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;
}


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},
		]
	};
};


export const cell16 = () => {
	const s2 = Math.sqrt(2) * 0.5;
	return {
		nodes: [
			{ id: 1, x: -s2, y: -s2, z: -s2, w: -s2 },
			{ id: 2, x:  s2, y:  s2, z: -s2, w: -s2 },
			{ id: 3, x:  s2, y: -s2, z:  s2, w: -s2 },
			{ id: 4, x: -s2, y:  s2, z:  s2, w: -s2 },
			{ id: 5, x:  s2, y: -s2, z: -s2, w:  s2 },
			{ id: 6, x: -s2, y:  s2, z: -s2, w:  s2 },
			{ id: 7, x: -s2, y: -s2, z:  s2, w:  s2 },
			{ id: 8, x:  s2, y:  s2, z:  s2, w:  s2 },
		],

		// opposite pairs: 1 - 8
		//                 2 - 7
		//                 3 - 6
		//                 4 - 5   .. these don't have edges

		// label 1 links: 1 / 3 / 8 / 6
		// label 1 links: 2 / 4 / 7 / 5

		// label 2 links: 1 / 4 / 8 / 5
		// label 2 links: 2 / 3 / 7 / 6  (??)
 
		links: [
			{ id: 1, source: 1, target: 2, label: 1 },
			{ id: 2, source: 1, target: 3, label: 2  },
			{ id: 3, source: 1, target: 4, label: 3  },
			{ id: 4, source: 2, target: 3, label: 3  },
			{ id: 5, source: 2, target: 4, label: 2  },
			{ id: 6, source: 3, target: 4, label: 1 },

			{ id: 7, source: 5, target: 6, label: 1 },
			{ id: 8, source: 5, target: 7, label: 2 },
			{ id: 9, source: 5, target: 8, label: 3 },
			{ id: 10, source: 6, target: 7, label: 3 },
			{ id: 11, source: 6, target: 8, label: 2 },
			{ id: 12, source: 7, target: 8, label: 1 },

			{ id: 13, source: 1, target: 5, label: 3 },
			{ id: 14, source: 1, target: 6, label: 2 },
			{ id: 15, source: 1, target: 7, label: 1 },
			{ id: 16, source: 2, target: 5, label: 2 },
			{ id: 17, source: 2, target: 6, label: 3 },
			{ id: 18, source: 2, target: 8, label: 1 },

			{ id: 19, source: 3, target: 5, label: 1 },
			{ id: 20, source: 3, target: 7, label: 3 },
			{ id: 21, source: 3, target: 8, label: 2 },
			{ id: 22, source: 4, target: 6, label: 1 },
			{ id: 23, source: 4, target: 7, label: 2 },
			{ id: 24, source: 4, target: 8, label: 3 },


		]
	}
};


export const tesseract = () => {
	const s2 = Math.sqrt(2) * 0.5;
	return {
		nodes: [
			{ id: 1,  label: 1, x: -s2, y: -s2, z: -s2, w: -s2 },
			{ id: 2,  label: 2, x:  s2, y: -s2, z: -s2, w: -s2 },
			{ id: 3,  label: 2, x: -s2, y:  s2, z: -s2, w: -s2 },
			{ id: 4,  label: 1, x:  s2, y:  s2, z: -s2, w: -s2 },
			{ id: 5,  label: 2, x: -s2, y: -s2, z:  s2, w: -s2 },
			{ id: 6,  label: 1, x:  s2, y: -s2, z:  s2, w: -s2 },
			{ id: 7,  label: 1, x: -s2, y:  s2, z:  s2, w: -s2 },
			{ id: 8,  label: 2, x:  s2, y:  s2, z:  s2, w: -s2 },
			{ id: 9,  label: 2, x: -s2, y: -s2, z: -s2, w:  s2 },
			{ id: 10, label: 1, x:  s2, y: -s2, z: -s2, w:  s2 },
			{ id: 11, label: 1, x: -s2, y:  s2, z: -s2, w:  s2 },
			{ id: 12, label: 2, x:  s2, y:  s2, z: -s2, w:  s2 },
			{ id: 13, label: 1, x: -s2, y: -s2, z:  s2, w:  s2 },
			{ id: 14, label: 2, x:  s2, y: -s2, z:  s2, w:  s2 },
			{ id: 15, label: 2, x: -s2, y:  s2, z:  s2, w:  s2 },
			{ id: 16, label: 1, x:  s2, y:  s2, z:  s2, w:  s2 },
		],
		links: [
			{ id: 1, source: 1, target: 2 },
			{ id: 2, source: 2, target: 4 },
			{ id: 3, source: 4, target: 3 },
			{ id: 4, source: 3, target: 1 },
			{ id: 5, source: 5, target: 6 },
			{ id: 6, source: 6, target: 8 },
			{ id: 7, source: 8, target: 7 },
			{ id: 8, source: 7, target: 5 },
			{ id: 9, source: 1, target: 5 },
			{ id: 10, source: 2, target: 6 },
			{ id: 11, source: 3, target: 7 },
			{ id: 12, source: 4, target: 8 },

