563 lines
11 KiB
JavaScript
563 lines
11 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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}
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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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manual_label_120cell(nodes, links);
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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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// Schoute's partition via https://arxiv.org/abs/1010.4353
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const partition600 = {
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"2,0,0,0": 1,
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"0,2,0,0": 1,
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"0,0,2,0": 1,
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"0,0,0,2": 1,
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"1,1,1,1": 1,
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"1,1,-1,-1": 1,
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"1,-1,1,-1": 1,
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"1,-1,-1,1": 1,
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"1,-1,-1,-1": 1,
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"1,-1,1,1": 1,
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"1,1,-1,1": 1,
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"1,1,1,-1": 1,
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"k,0,-t,-1": 2,
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"0,k,1,-t": 2,
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"t,-1,k,0": 2,
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"1,t,0,k": 2,
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"t,k,0,-1": 2,
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"1,0,k,t": 2,
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"k,-t,-1,0": 2,
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"0,1,-t,k": 2,
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"1,k,t,0": 2,
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"t,0,-1,k": 2,
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"0,t,-k,-1": 2,
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"k,-1,0,-t": 2,
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"t,0,1,k": 3,
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"0,t,-k,1": 3,
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"1,-k,-t,0": 3,
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"k,1,0,-t": 3,
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"0,k,1,t": 3,
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"t,1,-k,0": 3,
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"k,0,t,-1": 3,
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"1,-t,0,k": 3,
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"t,-k,0,-1": 3,
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"0,1,-t,-k": 3,
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"1,0,-k,t": 3,
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"k,t,1,0": 3,
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"t,0,-1,-k": 4,
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"0,t,k,-1": 4,
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"1,-k,t,0": 4,
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"k,1,0,t": 4,
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"t,1,k,0": 4,
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"0,k,-1,-t": 4,
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"1,-t,0,-k": 4,
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"k,0,-t,1": 4,
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"0,1,t,k": 4,
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"t,-k,0,1": 4,
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"k,t,-1,0": 4,
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"1,0,k,-t": 4,
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"k,0,t,1": 5,
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"0,k,-1,t": 5,
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"t,-1,-k,0": 5,
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"1,t,0,-k": 5,
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"1,0,-k,-t": 5,
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"t,k,0,1": 5,
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"0,1,t,-k": 5,
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"k,-t,1,0": 5,
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"t,0,1,-k": 5,
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"1,k,-t,0": 5,
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"k,-1,0,t": 5,
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"0,t,k,1": 5
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};
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function partition_coord(i, coords, invert) {
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const j = invert ? -i : i;
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if( j >= 0 ) {
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return coords[j];
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}
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return "-" + coords[-j];
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}
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function partition_fingerprint(n, coords, invert) {
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const p = ['x','y','z','w'].map((a) => partition_coord(n[a], coords, invert));
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const fp = p.join(',');
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return fp;
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}
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function label_vertex(n, coords, partition) {
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const fp = partition_fingerprint(n, coords, false);
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if( fp in partition ) {
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return partition[fp];
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} else {
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const ifp = partition_fingerprint(n, coords, true);
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if( ifp in partition ) {
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return partition[ifp];
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}
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console.log(`Map for ${fp} ${ifp} not found`);
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return 0;
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}
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}
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function map_coord(i, coords, values) {
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if( i >= 0 ) {
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return values[coords[i]];
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}
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return -values[coords[-i]];
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}
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function make_600cell_vertices() {
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const coords = {
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0: '0',
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1: '1',
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2: '2',
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3: 't',
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4: 'k'
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};
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const t = 0.5 * (1 + Math.sqrt(5));
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const values = {
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'0': 0,
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'1': 1,
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'2': 2,
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't': t,
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'k': 1 / t
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};
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const nodes = [
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PERMUTE.coordinates([0, 0, 0, 2], 0),
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PERMUTE.coordinates([1, 1, 1, 1], 0),
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PERMUTE.coordinates([3, 1, 4, 0], 0, true)
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].flat();
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for( const n of nodes ) {
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n.label = label_vertex(n, coords, partition600) - 1;
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}
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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] = map_coord(n[a], coords, values);
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}
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}
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index_nodes(nodes);
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scale_nodes(nodes, 0.75);
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return nodes;
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}
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function get_node(nodes, id) {
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const ns = nodes.filter((n) => n.id === id);
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if( ns ) {
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return ns[0]
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} else {
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return undefined;
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}
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}
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function audit_link_labels(nodes, links) {
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console.log("Link audit");
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for( const l of links ) {
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const n1 = get_node(nodes, l.source);
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const n2 = get_node(nodes, l.target);
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if( n1.label === n2.label ) {
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console.log(`link ${l.id} joins ${n1.id} ${n2.id} with label ${n2.label}`);
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}
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}
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}
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export const cell600 = () => {
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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
|
|
}
|
|
}
|
|
}
|
|
|
|
|