1208 lines
30 KiB
JavaScript
1208 lines
30 KiB
JavaScript
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// code for generating the 120-cell labels
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// has some overlap with permute - FIXME
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const THREE = require('three');
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function pandita(a) {
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const n = a.length;
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for( let k = n - 2; k >= 0; k-- ) {
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if( a[k] < a[k + 1] ) {
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for( let l = n - 1; l >= 0; l-- ) {
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if( a[k] < a[l] ) {
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const tmp = a[k];
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a[k] = a[l];
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a[l] = tmp;
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const revtail = a.slice(k + 1);
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revtail.reverse();
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for( let i = 0; i < revtail.length; i++ ) {
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a[k + 1 + i] = revtail[i];
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}
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return Math.floor(revtail.length / 2) + 1;
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}
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}
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console.log("Shouldn't get here");
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process.exit();
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}
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}
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return false;
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}
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function permutations_old(a) {
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a.sort();
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const ps = [ [...a] ];
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let running = true;
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while( running ) {
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const s = pandita(a);
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if( s ) {
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ps.push([...a]);
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} else {
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running = false;
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}
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}
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return ps;
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}
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function permutations(a) {
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a.sort();
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const ps = [ [...a] ];
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let running = true;
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while( pandita(a) > 0 ) {
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ps.push([...a]);
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}
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return ps;
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}
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function permutations_even(a) {
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a.sort();
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let parity = 'even';
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const ps = [ [...a] ];
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let running = true;
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while( running ) {
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const s = pandita(a);
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if( s ) {
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if( parity === 'even' ) {
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if( s % 2 === 1 ) {
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parity = 'odd';
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}
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} else {
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if( s % 2 === 1 ) {
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parity = 'even';
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}
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}
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if( parity === 'even' ) {
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ps.push([...a]);
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}
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} else {
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running = false;
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}
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}
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return ps;
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}
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// for a given permutation, say [ 1, 1, 0, 0 ], return all
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// of the valid changes of sign, so:
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// [ [1, 1, 0, 0 ], [ -1, 1, 0, 0 ], [ 1, -1, 0, 0 ], [-1, -1, 0, 0 ]]
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// ie don't do it on the zeros
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function expand_sign(a, label) {
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const expanded = [];
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const exv = a.map((v) => v ? [ -v, v ] : [ 0 ]);
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for( const xv of exv[0] ) {
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for( const yv of exv[1] ) {
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for( const zv of exv[2] ) {
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for( const wv of exv[3] ) {
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expanded.push({label: label, x: xv, y:yv, z:zv, w:wv});
