fourdjs/polytopes.js

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import * as PERMUTE from './permute.js';
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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) {
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);
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;
}
// too small and simple to calculate
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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 = () => {
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);
console.log('cell16 auto_detect_edges');
console.log(nodes);
const links = auto_detect_edges(nodes, 6);
return {
nodes: nodes,
links: links
};
};
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);
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return {
nodes: nodes,
links: links
};
}
export const cell24 = () => {
const nodes = scale_and_index(PERMUTE.coordinates([0, 0, 1, 1], 0), 1);
const links = auto_detect_edges(nodes, 6);
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return {
nodes: nodes,
links: links
};
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}
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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),
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PERMUTE.coordinates([phiinv, phiinv, phiinv, phi2], 0),
PERMUTE.coordinates([phi2, phi2inv, 1, 0], 0, true),
PERMUTE.coordinates([r5, phiinv, phi, 0], 0, true),
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PERMUTE.coordinates([2, 1, phi, phiinv], 0, true),
].flat();
return scale_and_index(nodes, 0.5);
}
export const cell120 = () => {
const nodes = make_120cell_vertices();
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const links = auto_detect_edges(nodes, 4);
return {
nodes: nodes,
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links: links
}
}
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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),
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PERMUTE.coordinates([phi, 1, 1 / phi, 0], 0, true)
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].flat();
return scale_and_index(nodes, 0.75);
}
export const cell600 = () => {
const nodes = make_600cell_vertices();
const links = auto_detect_edges(nodes, 20);
return {
nodes: nodes,
links: links
}
}