			{ id: 13, source: 9, target: 10 },
			{ id: 14, source: 10, target: 12 },
			{ id: 15, source: 12, target: 11 },
			{ id: 16, source: 11, target: 9 },
			{ id: 17, source: 13, target: 14 },
			{ id: 18, source: 14, target: 16 },
			{ id: 19, source: 16, target: 15 },
			{ id: 20, source: 15, target: 13 },
			{ id: 21, source: 9, target: 13 },
			{ id: 22, source: 10, target: 14 },
			{ id: 23, source: 11, target: 15 },
			{ id: 24, source: 12, target: 16 },

			{ id: 25, source: 1, target: 9 },
			{ id: 26, source: 2, target: 10 },
			{ id: 27, source: 3, target: 11 },
			{ id: 28, source: 4, target: 12 },
			{ id: 29, source: 5, target: 13 },
			{ id: 30, source: 6, target: 14 },
			{ id: 31, source: 7, target: 15 },
			{ id: 32, source: 8, target: 16 },

		]
	}
};

// this was done manually and I'm not sure if it's right

const CELL24_INDEXING = {
	x: { y: 1, z: 3, w: 2 },
	y: { z: 2, w: 3 },
	z: { w: 1 },
};

// note that this depends on the colour mapping in main.js, yuck

const CELL24_LINK_INDEXING = {
	1: { 2: 1, 3: 3 },
	2: { 1: 1, 3: 2 },
	3: { 1: 3, 2: 2 },
}

function make_24cell_vertices() {
	const axes = [ 'x', 'y', 'z', 'w' ];
	const nodes = [];
	let i = 1;
	for ( let p = 0; p < 3; p++ ) {
		for ( let q = p + 1; q < 4; q++ ) {
			const a1 = axes[p];
			const a2 = axes[q];
			const label = CELL24_INDEXING[a1][a2];
			for ( const v1 of [ -1, 1 ] ) {
				for ( const v2 of [ -1, 1 ] ) {
					const node = {
						id: i,
						x: 0, y: 0, z: 0, w:0,
						label: label
					};
					node[a1] = v1;
					node[a2] = v2;
					nodes.push(node);
					i++;
				}
			}
		}
	}
	return nodes;
}



function node_axes(n1) {
	return [ 'x', 'y', 'z', 'w' ].filter((a) => n1[a] !== 0 );
}

function make_24cell_edges(nodes) {
	const seen = {};
	const links = [];
	let id = 1;
	for( const n1 of nodes ) {
		const axes = node_axes(n1);
		const axeq = nodes.filter((n) => n[axes[0]] === n1[axes[0]] && n[axes[1]] === 0);
		const axeq2 = nodes.filter((n) => n[axes[1]] === n1[axes[1]] && n[axes[0]] === 0);
		for( const n2 of axeq.concat(axeq2) ) {
			const ids = [ n1.id, n2.id ];
			ids.sort();
			const fp = ids.join(',');
			if( !seen[fp] ) {
				seen[fp] = true;
				const label = CELL24_LINK_INDEXING[n1.label][n2.label];
				links.push({ id: id, label: label, source: n1.id, target: n2.id });
			}
		}
	}
	return links;
}

export const cell24 = () => {
	const nodes = make_24cell_vertices();
	const links = make_24cell_edges(nodes);

	return {
		nodes: nodes,
		links: links
	};
}


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

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


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 make_120cell_edges(nodes) {
	const seen = {};
	const nnodes = nodes.length;
	const links = [];
	let id = 1;
	for( const n1 of nodes ) {
		console.log(n1);
		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, 5);
		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++;
			}
		}
	}
	return links;
}


export const cell120 = () => {
	const nodes  = make_120cell_vertices();
	const links = make_120cell_edges(nodes);
	return {
		nodes: nodes,
		links: links
	}
}


const nodes = cell120();