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}
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}
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}
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}
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return expanded;
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}
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function coordinates(a, id0=1, 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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coords.push(...expanded);
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}
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return coords;
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}
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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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export 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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export 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([0, 0, 2, 2], 0),
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coordinates([1, 1, 1, r5], 0),
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coordinates([phi, phi, phi, phi2inv], 0),
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coordinates([phiinv, phiinv, phiinv, phi2], 0),
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coordinates([phi2, phi2inv, 1, 0], 0, true),
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coordinates([r5, phiinv, phi, 0], 0, true),
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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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// 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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export 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, edge: edge.id, v1: edge.source, v2: edge.target, fingerprint: fp, 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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// trying to go from faces to dodecahedra
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function shared_vertices(f1, f2) {
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return f1.nodes.filter((f) => f2.nodes.includes(f));
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}
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function adjacent_faces(f1, f2) {
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// adjacent faces which share an edge, not just a vertex
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const intersect = shared_vertices(f1, f2);
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if( intersect.length < 2 ) {
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return false;
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}
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if( intersect.length > 2 ) {
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console.log(`warning: faces ${f1.id} and ${f2.id} have too many common vertices`);
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}
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return true;
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}
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function find_adjacent_faces(faces, face) {
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const neighbours = faces.filter((f) => f.id !== face.id && adjacent_faces(f, face));
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return neighbours;
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}
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function find_dodeca_mutuals(faces, f1, f2) {
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// for any two adjacent faces, find their common neighbours where
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// all three share exactly one vertex (this, I think, guarantees that
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// all are on the same dodecahedron)
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const n1 = find_adjacent_faces(faces, f1);
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const n2 = find_adjacent_faces(faces, f2);
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const common = n1.filter((f1) => n2.filter((f2) => f1.id === f2.id).length > 0 );
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// there's one extra here - the third which has two nodes in common with
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// both f1 and f2 - filter it out
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const mutuals = common.filter((cf) => {
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const shared = cf.nodes.filter((n) => f1.nodes.includes(n) && f2.nodes.includes(n));
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return shared.length === 1
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});
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return mutuals;
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}
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function find_dodeca_next(faces, dodeca, f1, f2) {
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// of a pair of mutuals, return the one we haven't already got
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const m = find_dodeca_mutuals(faces, f1, f2);
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if( dodeca.filter((f) => f.id === m[0].id ).length > 0 ) {
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m.shift();
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}
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return m[0];
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}
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function faces_to_dodecahedron(faces, f1, f2, flip=false) {
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const dodecahedron = [ f1, f2 ];
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// take f1 as the 'center', get the other four around it from f2
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const fs = find_dodeca_mutuals(faces, f1, f2);
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const f3 = flip ? fs[1] : fs[0];
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const f6 = flip ? fs[0] : fs[1];
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dodecahedron.push(f3);
