613 lines
16 KiB
JavaScript
613 lines
16 KiB
JavaScript
import * as PERMUTE from './permute.js';
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import * as DODECAHEDRA from './dodecahedra.js';
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function index_nodes(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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}
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}
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function scale_nodes(nodes, scale) {
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for( const n of nodes ) {
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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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}
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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, debug=false) {
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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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if( debug ) {
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console.log(`closest = ${closest.length}`);
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console.log(closest);
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}
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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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if( debug ) {
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console.log(`Found ${links.length} edges`)
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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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const r2 = Math.sqrt(2) / 2;
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return {
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nodes: [
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{id:1, label: 0, x: r2, y: r2, z: r2, w: -r2 / r5 },
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{id:2, label: 1, x: r2, y: -r2, z: -r2, w: -r2 / r5 },
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{id:3, label: 2, x: -r2, y: r2, z: -r2, w: -r2 / r5 },
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{id:4, label: 3, x: -r2, y: -r2, z: r2, w: -r2 / r5 },
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{id:5, label: 4, 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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{ id:2, source:1, target: 3},
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{ id:3, source:1, target: 4},
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{ id:4, source:1, target: 5},
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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:3, target: 4},
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{ id:9, source:3, target: 5},
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{ id:10, source:4, target: 5},
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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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};
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};
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export const cell16 = () => {
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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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nodes[0].label = 0;
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nodes[3].label = 1;
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nodes[5].label = 2;
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nodes[6].label = 3;
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nodes[7].label = 0;
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nodes[4].label = 1;
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nodes[2].label = 2;
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nodes[1].label = 3;
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index_nodes(nodes);
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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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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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};
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};
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export const tesseract = () => {
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const nodes = PERMUTE.coordinates([1, 1, 1, 1], 0);
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index_nodes(nodes);
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for( const n of nodes ) {
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if( n.x * n.y * n.z * n.w > 0 ) {
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n.label = 1;
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}
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}
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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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return {
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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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};
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}
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const CELL24_INDEXING = {
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x: { y: 0, z: 2, w: 1 },
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y: { z: 1, w: 2 },
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z: { w: 0 }
