Several different broken attempts at indexing

permute_testbed.js

@@ -0,0 +1,391 @@
+
+// Utilities for generating sets of coordinates based on 
+// permutations, even permutations and changes of sign.
+// Based on https://www.qfbox.info/epermute
+
+
+function pandita(a) {
+	const n = a.length;
+	for( let k = n - 2; k >= 0; k-- ) {
+		if( a[k] < a[k + 1] ) {
+			for( let l = n - 1; l >= 0; l-- ) {
+				if( a[k] < a[l] ) {
+					const tmp = a[k];
+					a[k] = a[l];
+					a[l] = tmp;
+					const revtail = a.slice(k + 1);
+					revtail.reverse();
+					for( let i = 0; i < revtail.length; i++ ) {
+						a[k + 1 + i] = revtail[i];
+					}
+					return Math.floor(revtail.length / 2) + 1;
+				}
+			}
+			console.log("Shouldn't get here");
+			process.exit();
+		}
+	}
+	return false;
+}
+
+function permutations_old(a) {
+	a.sort();
+	const ps = [ [...a] ];
+	let running = true;
+	while( running ) {
+		const s = pandita(a);
+		if( s ) {
+			ps.push([...a]);
+		} else {
+			running = false;
+		}
+	}
+	return ps;
+}
+
+function permutations(a) {
+	a.sort();
+	const ps = [ [...a] ];
+	let running = true;
+	while( pandita(a) > 0 ) {
+		ps.push([...a]);
+	}
+	return ps;
+}
+
+
+function permutations_even(a) {
+	a.sort();
+	let parity = 'even';
+	const ps = [ [...a] ];
+	let running = true;
+	while( running ) {
+		const s = pandita(a);
+		if( s ) {
+			if( parity === 'even' ) {
+				if( s % 2 === 1 ) {
+					parity = 'odd';
+				}
+			} else {
+				if( s % 2 === 1 ) {
+					parity = 'even';
+				}
+			}
+			if( parity === 'even' ) {
+				ps.push([...a]);
+			}
+		} else {
+			running = false;
+		}
+	}
+	return ps;
+}
+
+// for a given permutation, say [ 1, 1, 0, 0 ], return all
+// of the valid changes of sign, so:
+// [ [1, 1, 0, 0 ], [ -1, 1, 0, 0 ], [ 1, -1, 0, 0 ], [-1, -1, 0, 0 ]]
+// ie don't do it on the zeros
+
+function expand_sign(a, label) {
+	const expanded = [];
+	const exv = a.map((v) => v ? [ -v, v ] : [ 0 ]);
+	for( const xv of exv[0] ) {
+		for( const yv of exv[1] ) {
+			for( const zv of exv[2] ) {
+				for( const wv of exv[3] ) {
+					expanded.push({label: label, x: xv, y:yv, z:zv, w:wv});
+				}
+			}
+		}
+	}
+	return expanded;
+}
+
+
+function coordinates(a, id0=1, even=false) {
+	const ps = even ? permutations_even(a) : permutations(a);
+	const coords = [];
+	for( const p of ps ) {
+		const expanded = expand_sign(p, 0);
+		coords.push(...expanded);
+	}
+	return coords;
+}
+
+
+
+function index_nodes(nodes, scale) {
+	let i = 1;
+	for( const n of nodes ) {
+		n["id"] = i;
+		i++;
+	}
+}
+
+function scale_nodes(nodes, scale) {
+	for( const n of nodes ) {
+		for( const a of [ 'x', 'y', 'z', 'w' ] ) {
+			n[a] = scale * n[a];
+		}
+	}
+}
+
+function dist2(n1, n2) {
+	return (n1.x - n2.x) ** 2 + (n1.y - n2.y) ** 2 + (n1.z - n2.z) ** 2 + (n1.w - n2.w) ** 2;
+}
+
+function auto_detect_edges(nodes, neighbours, debug=false) {
+	const seen = {};
+	const nnodes = nodes.length;
+	const links = [];
+	let id = 1;
+	for( const n1 of nodes ) {
+		const d2 = [];
+		for( const n2 of nodes ) {
+			d2.push({ d2: dist2(n1, n2), id: n2.id });
+		}
+		d2.sort((a, b) => a.d2 - b.d2);
+		const closest = d2.slice(1, neighbours + 1);
+		if( debug ) {
+			console.log(`closest = ${closest.length}`);
+			console.log(closest);
+		}
+		for( const e of closest ) {
+			const ids = [ n1.id, e.id ];
+			ids.sort();
+			const fp = ids.join(',');
+			if( !seen[fp] ) {
+				seen[fp] = true;
+				links.push({ id: id, label: 0, source: n1.id, target: e.id });
+				id++;
+			}
+		}
+	}
+	if( debug ) {
+		console.log(`Found ${links.length} edges`)
+	}
+	return links;
+}
+
+// too small and simple to calculate
+
+const cell5 = () => {
+	const r5 = Math.sqrt(5);
+	const r2 = Math.sqrt(2) / 2;
+	return {
+		nodes: [
+	      {id:1, x: r2, y: r2, z: r2, w: -r2 / r5 },
+	      {id:2, x: r2, y: -r2, z: -r2, w: -r2 / r5 },
+	      {id:3, x: -r2, y: r2, z: -r2, w: -r2 / r5 },