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const f4 = find_dodeca_next(faces, dodecahedron, f1, f3);
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dodecahedron.push(f4);
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const f5 = find_dodeca_next(faces, dodecahedron, f1, f4);
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dodecahedron.push(f5);
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dodecahedron.push(f6);
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// get the next ring
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const f7 = find_dodeca_next(faces, dodecahedron, f6, f2);
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dodecahedron.push(f7);
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const f8 = find_dodeca_next(faces, dodecahedron, f2, f3);
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dodecahedron.push(f8);
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const f9 = find_dodeca_next(faces, dodecahedron, f3, f4);
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dodecahedron.push(f9);
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const f10 = find_dodeca_next(faces, dodecahedron, f4, f5);
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dodecahedron.push(f10);
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const f11 = find_dodeca_next(faces, dodecahedron, f5, f6);
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dodecahedron.push(f11);
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// get the last
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const f12 = find_dodeca_next(faces, dodecahedron, f7, f8);
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dodecahedron.push(f12);
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return dodecahedron;
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}
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// from a face and one neighbouring node, return a dodecahedron
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// Set 'flip' to true if we're coming to this dodecahedron from a
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// face on a previous one so that the chirality doesn't get inverted
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function face_plus_to_dodecahedron(faces, f1, node, flip=false) {
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const neighbours = find_adjacent_faces(faces, f1);
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const nodens = neighbours.filter((f) => f.nodes.includes(node));
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return faces_to_dodecahedron(faces, f1, nodens[0], flip); // does it matter which?
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}
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// for three faces, return their common vertex (if they have one)
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function find_dodeca_vertex(f1, f2, f3) {
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const v12 = f1.nodes.filter((n) => f2.nodes.includes(n));
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const v123 = v12.filter((n) => f3.nodes.includes(n));
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if( v123.length === 1 ) {
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return v123[0];
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} else {
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console.log(`warning: faces ${f1.id} ${f2.id} ${f3.id} don't share 1 vertex`);
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return false;
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}
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}
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const VERTEX_MAP = [
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[ 0, 1, 5 ],
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[ 0, 1, 2 ],
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[ 0, 2, 3 ],
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[ 0, 3, 4 ],
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[ 0, 4, 5 ],
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[ 1, 5, 6 ],
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[ 1, 2, 7 ],
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[ 2, 3, 8 ],
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[ 3, 4, 9 ],
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[ 4, 5, 10 ],
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[ 1, 6, 7 ],
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[ 2, 7, 8 ],
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[ 3, 8, 9 ],
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[ 4, 9, 10 ],
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[ 5, 6, 10 ],
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[ 6, 7, 11 ],
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[ 7, 8, 11 ],
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[ 8, 9, 11 ],
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[ 9, 10, 11 ],
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[ 6, 10, 11 ],
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];
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function dodecahedron_vertices(faces) {
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const face_sets = VERTEX_MAP.map((vs) => vs.map((v) => faces[v]));
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return face_sets.map((fs) => find_dodeca_vertex(...fs));
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}
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// p is the permutation of the first face
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function dodecahedron_colours(vertices, p) {
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const LEFT_PART = [
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1, 2, 3, 4, 5, 3, 4, 5, 1, 2, 5, 1, 2, 3, 4, 2, 3, 4, 5, 1,
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];
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const RIGHT_PART = [
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1, 2, 3, 4, 5, 4, 5, 1, 2, 3, 3, 4, 5, 1, 2, 1, 2, 3, 4, 5,
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];
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const part = LEFT_PART;
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const colours = {};
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for( let i = 0; i < 20; i++ ) {