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};
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export const cell24 = () => {
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const nodes = PERMUTE.coordinates([0, 0, 1, 1], 0);
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for( const n of nodes ) {
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const axes = ['x', 'y', 'z', 'w'].filter((a) => n[a] !== 0);
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n.label = CELL24_INDEXING[axes[0]][axes[1]];
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}
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index_nodes(nodes);
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const links = auto_detect_edges(nodes, 8);
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return {
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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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};
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}
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// face detection for the 120-cell
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// NOTE: all of these return node ids, not nodes
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// return all the links which connect to a node
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function nodes_links(links, nodeid) {
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return links.filter((l) => l.source === nodeid || l.target === nodeid);
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}
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// filter to remove a link to a given id from a set of links
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function not_to_this(link, nodeid) {
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return !(link.source === nodeid || link.target === nodeid);
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}
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// given nodes n1, n2, return all neighbours of n2 which are not n1
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function unmutuals(links, n1id, n2id) {
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const nlinks = nodes_links(links, n2id).filter((l) => not_to_this(l, n1id));
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return nlinks.map((l) => {
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if( l.source === n2id ) {
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return l.target;
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} else {
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return l.source;
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}
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})
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}
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function fingerprint(ids) {
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const sids = [...ids];
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sids.sort();
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return sids.join(',');
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}
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function auto_120cell_faces(links) {
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const faces = [];
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const seen = {};
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let id = 1;
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for( const edge of links ) {
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const v1 = edge.source;
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const v2 = edge.target;
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const n1 = unmutuals(links, v2, v1);
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const n2 = unmutuals(links, v1, v2);
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const shared = [];
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for( const a of n1 ) {
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const an = unmutuals(links, v1, a);
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for( const d of n2 ) {
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const dn = unmutuals(links, v2, d);
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for( const x of an ) {
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for( const y of dn ) {
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if( x == y ) {
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shared.push([v1, a, x, d, v2])
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}
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}
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}
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}
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}
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if( shared.length !== 3 ) {
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console.log(`Bad shared faces for ${edge.id} ${v1} ${v2}`);
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}
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for( const face of shared ) {
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const fp = fingerprint(face);
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if( !seen[fp] ) {
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faces.push({ id: id, nodes: face });
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id++;
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seen[fp] = true;
