fp] ) {
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seen[fp] = true;
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const label = CELL24_LINK_INDEXING[n1.label][n2.label];
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links.push({ id: id, label: label, source: n1.id, target: n2.id });
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}
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}
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}
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return links;
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}
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export const cell24 = () => {
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const nodes = make_24cell_vertices();
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const links = make_24cell_edges(nodes);
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const nodes = scale_and_index(PERMUTE.coordinates([1, 1, 1, 1], 0), Math.sqrt(2) / 2);
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const links = auto_detect_edges(nodes, 4);
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return {
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nodes: nodes,
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@ -244,40 +99,20 @@ export const cell24 = () => {
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}
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// above ^^ fix me convert to new style
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function dist2(n1, n2) {
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return (n1.x - n2.x) ** 2 + (n1.y - n2.y) ** 2 + (n1.z - n2.z) ** 2 + (n1.w - n2.w) ** 2;
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export const cell24 = () => {
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const nodes = scale_and_index(PERMUTE.coordinates([0, 0, 1, 1], 0), 1);
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const links = auto_detect_edges(nodes, 6);
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return {
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nodes: nodes,
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links: links
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};
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}
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function auto_detect_edges(nodes, neighbours) {
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const seen = {};
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const nnodes = nodes.length;
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const links = [];
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let id = 1;
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for( const n1 of nodes ) {
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const d2 = [];
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for( const n2 of nodes ) {
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d2.push({ d2: dist2(n1, n2), id: n2.id });
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}
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d2.sort((a, b) => a.d2 - b.d2);
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const closest = d2.slice(1, neighbours + 1);
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for( const e of closest ) {
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||||
const ids = [ n1.id, e.id ];
|
||||
ids.sort();
|
||||
const fp = ids.join(',');
|
||||
if( !seen[fp] ) {
|
||||
seen[fp] = true;
|
||||
links.push({ id: id, label: 0, source: n1.id, target: e.id });
|
||||
id++;
|
||||
}
|
||||
}
|
||||
}
|
||||
return links;
|
||||
}
|
||||
|
||||
|
||||
function make_120cell_vertices() {
|
||||
const phi = 0.5 * (1 + Math.sqrt(5));
|
||||
|
|
@ -288,12 +123,12 @@ function make_120cell_vertices() {
|
|||
|
||||
const nodes = [
|
||||
PERMUTE.coordinates([0, 0, 2, 2], 0),
|
||||
PERMUTE.coordinates([1, 1, 1, r5], 1),
|
||||
PERMUTE.coordinates([phi, phi, phi, phi2inv], 2),
|
||||
PERMUTE.coordinates([1, 1, 1, r5], 0),
|
||||
PERMUTE.coordinates([phi, phi, phi, phi2inv], 0),
|
||||
PERMUTE.coordinates([phiinv, phiinv, phiinv, phi2], 0),
|
||||
|
||||
PERMUTE.coordinates([phi2, phi2inv, 1, 0], 1, true),
|
||||
PERMUTE.coordinates([r5, phiinv, phi, 0], 2, true),
|
||||
PERMUTE.coordinates([phi2, phi2inv, 1, 0], 0, true),
|
||||
PERMUTE.coordinates([r5, phiinv, phi, 0], 0, true),
|
||||
PERMUTE.coordinates([2, 1, phi, phiinv], 0, true),
|
||||
].flat();
|
||||
return scale_and_index(nodes, 0.5);
|
||||
|
|
@ -315,9 +150,9 @@ function make_600cell_vertices() {
|
|||
|
||||
const nodes = [
|
||||
PERMUTE.coordinates([0, 0, 0, 2], 0),
|
||||
PERMUTE.coordinates([1, 1, 1, 1], 1),
|
||||
PERMUTE.coordinates([1, 1, 1, 1], 0),
|
||||
|
||||
PERMUTE.coordinates([phi, 1, 1 / phi, 0], 1, true)
|
||||
PERMUTE.coordinates([phi, 1, 1 / phi, 0], 0, true)
|
||||
].flat();
|
||||
return scale_and_index(nodes, 0.75);
|
||||
}
|
||||
|
|
|
|||
Loading…
Reference in New Issue