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const v = vertices[i];
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const colour = p[part[i] - 1];
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colours[v] = colour;
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}
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return colours;
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}
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// p is the permutation of the first face
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function colour_dodecahedron_from_face(dd, p) {
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const vertices = dodecahedron_vertices(dd);
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return dodecahedron_colours(vertices, p);
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}
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// from a dodecahedron and a face, get the adjoining dodecahedron
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function follow_face_to_dodeca(faces, startdd, nextf, flip=false) {
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const neighbours = find_adjacent_faces(faces, nextf);
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const nextnbors = neighbours.filter((f) => !startdd.includes(f));
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return faces_to_dodecahedron(faces, nextf, nextnbors[0], flip);
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}
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function find_edges(links, nid) {
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return links.filter((l) => l.source === nid || l.target === nid );
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}
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function find_adjacent_nodes(links, nid) {
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return find_edges(links, nid).map((l) => {
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if( l.source === nid ) {
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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 node_by_id(nodes, nid) {
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const ns = nodes.filter((n) => n.id === nid);
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return ns[0];
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}
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function find_adjacent_labels(nodes, links, nid) {
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return find_adjacent_nodes(links, nid).map(
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(nid) => node_by_id(nodes, nid).label
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);
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}
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function colour_next_dodeca_maybe(nodes, links, faces, colours, dd, nextf, nextdd) {
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const lastvs = dodecahedron_vertices(dd);
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const nextvs = dodecahedron_vertices(nextdd);
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// get the initial colour permutations from the existing labels;
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const p = [];
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for( let i = 0; i < 5; i ++ ) {
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p[i] = colours[nextvs[i]];
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}
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const nlabels = colour_dodecahedron_from_face(nextdd, p);
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// check if this is inconsistent with the original dd
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const n = nextf.nodes[0];
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const nbors = find_adjacent_nodes(links, n);
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const nextns = nbors.filter((n) => !lastvs.includes(n));
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const lastns = nbors.filter((n) => !nextvs.includes(n));
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const lastcol = colours[lastns[0]];
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const nextcol = nlabels[nextns[0]];
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if( lastcol === nextcol ) {
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// one node in the adjoining face has two same-coloured neighbours
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// console.log('chirality mismatch');
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// console.log(` test node ${n}`);
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// console.log(` neighbours ${lastns[0]} ${nextns[0]}`);
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return false;
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}
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return nlabels;
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}
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function meridian(nodes, links, faces, startf, startn, dir=11, max=10) {
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const o = face_plus_to_dodecahedron(faces, startf, startn);
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const colours = colour_dodecahedron_from_face(o, [ 1, 2, 3, 4, 5 ] );
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const dds = follow_meridian(nodes, links, faces, colours, o, dir, max);
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const labels = { 1: [], 2:[], 3:[], 4:[], 5:[] };
|
|
for( const vstr in colours ) {
|
|
labels[colours[vstr]].push(Number(vstr));
|
|
}
|
|
|
|
return { dodecahedra: dds, labels: labels };
|
|
|
|
}
|
|
|
|
|
|
function meridian_bump(nodes, links, faces, startf, startn, bumpdir=6) {
|
|
const o = face_plus_to_dodecahedron(faces, startf, startn);
|
|
const dir = 11;
|
|
const max = 10;
|
|
|
|
const colours = colour_dodecahedron_from_face(o, [ 1, 2, 3, 4, 5 ] );
|
|
|
|
const dds = follow_meridian(nodes, links, faces, colours, o, dir, max);
|
|
|
|
const dd4 = dds[4];
|
|
const nextf = dd4[bumpdir];
|
|
const bump = follow_face_to_dodeca(faces, dd4, nextf);
|
|
const ncolours = colour_next_dodeca_maybe(nodes, links, faces, colours, dd4, nextf, bump);
|
|
|
|