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}
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}
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}
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return faces;
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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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PERMUTE.coordinates([0, 0, 2, 2], 0),
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PERMUTE.coordinates([1, 1, 1, r5], 0),
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PERMUTE.coordinates([phi, phi, phi, phi2inv], 0),
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PERMUTE.coordinates([phiinv, phiinv, phiinv, phi2], 0),
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PERMUTE.coordinates([phi2, phi2inv, 1, 0], 0, true),
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PERMUTE.coordinates([r5, phiinv, phi, 0], 0, true),
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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, 0.5);
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return nodes;
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}
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function label_nodes(nodes, ids, label) {
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nodes.filter((n) => ids.includes(n.id)).map((n) => n.label = label);
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}
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function label_faces_120cell(nodes, faces, cfaces, label) {
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const ns = new Set();
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console.log(`label faces from ${cfaces}`);
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for( const fid of cfaces ) {
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const face = faces.filter((f)=> f.id === fid );
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if( face.length > 0 ) {
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for ( const nid of face[0].nodes ) {
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ns.add(nid);
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}
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}
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}
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label_nodes(nodes, Array.from(ns), label);
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}
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function basic_auto_label_120cell(nodes, links) {
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const faces = auto_120cell_faces(links);
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const dodecas = DODECAHEDRA.DODECAHEDRA;
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//const cfaces = [ 1, 2, 4, 145, 169 ];
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let colour = 1;
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for( const dd of dodecas ) {
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label_faces_120cell(nodes, faces, dd, colour);
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colour++;
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if( colour > 8 ) {
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colour = 1;
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}
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}
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// label_faces_120cell(nodes, faces, [
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// 1, 2, 4, 169, 626,
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// 145, 149, 553, 173, 171,
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// 147, 554
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// ], 2);
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// label_faces_120cell(nodes, faces, [
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// 1, 5, 3, 193, 641,
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// 217, 221, 565, 197, 195,
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// 219, 566
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// ], 3);
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}
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// manual compound-of-tetrahedra colouring
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function manual_label_120cell(nodes, links) {
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label_nodes(nodes, [1, 153, 29, 105], 1);
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label_nodes(nodes, [317, 409, 265, 109], 2);
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label_nodes(nodes, [221, 337, 25, 509], 3);
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label_nodes(nodes, [217, 413, 457, 361], 4);
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label_nodes(nodes, [313, 157, 461, 505], 5);
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// second dodecahedron needs to have opposite chirality
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label_nodes(nodes, [ 165, 33, 117 ], 1);
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label_nodes(nodes, [ 161, 465, 517 ], 2);
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label_nodes(nodes, [ 417, 469, 365 ], 3);
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label_nodes(nodes, [ 341, 37, 513 ], 4);
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label_nodes(nodes, [ 421, 269, 113 ], 5);
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// third
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label_nodes(nodes, [ 45, 101, 181 ], 1);