+	      {id:4, x: -r2, y: -r2, z: r2, w: -r2 / r5 },
+	      {id:5, x: 0, y: 0, z: 0, w: 4 * r2 / r5 },
+		],
+		links: [
+			{ id:1, source:1, target: 2},
+			{ id:2, source:1, target: 3},
+			{ id:3, source:1, target: 4},
+			{ id:4, source:1, target: 5},
+			{ id:5, source:2, target: 3},
+			{ id:6, source:2, target: 4},
+			{ id:7, source:2, target: 5},
+			{ id:8, source:3, target: 4},
+			{ id:9, source:3, target: 5},
+			{ id:10, source:4, target: 5},
+		],
+		geometry: {
+			node_size: 0.02,
+			link_size: 0.02
+		}
+	};
+};
+
+
+const cell16 = () => {
+	let nodes = coordinates([1, 1, 1, 1],  0);
+	nodes = nodes.filter((n) => n.x * n.y * n.z * n.w > 0);
+	index_nodes(nodes);
+	scale_nodes(nodes, 0.75);
+	const links = auto_detect_edges(nodes, 6);
+
+	return {
+		nodes: nodes,
+		links: links,
+		geometry: {
+			node_size: 0.02,
+			link_size: 0.02
+		}
+	};
+};
+
+
+
+const tesseract = () => {
+	const nodes = coordinates([1, 1, 1, 1],  0);
+	index_nodes(nodes);
+	scale_nodes(nodes, Math.sqrt(2) / 2);
+	const links = auto_detect_edges(nodes, 4);
+
+	return {
+		nodes: nodes,
+		links: links,
+		geometry: {
+			node_size: 0.02,
+			link_size: 0.02
+		}
+	};
+}
+
+
+
+
+const cell24 = () => {
+	const nodes = coordinates([0, 0, 1, 1], 0);
+	index_nodes(nodes);
+	const links = auto_detect_edges(nodes, 6);
+
+	return {
+		nodes: nodes,
+		links: links,
+		geometry: {
+			node_size: 0.02,
+			link_size: 0.02
+		}
+	};
+}
+
+
+
+
+function make_120cell_vertices() {
+	const phi = 0.5 * (1 + Math.sqrt(5));  
+	const r5 = Math.sqrt(5);   
+	const phi2 = phi * phi;    
+	const phiinv = 1 / phi;    
+	const phi2inv = 1 / phi2;  
+
+	const nodes = [
+		coordinates([0, 0, 2, 2],  0),
+		coordinates([1, 1, 1, r5], 0),
+		coordinates([phi, phi, phi, phi2inv], 0),
+		coordinates([phiinv, phiinv, phiinv, phi2], 0),
+
+		coordinates([phi2, phi2inv, 1, 0], 0, true),
+		coordinates([r5, phiinv, phi, 0], 0, true),
+		coordinates([2, 1, phi, phiinv], 0, true),
+		].flat();
+	index_nodes(nodes);
+	scale_nodes(nodes, 0.5);
+	return nodes;
+}
+
+
+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 make_600cell_vertices() {
+	const phi = 0.5 * (1 + Math.sqrt(5));  
+
+	const nodes = [
+		coordinates([0, 0, 0, 2],  0),
+		coordinates([1, 1, 1, 1],  1),
+
+		coordinates([phi, 1, 1 / phi, 0], 1, true)
+		].flat();
+
+	index_nodes(nodes);
+	return nodes;
+}
+
+
+function find_peers(nodesid, seen, n, d) {
+	const EPSILON = 0.02;
+	console.log(`find_peers ${n} (already seen ${seen})`)
+	return Object.keys(nodesid).filter((n1) => {
+		if( seen.includes(n1) ) {
+			return false;
+		}
+		const d2 = dist2(nodesid[n1], nodesid[n]);
+		return Math.abs(d2 - d ** 2) < EPSILON;
+	});
+}
+
+
+
+
+
+function partition_from_node(nodesid, start, d) {
+	const group = [];
+	const looping = true;
+	let ns = find_peers(nodesid, group, start, d);
+	console.log(`0 ${ns}`);
+	let i = 1;
+	while( ns.length > 0 && i < ns.length ) {
+		group.push(...ns);
+		ns = find_peers(nodesid, group, ns[i], d);
+		console.log(`${i} ${ns}`);
+		i++;
+	}
+	return group;
+}
+
+
+function partition_nodes_by_distance(nodes, d) {
+	const groups = [];
+	const nodesid = {};
+	const EPSILON = 0.005;
+
+	for( const node of nodes ) {
+		nodesid[node.id] = node;
+	}
+
+	while( Object.keys(nodesid).length > 0 ) {
+		const start = Object.keys(nodesid)[0];
+		console.log(`Start node = ${start}`);
+		const group = partition_from_node(nodesid, start, d);
+		if( group.length < 1 ) {
+			console.log("something went wrong, empty neighbour group");
+			break;
+		}
+		for( const g of group ) {
+			delete nodesid[g];
+		}
+		groups.push(group);
+		console.log(`Added group ${group}`);
+	}
+	return groups;
+}
+
+
+
+
+
+const cell600 = () => {
+	const nodes  = make_600cell_vertices();
+	const links = auto_detect_edges(nodes, 12);
+	return {
+		nodes: nodes,
+		links: links,
+		geometry: {
+			node_size: 0.08,
+			link_size: 0.02
+		}
+	}
+}
+
+
+
+