add_colours(colours, ncolours);
|
|
|
|
const labels = { 1: [], 2:[], 3:[], 4:[], 5:[] };
|
|
for( const vstr in colours ) {
|
|
labels[colours[vstr]].push(Number(vstr));
|
|
}
|
|
|
|
return { dodecahedra: dds, labels: labels };
|
|
|
|
}
|
|
|
|
|
|
|
|
function all_meridians(nodes, links, faces, startf, startn) {
|
|
const o = face_plus_to_dodecahedron(faces, startf, startn);
|
|
|
|
const colours = colour_dodecahedron_from_face(o, [ 1, 2, 3, 4, 5 ] );
|
|
|
|
// first meridian
|
|
const dds = follow_meridian(nodes, links, faces, colours, o, 11, 10);
|
|
for ( const f of [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ] ) {
|
|
follow_meridian(nodes, links, faces, colours, o, f, 4);
|
|
}
|
|
|
|
const labels = { 1: [], 2:[], 3:[], 4:[], 5:[] };
|
|
for( const vstr in colours ) {
|
|
labels[colours[vstr]].push(Number(vstr));
|
|
}
|
|
|
|
return labels;
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
// go along a meridian
|
|
// modifies colours
|
|
|
|
function follow_meridian(nodes, links, faces, colours, odd, dir, max) {
|
|
let ncolours = {};
|
|
const dds = [ odd ];
|
|
while( ncolours && dds.length < max ) {
|
|
const dd = dds[dds.length - 1];
|
|
const nextf = dds.length === 1 ? dd[dir] : dd[11];
|
|
|
|
let nextdd = follow_face_to_dodeca(faces, dd, nextf);
|
|
ncolours = colour_next_dodeca_maybe(nodes, links, faces, colours, dd, nextf, nextdd);
|
|
|
|
if( !ncolours ) {
|
|
nextdd = follow_face_to_dodeca(faces, dd, nextf, true);
|
|
ncolours = colour_next_dodeca_maybe(nodes, links, faces, colours, dd, nextf, nextdd);
|
|
if( !ncolours ) {
|
|
console.log("*** two mismatches");
|
|
}
|
|
}
|
|
|
|
for( const vertex in ncolours ) {
|
|
if( vertex in colours ) {
|
|
if( colours[vertex] !== ncolours[vertex] ) {
|
|
console.log(`*** label mismatch at ${vertex}: ${colours[vertex]}/${ncolours[vertex]}`);
|
|
}
|
|
} else {
|
|
colours[vertex] = ncolours[vertex];
|
|
}
|
|
}
|
|
dds.push(nextdd);
|
|
}
|
|
return dds;
|
|
}
|
|
|
|
|
|
function follow_and_colour(nodes, links, faces, colours, dd, face) {
|
|
let nextdd = follow_face_to_dodeca(faces, dd, face);
|
|
let ncolours = colour_next_dodeca_maybe(nodes, links, faces, colours, dd, face, nextdd);
|
|
|
|
if( !ncolours ) {
|
|
nextdd = follow_face_to_dodeca(faces, dd, face, true);
|
|
ncolours = colour_next_dodeca_maybe(nodes, links, faces, colours, dd, face, nextdd);
|
|
if( !ncolours ) {
|
|
console.log("two mismatches");
|
|
}
|
|
}
|
|
return [ nextdd, ncolours ];
|
|
}
|
|
|
|
|
|
function add_colours(colours, ncolours) {
|
|
for( const vertex in ncolours ) {
|
|
if( vertex in colours ) {
|
|
if( colours[vertex] !== ncolours[vertex] ) {
|
|
console.log(`label mismatch at ${vertex}: ${colours[vertex]}/${ncolours[vertex]}`);
|
|
}
|
|
} else {
|
|
colours[vertex] = ncolours[vertex];
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
// "arctic circle" - this one works
|
|
|
|
function arctic(nodes, links, faces, startf, startn, max) {
|
|
console.log(startf);
|
|
const pole = face_plus_to_dodecahedron(faces, startf, startn);
|
|
const dds = [ pole ];
|
|
// colour first cell
|
|
|
|
const colours = colour_dodecahedron_from_face(dds[0], [ 1, 2, 3, 4, 5 ] );
|
|
const vs = dodecahedron_vertices(dds[0]);
|
|
|
|
let ncolours = {};
|
|
|
|
for( const face of pole ) {
|
|
|
|
let nextdd = follow_face_to_dodeca(faces, pole, face);
|
|
ncolours = colour_next_dodeca_maybe(nodes, links, faces, colours, pole, face, nextdd);
|
|
|
|
if( !ncolours ) {
|
|
nextdd = follow_face_to_dodeca(faces, pole, face, true);
|
|
ncolours = colour_next_dodeca_maybe(nodes, links, faces, colours, pole, face, nextdd);
|
|
if( !ncolours ) {
|
|
console.log("two mismatches");
|
|
}
|
|
}
|
|
for( const vertex in ncolours ) {
|
|
if( vertex in colours ) {
|
|
if( colours[vertex] !== ncolours[vertex] ) {
|
|
console.log(`label mismatch at ${vertex}: ${colours[vertex]}/${ncolours[vertex]}`);
|
|
}
|
|
} else {
|
|
colours[vertex] = ncolours[vertex];
|
|
}
|
|
}
|
|
dds.push(nextdd);
|
|
}
|
|
|
|
|
|
const labels = { 1: [], 2:[], 3:[], 4:[], 5:[] };
|
|
for( const vstr in colours ) {
|
|
labels[colours[vstr]].push(Number(vstr));
|
|
}
|
|
|
|
|
|
return { dodecahedra: dds, labels: labels };
|
|
|
|
|
|
|
|
}
|
|
|
|
|
|
|
|
// this is the final one that works for the whole 120-cell
|
|
|
|
export function label_120cell(nodes, links, faces, startf, startn) {
|
|
const pole = face_plus_to_dodecahedron(faces, startf, startn);
|
|
const dds = [ pole ];
|
|
|
|
const seen = {};
|
|
seen[dd_fingerprint(pole)] = true;
|
|
|
|
const colours = colour_dodecahedron_from_face(dds[0], [ 1, 2, 3, 4, 5 ] );
|
|
const vs = dodecahedron_vertices(dds[0]);
|
|
|
|
for( const face of pole ) {
|
|
const [ nextdd, ncolours ] = follow_and_colour(
|
|
nodes, links, faces, colours, pole, face
|
|
);
|
|
add_colours(colours, ncolours);
|
|
dds.push(nextdd);
|
|
seen[dd_fingerprint(nextdd)] = true;
|
|
}
|
|
|
|
|
|
for( const a of dds.slice(1, 13) ) {
|
|
for( const i of [ 6, 7, 8, 9, 10 ] ) {
|
|
const [ nextdd, ncolours ] = follow_and_colour(
|
|
nodes, links, faces, colours, a, a[i]
|
|
);
|
|
const fp = dd_fingerprint(nextdd);
|
|
if( !(fp in seen) ) {
|
|
add_colours(colours, ncolours);
|
|
dds.push(nextdd);
|
|
seen[fp] = true;
|
|
}
|
|
}
|
|
}
|
|
|
|
// meridians = 45
|
|
|
|
for( const a of dds.slice(1, 13) ) {
|
|
const [ nextdd, ncolours ] = follow_and_colour(
|
|
nodes, links, faces, colours, a, a[11]
|
|
);
|
|
const fp = dd_fingerprint(nextdd);
|
|
if( !(fp in seen) ) {
|
|
add_colours(colours, ncolours);
|
|
dds.push(nextdd);
|
|
seen[fp] = true;
|
|
}
|
|
}
|
|
|
|
// the 30 equatorials?
|
|
|
|
|
|
for( const a of dds.slice(13, 46) ) {
|
|
for( const i of [ 6, 7, 8, 9, 10 ] ) {
|
|
const [ nextdd, ncolours ] = follow_and_colour(
|
|
nodes, links, faces, colours, a, a[i]
|
|
);
|
|
const fp = dd_fingerprint(nextdd);
|
|
if( !(fp in seen) ) {
|
|
add_colours(colours, ncolours);
|
|
dds.push(nextdd);
|
|
seen[fp] = true;
|
|
}
|
|
}
|
|
}
|
|
|
|
for( const a of dds.slice(33, 76) ) {
|
|
for( const i of [ 6, 7, 8, 9, 10 ] ) {
|
|
const [ nextdd, ncolours ] = follow_and_colour(
|
|
nodes, links, faces, colours, a, a[i]
|
|
);
|
|
const fp = dd_fingerprint(nextdd);
|
|
if( !(fp in seen) ) {
|
|
add_colours(colours, ncolours);
|
|
dds.push(nextdd);
|
|
seen[fp] = true;
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
// this should get the rest or explode!