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label_nodes(nodes, [ 241, 429, 53 ], 2);
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label_nodes(nodes, [ 93, 229 ], 3);
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label_nodes(nodes, [ 173, 437 ], 4);
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label_nodes(nodes, [ 245, 325 ], 5);
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// fourth (id = 3)
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label_nodes(nodes, [ 89, 169, 49 ], 1);
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label_nodes(nodes, [ 321 ], 2);
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label_nodes(nodes, [ 425, 177 ], 3);
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label_nodes(nodes, [ 97, 225 ], 4);
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label_nodes(nodes, [ 41, 433], 5);
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}
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function meridian_label_120cell(nodes) {
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const MERIDIAN_COLOURED ={"1":[27,38,49,61,68,74,87,105,120,126,131,140,149,156,165,174,179,185,200,207,210,218,223,226,231,234,239,241,253,258,263,265,272,274,279,284,285,289,296,300,301,306,311,313,320,324,325,331,334,339,342,347,350,356,357,367,369,376,378,383,388,389,393,400,413,414,419,420,425,440,449,453,458,460,469,471,473,474,487,488,490,494,499,503,511,512,513,514,525,527,530,532,539,543,546,550,555,558,563,566,572,573,580,581,592,593],"2":[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,21,22,23,24,25,28,30,31,34,35,37,40,41,46,47,50,51,53,56,57,60,62,63,66,67,69,72,73,76,78,83,85,88,90,93,97,103,106,107,109,112,113,116,118,119,122,123,125,129,132,134,135,138,139,141,144,145,148,150,151,155,157,160,161,164,166,167,170,171,173,177,180,182,183,187,189,192,193,196,198,202,203,205,208,209,212,214,215],"3":[26,39,45,52,64,65,94,99,108,117,127,130,137,152,153,168,175,178,188,197,206,211,219,222,227,230,235,238,245,251,268,269,273,280,283,286,292,293,299,302,305,312,316,317,321,328,330,335,349,355,358,363,366,370,375,377,384,385,392,394,399,404,405,415,416,417,418,426,437,439,441,445,452,456,457,459,470,472,475,485,486,491,495,498,502,509,510,515,516,526,529,531,538,542,547,551,554,559,562,567,569,576,577,584,588,597],"4":[32,33,43,54,58,71,77,84,101,110,115,121,136,143,146,159,162,169,184,204,213,220,221,228,229,236,237,249,260,261,271,276,277,281,288,290,295,297,304,308,309,315,318,322,327,329,336,340,341,351,354,359,361,368,371,374,379,382,387,390,396,397,409,410,423,424,430,433,435,443,447,450,454,461,463,466,468,477,478,483,484,489,493,500,504,507,508,517,518,522,533,535,540,544,545,549,553,560,561,568,570,583,587,590,595,598],"5":[29,36,42,55,59,70,80,81,89,111,114,133,142,147,163,181,191,194,201,216,217,224,225,232,233,240,243,246,255,267,270,275,278,282,287,291,294,298,303,307,310,314,319,323,326,332,333,337,344,345,352,353,360,364,365,372,373,380,381,395,398,402,407,411,412,421,422,429,436,442,446,451,455,462,464,465,467,479,481,482,492,496,497,501,505,506,519,520,521,523,534,536,537,541,548,552,556,557,564,565,574,579,586,591,594,599]};
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for( const cstr in MERIDIAN_COLOURED ) {
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label_nodes(nodes, MERIDIAN_COLOURED[cstr], Number(cstr));
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}
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//label_nodes(nodes, [313], 6);
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}
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function arctic_label_120cell(nodes) {
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const ARCTIC_COLOURED = {"1":[27,38,48,49,61,68,74,87,95,98,105,120,126,131,140,149,156,165,174,179,185,200,207,210,218,223,226,231,234,239,241,248,252,253,258,263,265,272,274,279,284,285,289,296,300,301,306,311,313,320,324,325,331,334,339,342,347,350,356,357,362,367,369,376,378,383,388,389,393,400,403,406,413,414,419,420,425,427,438,440,444,448,449,453,458,460,469,471,473,474,487,488,490,494,499,503,511,512,513,514,525,527,530,532,539,543,546,550,555,558,563,566,572,573,580,581,585,592,593,600],"2":[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,28,30,31,34,35,37,40,41,44,46,47,50,51,53,56,57,60,62,63,66,67,69,72,73,76,78,79,82,83,85,88,90,91,93,96,97,100,102,103,106,107,109,112,113,116,118,119,122,123,125,128,129,132,134,135,138,139,141,144,145,148,150,151,154,155,157,160,161,164,166,167,170,171,173,176,177,180,182,183,186,187,189,192,193,196,198,199,202,203,205,208,209,212,214,215],"3":[26,39,45,52,64,65,75,86,94,99,108,117,127,130,137,152,153,168,175,178,188,197,206,211,219,222,227,230,235,238,244,245,251,254,257,264,268,269,273,280,283,286,292,293,299,302,305,312,316,317,321,328,330,335,338,343,348,349,355,358,363,366,370,375,377,384,385,392,394,399,404,405,415,416,417,418,426,428,437,439,441,445,452,456,457,459,470,472,475,476,485,486,491,495,498,502,509,510,515,516,526,528,529,531,538,542,547,551,554,559,562,567,569,576,577,584,588,589,596,597],"4":[32,33,43,54,58,71,77,84,92,101,110,115,121,136,143,146,159,162,169,184,190,195,204,213,220,221,228,229,236,237,242,247,249,256,260,261,266,271,276,277,281,288,290,295,297,304,308,309,315,318,322,327,329,336,340,341,346,351,354,359,361,368,371,374,379,382,387,390,396,397,401,408,409,410,423,424,430,432,433,435,443,447,450,454,461,463,466,468,477,478,483,484,489,493,500,504,507,508,517,518,522,524,533,535,540,544,545,549,553,560,561,568,570,575,578,583,587,590,595,598],"5":[29,36,42,55,59,70,80,81,89,104,111,114,124,133,142,147,158,163,172,181,191,194,201,216,217,224,225,232,233,240,243,246,250,255,259,262,267,270,275,278,282,287,291,294,298,303,307,310,314,319,323,326,332,333,337,344,345,352,353,360,364,365,372,373,380,381,386,391,395,398,402,407,411,412,421,422,429,431,434,436,442,446,451,455,462,464,465,467,479,480,481,482,492,496,497,501,505,506,519,520,521,523,534,536,537,541,548,552,556,557,564,565,571,574,579,582,586,591,594,599]};
