fourdjs/polytopes.js

import * as PERMUTE from './permute.js';

function scale_and_index(nodes, scale) {
	let i = 1;
	for( const n of nodes ) {
		n["id"] = i;
		i++;
		for( const a of [ 'x', 'y', 'z', 'w' ] ) {
			n[a] = scale * n[a];
		}
	}
	return nodes;
}

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

export 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
		}
	};
};


export const cell16 = () => {
	let nodes = PERMUTE.coordinates([1, 1, 1, 1],  0);
	nodes = nodes.filter((n) => n.x * n.y * n.z * n.w > 0);
	scale_and_index(nodes, 0.75);
	const links = auto_detect_edges(nodes, 6);

	return {
		nodes: nodes,
		links: links,
		geometry: {
			node_size: 0.02,
			link_size: 0.02
		}
	};
};



export const tesseract = () => {
	const nodes = scale_and_index(PERMUTE.coordinates([1, 1, 1, 1],  0), 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
		}
	};
}




export const cell24 = () => {
	const nodes = scale_and_index(PERMUTE.coordinates([0, 0, 1, 1],  0), 1);
	const links = auto_detect_edges(nodes, 6);

	return {
		nodes: nodes,
		links: links,
		geometry: {
			node_size: 0.02,
			link_size: 0.02
		}
	};
}


// face detection for the 120-cell

// NOTE: all of these return node ids, not nodes

// return all the links which connect to a node

function nodes_links(links, nodeid) {
	return links.filter((l) => l.source === nodeid || l.target === nodeid);
}

// filter to remove a link to a given id from a set of links

function not_to_this(link, nodeid) {
	return !(link.source === nodeid || link.target === nodeid);
}

// given nodes n1, n2, return all neighbours of n2 which are not n1

function unmutuals(links, n1id, n2id) {
	const nlinks = nodes_links(links, n2id).filter((l) => not_to_this(l, n1id));
	return nlinks.map((l) => {
		if( l.source === n2id ) {
			return l.target;
		} else {
			return l.source;
		}
	})
}


function fingerprint(ids) {
	const sids = [...ids];
	sids.sort();
	return sids.join(',');
}



function auto_120cell_faces(links) {
	const faces = [];
	const seen = {};
	let id = 1;
	for( const edge of links ) {
		const v1 = edge.source;
		const v2 = edge.target;
		const n1 = unmutuals(links, v2, v1);
		const n2 = unmutuals(links, v1, v2);
		const shared = [];
		for( const a of n1 ) {
			const an = unmutuals(links, v1, a);
			for( const d of n2 ) {
				const dn = unmutuals(links, v2, d);
				for( const x of an ) {
					for( const y of dn ) {
						if( x == y ) {
							shared.push([v1, a, x, d, v2])
						}
					}
				}
			}
		}
		if( shared.length !== 3 ) {
			console.log(`Bad shared faces for ${edge.id} ${v1} ${v2}`);
		}
		for( const face of shared ) {
			const fp = fingerprint(face);
			if( !seen[fp] ) {
				faces.push({ id: id, nodes: face });
				id++;
				seen[fp] = true;
			}
		}
	}
	return faces;
}



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 = [
		PERMUTE.coordinates([0, 0, 2, 2],  0),
		PERMUTE.coordinates([1, 1, 1, r5], 0),
		PERMUTE.coordinates([phi, phi, phi, phi2inv], 0),
		PERMUTE.coordinates([phiinv, phiinv, phiinv, phi2], 0),

		PERMUTE.coordinates([phi2, phi2inv, 1, 0], 0, true),
		PERMUTE.coordinates([r5, phiinv, phi, 0], 0, true),
		PERMUTE.coordinates([2, 1, phi, phiinv], 0, true),
		].flat();
	return scale_and_index(nodes, 0.5);
}


export const cell120 = () => {
	const nodes  = make_120cell_vertices();
	const links = auto_detect_edges(nodes, 4);
	const faces = auto_120cell_faces(links);
	return {
		nodes: nodes,
		links: links,
		geometry: {
			node_size: 0.02,
			link_size: 0.02
		},
		faces: faces
	}
}


function make_600cell_vertices() {
	const phi = 0.5 * (1 + Math.sqrt(5));  

	const nodes = [
		PERMUTE.coordinates([0, 0, 0, 2],  0),
		PERMUTE.coordinates([1, 1, 1, 1],  0),

		PERMUTE.coordinates([phi, 1, 1 / phi, 0], 0, true)
		].flat();
	return scale_and_index(nodes, 0.75);
}


export const cell600 = () => {
	const nodes  = make_600cell_vertices();
	const links = auto_detect_edges(nodes, 12);
	return {
		nodes: nodes,
		links: links,
		geometry: {
			node_size: 0.02,
			link_size: 0.02
		}
	}
}