|
|
|
|
|
|
for( const a of dds ) {
|
|
for( const i of [ 6, 7, 8, 9, 10 ] ) {
|
|
const [ nextdd, ncolours ] = follow_and_colour(
|
|
nodes, links, faces, colours, a, a[i]
|
|
);
|
|
const fp = dd_fingerprint(nextdd);
|
|
if( !(fp in seen) ) {
|
|
add_colours(colours, ncolours);
|
|
dds.push(nextdd);
|
|
seen[fp] = true;
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
const labels = { 1: [], 2:[], 3:[], 4:[], 5:[] };
|
|
for( const vstr in colours ) {
|
|
labels[colours[vstr]].push(Number(vstr));
|
|
}
|
|
|
|
|
|
return { dodecahedra: dds, labels: labels };
|
|
}
|
|
|
|
|
|
|
|
|
|
export function cell120_layers(nodes, links, faces, startf, startn, max_layer) {
|
|
const pole = face_plus_to_dodecahedron(faces, startf, startn);
|
|
const dds = [ pole ];
|
|
const dd_families = { "0": [ pole ] }
|
|
|
|
const seen = {};
|
|
seen[dd_fingerprint(pole)] = true;
|
|
|
|
const colours = colour_dodecahedron_from_face(dds[0], [ 1, 2, 3, 4, 5 ] );
|
|
const vs = dodecahedron_vertices(dds[0]);
|
|
|
|
// arctic
|
|
|
|
if( max_layer > 0 ) {
|
|
dd_families["1"] = [];
|
|
|
|
for( const face of pole ) {
|
|
const [ nextdd, ncolours ] = follow_and_colour(
|
|
nodes, links, faces, colours, pole, face
|
|
);
|
|
add_colours(colours, ncolours);
|
|
dds.push(nextdd);
|
|
dd_families["1"].push(nextdd);
|
|
seen[dd_fingerprint(nextdd)] = true;
|
|
}
|
|
}
|
|
|
|
// subarctic - interstitial
|
|
|
|
if( max_layer > 1 ) {
|
|
dd_families["2"] = [];
|
|
|
|
for( const a of dd_families["1"] ) {
|
|
for( const i of [ 6, 7, 8, 9, 10 ] ) {
|
|
const [ nextdd, ncolours ] = follow_and_colour(
|
|
nodes, links, faces, colours, a, a[i]
|
|
);
|
|
const fp = dd_fingerprint(nextdd);
|
|
if( !(fp in seen) ) {
|
|
add_colours(colours, ncolours);
|
|
dds.push(nextdd);
|
|
dd_families["2"].push(nextdd);
|
|
seen[fp] = true;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
// tropic of cancer
|
|
|
|
if( max_layer > 2 ) {
|
|
dd_families["3"] = [];
|
|
|
|
for( const a of dd_families["1"] ) {
|
|
const [ nextdd, ncolours ] = follow_and_colour(
|
|
nodes, links, faces, colours, a, a[11]
|
|
);
|
|
const fp = dd_fingerprint(nextdd);
|
|
if( !(fp in seen) ) {
|
|
add_colours(colours, ncolours);
|
|
dds.push(nextdd);
|
|
dd_families["3"].push(nextdd);
|
|
seen[fp] = true;
|
|
}
|
|
}
|
|
}
|
|
|
|
if( max_layer > 3 ) {
|
|
// equator
|
|
|
|
dd_families["4"] = [];
|
|
|
|
for( const a of dds.slice(13, 46) ) {
|
|
for( const i of [ 6, 7, 8, 9, 10 ] ) {
|
|
const [ nextdd, ncolours ] = follow_and_colour(
|
|
nodes, links, faces, colours, a, a[i]
|
|
);
|
|
const fp = dd_fingerprint(nextdd);
|
|
if( !(fp in seen) ) {
|
|
add_colours(colours, ncolours);
|
|
dd_families["4"].push(nextdd);
|
|
dds.push(nextdd);
|
|
seen[fp] = true;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
if( max_layer > 4 ) {
|
|
dd_families["5"] = [];
|
|
|
|
for( const a of dd_families["4"] ) {
|
|
for( const i of [ 6, 7, 8, 9, 10 ] ) {
|
|
const [ nextdd, ncolours ] = follow_and_colour(
|
|
nodes, links, faces, colours, a, a[i]
|
|
);
|
|
const fp = dd_fingerprint(nextdd);
|
|
if( !(fp in seen) ) {
|
|
add_colours(colours, ncolours);
|
|
dds.push(nextdd);
|
|
dd_families["5"].push(nextdd);
|
|
seen[fp] = true;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
const labels = { 1: [], 2:[], 3:[], 4:[], 5:[] };
|
|
for( const vstr in colours ) {
|
|
labels[colours[vstr]].push(Number(vstr));
|
|
}
|
|
|
|
|
|
return { dodecahedra: dds, labels: labels, families: dd_families };
|
|
}
|
|
|
|
|
|
|
|
|
|
// for a face, pick an edge, and then find the other two faces which
|
|
// share this edge. These can be used as the starting points for the
|
|
// first face's two dodecahedra
|
|
|
|
function find_edge_neighbours(faces, face) {
|
|
const n1 = face.nodes[0];
|
|
const n2 = face.nodes[1];
|
|
return faces.filter((f) => f.id !== face.id && f.nodes.includes(n1) && f.nodes.includes(n2));
|
|
}
|
|
|
|
|
|
// each face is in two dodecahedra: this returns them both
|
|
|
|
function face_to_dodecahedra(faces, f) {
|
|
const edge_friends = find_edge_neighbours(faces, f);
|
|
const d1 = make_dodecahedron(faces, f, edge_friends[0]);
|
|
const d2 = make_dodecahedron(faces, f, edge_friends[1]);
|
|
return [ d1, d2 ];
|
|
}
|
|
|
|
// brute-force calculation of all dodecahedra
|
|
|
|
function dd_fingerprint(dodecahedron) {
|
|
const ids = dodecahedron.map((face) => face.id);
|
|
ids.sort((a, b) => a - b);
|
|
return ids.join(',');
|
|
}
|
|
|
|
function make_120cell_cells(faces) {
|
|
const dodecas = [];
|
|
const seen = {};
|
|
let i = 1;
|
|
for( const face of faces ) {
|
|
const dds = face_to_dodecahedra(faces, face);
|
|
for( const dd of dds ) {
|
|
const fp = dd_fingerprint(dd);
|
|
if( ! (fp in seen) ) {
|
|
const d = {
|
|
id: i,
|
|
faces: dd,
|
|
nodes: dodecahedron_vertices(dd),
|
|
}
|
|
dodecas.push(d);
|
|
i += 1;
|
|
seen[fp] = 1;
|
|
}
|
|
}
|
|
}
|
|
return dodecas;
|
|
}
|
|
|
|
|
|
|
|
function dodeca_travers(nodes, links, n, fn) {
|
|
const queue = [];
|
|
const seen = {};
|
|
const nodes_id = {};
|
|
|
|
queue.push(n.id);
|
|
|
|
while( queue.length > 0 ) {
|
|
const v = queue.shift();
|
|
find_adjacent(links, v).map((aid) => {
|
|
if( !(aid in seen) ) {
|
|
seen[aid] = true;
|
|
queue.push(aid);
|
|
fn(nodes_id[aid]);
|
|
}
|
|
})
|
|
}
|
|
}
|
|
|
|
|
|
|
|
const cell120 = () => {
|
|
const nodes = make_120cell_vertices();