polytopes.js

@@ -203,9 +203,9 @@ function make_600cell_vertices() {
 // I think that all of the vertices which belong to the same 24-cell group
 // are 2 units apart.
 
-function partition_nodes_by_distance(nodes, d) {
+function partition_nodes_by_distance_bad(nodes, d) {
 	const groups = [];
-	const EPSILON = 0.1;
+	const EPSILON = 0.002;
 	for( const n1 of nodes ) {
 		let matched = false;
 		for( const group of groups ) {
@@ -236,6 +236,55 @@ function partition_nodes_by_distance(nodes, d) {
 	return groups;
 }
 
+// find all nodes in nodesid which are d away from n (and are not n)
+
+function nodes_by_distance(nodesid, n, d) {
+	const EPSILON = 0.02;
+	const neighbours = Object.keys(nodesid).filter((n1id) => {
+		if( n1id !== n.id ) {
+			const d2 = dist2(nodesid[n1id], nodesid[n]);
+			console.log(`${n} ${n1id} ${d2}`);
+			return Math.abs(d2 - d ** 2) < EPSILON;
+		} else {
+			return false;
+		}
+	});
+	console.log(`neighbours at ${d} ${neighbours}`);
+	return neighbours;
+}
+
+
+
+
+
+function partition_nodes_by_distance(nodes, d) {
+	const groups = [];
+	const nodesid = {};
+	const EPSILON = 0.02;
+
+	for( const node of nodes ) {
+		nodesid[node.id] = node;
+	}
+
+	while( Object.keys(nodesid).length > 0 ) {
+		const start = Object.keys(nodesid)[0];
+		const group = [ start ];
+		
+		const neighbours = nodes_by_distance(nodesid, n, d).filter((n2) => !(n2 in group));
+		if( neighbours ) {
+			group.push(...neighbours);
+		}
+
+		const group = partition_r(nodesid, [ start ], start, d);
+		console.log(group);
+		for( const g of group ) {
+			delete nodesid[g];
+		}
+		groups.push(group);
+	}
+}
+
+