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for( const cstr in ARCTIC_COLOURED ) {
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label_nodes(nodes, ARCTIC_COLOURED[cstr], Number(cstr));
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}
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}
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|
function link_labels(nodes, link) {
|
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const n1 = nodes.filter((n) => n.id === link.source);
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const n2 = nodes.filter((n) => n.id === link.target);
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return [ n1[0].label, n2[0].label ];
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}
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|
|
|
|
|
|
|
export const cell120 = () => {
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const nodes = make_120cell_vertices();
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const links = auto_detect_edges(nodes, 4);
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|
|
|
arctic_label_120cell(nodes);
|
|
|
|
const links_f = links.filter((l) => {
|
|
const labels = link_labels(nodes, l);
|
|
return ( labels[0] > 0 && labels[1] > 0 );
|
|
});
|
|
|
|
return {
|
|
nodes: nodes,
|
|
links: links_f,
|
|
geometry: {
|
|
node_size: 0.02,
|
|
link_size: 0.02
|
|
},
|
|
}
|
|
}
|
|
|
|
// Schoute's partition via https://arxiv.org/abs/1010.4353
|
|
|
|
const partition600 = {
|
|
|
|
"2,0,0,0": 1,
|
|
"0,2,0,0": 1,
|
|
"0,0,2,0": 1,
|
|
"0,0,0,2": 1,
|
|
"1,1,1,1": 1,
|
|
"1,1,-1,-1": 1,
|
|
"1,-1,1,-1": 1,
|
|
"1,-1,-1,1": 1,
|
|
"1,-1,-1,-1": 1,
|
|
"1,-1,1,1": 1,
|
|
"1,1,-1,1": 1,
|
|
"1,1,1,-1": 1,
|
|
|
|
"k,0,-t,-1": 2,
|
|
"0,k,1,-t": 2,
|
|
"t,-1,k,0": 2,
|
|
"1,t,0,k": 2,
|
|
"t,k,0,-1": 2,
|
|
"1,0,k,t": 2,
|
|
"k,-t,-1,0": 2,
|
|
"0,1,-t,k": 2,
|
|
"1,k,t,0": 2,
|
|
"t,0,-1,k": 2,
|
|
"0,t,-k,-1": 2,
|
|
"k,-1,0,-t": 2,
|
|
|
|
"t,0,1,k": 3,
|
|
"0,t,-k,1": 3,
|
|
"1,-k,-t,0": 3,
|
|
"k,1,0,-t": 3,
|
|
"0,k,1,t": 3,
|
|
"t,1,-k,0": 3,
|
|
"k,0,t,-1": 3,
|
|
"1,-t,0,k": 3,
|
|
"t,-k,0,-1": 3,
|
|
"0,1,-t,-k": 3,
|
|
"1,0,-k,t": 3,
|
|
"k,t,1,0": 3,
|
|
|
|
"t,0,-1,-k": 4,
|
|
"0,t,k,-1": 4,
|
|
"1,-k,t,0": 4,
|
|
"k,1,0,t": 4,
|
|
"t,1,k,0": 4,
|
|
"0,k,-1,-t": 4,
|
|
"1,-t,0,-k": 4,
|
|
"k,0,-t,1": 4,
|
|
"0,1,t,k": 4,
|
|
"t,-k,0,1": 4,
|
|
"k,t,-1,0": 4,
|
|
"1,0,k,-t": 4,
|
|
|
|
"k,0,t,1": 5,
|
|
"0,k,-1,t": 5,
|
|
"t,-1,-k,0": 5,
|
|
"1,t,0,-k": 5,
|
|
"1,0,-k,-t": 5,
|
|
"t,k,0,1": 5,
|
|
"0,1,t,-k": 5,
|
|
"k,-t,1,0": 5,
|
|
"t,0,1,-k": 5,
|
|
"1,k,-t,0": 5,
|
|
"k,-1,0,t": 5,
|
|
"0,t,k,1": 5
|
|
};
|
|
|
|
|
|
|
|
function partition_coord(i, coords, invert) {
|
|
const j = invert ? -i : i;
|
|
if( j >= 0 ) {
|
|
return coords[j];
|
|
}
|
|
return "-" + coords[-j];
|
|
}
|
|
|
|
function partition_fingerprint(n, coords, invert) {
|
|
const p = ['x','y','z','w'].map((a) => partition_coord(n[a], coords, invert));
|
|
const fp = p.join(',');
|
|
return fp;
|
|
}
|
|
|
|
|
|
function label_vertex(n, coords, partition) {
|
|
const fp = partition_fingerprint(n, coords, false);
|
|
if( fp in partition ) {
|
|
return partition[fp];
|
|
} else {
|
|
const ifp = partition_fingerprint(n, coords, true);
|
|
if( ifp in partition ) {
|
|
return partition[ifp];
|
|
}
|
|
console.log(`Map for ${fp} ${ifp} not found`);
|
|
return 0;
|
|
}
|
|
}
|
|
|
|
|
|
function map_coord(i, coords, values) {
|
|
if( i >= 0 ) {
|
|
return values[coords[i]];
|
|
}
|
|
return -values[coords[-i]];
|
|
}
|
|
|
|
|
|
function make_600cell_vertices() {
|
|
const coords = {
|
|
0: '0',
|
|
1: '1',
|
|
2: '2',
|
|
3: 't',
|
|
4: 'k'
|
|
};
|
|
const t = 0.5 * (1 + Math.sqrt(5));
|
|
const values = {
|
|
'0': 0,
|
|
'1': 1,
|
|
'2': 2,
|
|
't': t,
|
|
'k': 1 / t
|
|
};
|
|
|
|
const nodes = [
|
|
PERMUTE.coordinates([0, 0, 0, 2], 0),
|
|
PERMUTE.coordinates([1, 1, 1, 1], 0),
|
|
PERMUTE.coordinates([3, 1, 4, 0], 0, true)
|
|
].flat();
|
|
|
|
for( const n of nodes ) {
|
|
n.label = label_vertex(n, coords, partition600) - 1;
|
|
}
|
|
|
|
for( const n of nodes ) {
|
|
for( const a of [ 'x', 'y', 'z', 'w'] ) {
|
|
n[a] = map_coord(n[a], coords, values);
|
|
}
|
|
}
|
|
|
|
|
|
index_nodes(nodes);
|
|
scale_nodes(nodes, 0.75);
|
|
return nodes;
|
|
}
|
|
|
|
function get_node(nodes, id) {
|
|
const ns = nodes.filter((n) => n.id === id);
|
|
if( ns ) {
|
|
return ns[0]
|
|
} else {
|
|
return undefined;
|
|
}
|
|
}
|
|
|
|
function audit_link_labels(nodes, links) {
|
|
console.log("Link audit");
|
|
for( const l of links ) {
|
|
const n1 = get_node(nodes, l.source);
|
|
const n2 = get_node(nodes, l.target);
|
|
if( n1.label === n2.label ) {
|
|
console.log(`link ${l.id} joins ${n1.id} ${n2.id} with label ${n2.label}`);
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
|
|
export const cell600 = () => {
|
|
const nodes = make_600cell_vertices();
|
|
const links = auto_detect_edges(nodes, 12);
|
|
|
|
return {
|
|
nodes: nodes,
|
|
links: links,
|
|
geometry: {
|
|
node_size: 0.02,
|
|
link_size: 0.02
|
|
}
|
|
}
|
|
}
|
|
|
|
|