|
|
const links = auto_detect_edges(nodes, 4);
|
|
return {
|
|
nodes: nodes,
|
|
links: links,
|
|
geometry: {
|
|
node_size: 0.02,
|
|
link_size: 0.02
|
|
}
|
|
|
|
}
|
|
}
|
|
|
|
|
|
function dodeca_nodes(dd) {
|
|
const ns = new Set();
|
|
for( const face of dd.faces ) {
|
|
for( const node of face.nodes ) {
|
|
ns.add(node);
|
|
}
|
|
}
|
|
dd.nodes = Array.from(ns);
|
|
}
|
|
|
|
|
|
function label_nodes(nodes, ids, label) {
|
|
nodes.filter((n) => ids.includes(n.id)).map((n) => n.label = label);
|
|
}
|
|
|
|
function meridian_label_120cell(nodes) {
|
|
|
|
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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1
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function check_120cell_nodes(nodes) {
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nodes.map((n) => {
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const vs = find_adjacent_labels(nodes, links, n.id);
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vs.push(n.label);
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console.log(`Node ${n.id} and neighbours ${vs}`);
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const fp = vs.sort().join(',');
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if( fp !== "1,2,3,4,5" ) {
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console.log(`Label error ${n.id} ${fp}`)
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}
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});
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}
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function make_dodecahedron_vertices() {
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const phi = 0.5 * (1 + Math.sqrt(5));
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const phiinv = 1 / phi;
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const nodes = [
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{ x: 1, y: 1, z: 1, w: 0 },
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{ x: 1, y: 1, z: -1, w: 0 },
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{ x: 1, y: -1, z: 1, w: 0 },
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{ x: 1, y: -1, z: -1, w: 0 },
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{ x: -1, y: 1, z: 1, w: 0 },
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{ x: -1, y: 1, z: -1, w: 0 },
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{ x: -1, y: -1, z: 1, w: 0 },
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{ x: -1, y: -1, z: -1, w: 0 }
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].flat();
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scale_nodes(nodes, 0.5);
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return nodes;
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}
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// this one does the coherent indexing / partition into 600-cells
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export function make_labelled_120cell() {
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const nodes = make_120cell_vertices();
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const links = auto_detect_edges(nodes, 4);
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const faces = auto_120cell_faces(links);
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const labelled = label_120cell(nodes, links, faces, faces[0], 341);
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return labelled;
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}
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// calculate the w-distance of a dodecahedron's centroid
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export function dd_w_distance(nodes, dd) {
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const vertices = new Set();
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dd.map((f) => f.nodes.map((n) => vertices.add(n)));
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let w = 0;
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for( const nid of vertices ) {
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const node = node_by_id(nodes, nid);
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w += node.w;
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}
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return w / 20;
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}
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export function sort_dds_w(nodes, dds) {
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dds.sort((a, b) => {
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return dd_w_distance(nodes, a) - dd_w_distance(nodes, b)
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})
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}
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export function find_antipode_dd(nodes, links, dd) {
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}
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// notes because I'm too sick to continue working on this today
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// the vertices which aren't counted by the layers are showing
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// up in the visualisation because they are labelled "0" by default -
