187 lines
3.7 KiB
JavaScript
187 lines
3.7 KiB
JavaScript
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// Utilities for generating sets of coordinates based on
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// permutations, even permutations and changes of sign.
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// Based on https://www.qfbox.info/epermute
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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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export 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 scale_and_index(nodes, scale) {
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let i = 1;
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for( const n of nodes ) {
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n["id"] = i;
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i++;
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for( const a of [ 'x', 'y', 'z', 'w' ] ) {
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n[a] = scale * n[a];
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}
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}
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return nodes;
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}
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function make_120cell_vertices() {
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const phi = 0.5 * (1 + Math.sqrt(5));
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const r5 = Math.sqrt(5);
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const phi2 = phi * phi;
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const phiinv = 1 / phi;
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const phi2inv = 1 / phi2;
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const nodes = [
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coordinates([2, 2, 0, 0], 0),
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coordinates([r5, 1, 1, 1], 1),
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coordinates([phi, phi, phi, phi2inv], 2),
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coordinates([phi, phiinv, phiinv, phiinv], 0),
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coordinates([phi2, phi2inv, 1, 0], 1, true),
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coordinates([r5, phiinv, phi, 0], 2, true),
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coordinates([2, 1, phi, phiinv], 0, true),
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].flat();
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return scale_and_index(nodes, 0.5);
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}
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function dist2(n1, n2) {
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return (n1.x - n2.x) ** 2 + (n1.y - n2.y) ** 2 + (n1.z - n2.z) ** 2 + (n1.w - n2.w) ** 2;
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}
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function make_120cell_edges(nodes) {
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const seen = {};
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const nnodes = nodes.length;
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const links = [];
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let id = 1;
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for( let i = 0; i < nnodes - 1; i++ ) {
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const d2 = [];
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for( let j = 0; j < nnodes; j++ ) {
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d2.push({ d2: dist2(nodes[i], nodes[j]), id: j });
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}
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d2.sort((a, b) => b.d2 - a.d2);
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const closest = d2.slice(1, 4);
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for( const e in closest ) {
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const ids = [ nodes[i].id, e.id ];
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ids.sort();
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const fp = ids.join(',');
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if( !seen[fp] ) {
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seen[fp] = true;
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links.push({ id: id, label: 0, source: nodes[i].id, target: e.id });
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id++;
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}
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}
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}
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return links;
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}
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const nodes = make_120cell_vertices();
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const links = make_120cell_edges(nodes);
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console.log(links); |