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// for this to work better there needs to be a value which is never
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// displayed.
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// in the current layer algorithm, layer '5' (the one after the equator)
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// is too greedy
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export function make_layered_120cell(max_layer) {
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const nodes = make_120cell_vertices();
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const links = auto_detect_edges(nodes, 4);
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const faces = auto_120cell_faces(links);
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const labelled = label_120cell(nodes, links, faces, faces[628], 250, max_layer);
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// get layers from sorted w-distance order
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const dds = labelled.dodecahedra;
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dds.sort((a, b) => dd_w_distance(nodes, b) - dd_w_distance(nodes, a));
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const LAYERS = [
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[ "0", 1 ],
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[ "1", 12 ],
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[ "2", 20 ],
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[ "3", 12 ],
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[ "4", 30 ],
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[ "5", 12 ],
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[ "6", 20 ],
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[ "7", 12 ],
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[ "8", 1]
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];
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const layer_dds = labelled["families"];
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const vertices_layers = {};
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const seen = {};
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let i = 0;
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for( const layer of LAYERS ) {
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const label = layer[0];
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const n = layer[1];
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vertices_layers[label] = [];
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console.log(`Layer ${label} starting at ${i}`);
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for( const dd of dds.slice(i, i + n) ) {
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console.log(dd_w_distance(nodes, dd));
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for( const face of dd ) {
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for( const n of face.nodes ) {
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if( !seen[n] ) {
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vertices_layers[label].push(n);
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seen[n] = true;
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}
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}
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}
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}
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i += n;
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}
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return JSON.stringify(vertices_layers);
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}
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export function make_meridians(bumpdir) {
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const nodes = make_120cell_vertices();
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const links = auto_detect_edges(nodes, 4);
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const faces = auto_120cell_faces(links);
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const mbs ={}
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for( const bumpdir of [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 ] ) {
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mbs[bumpdir] = meridian_bump(nodes, links, faces, faces[0], 341, bumpdir)
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}
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return mbs;
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//
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}
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// console.log("Calculating 120-cell colours")
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// const a2 = arctic_two(nodes, links, faces, faces[0], 341)
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// console.log(`got ${a2.dodecahedra.length}`);
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// const labels = a2.labels;
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// console.log("labelling nodes");
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// for( const cstr in labels ) {
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// label_nodes(nodes, labels[cstr], Number(cstr));
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// }
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