fourdjs/testbed.js

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//testbed for playing with stuff in node repl
const THREE =require('three');
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;
}
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;
}
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// 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] ) {
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faces.push({ id: id, edge: edge.id, v1: edge.source, v2: edge.target, fingerprint: fp, nodes: face });
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id++;
seen[fp] = true;
}
}
}
return faces;
}
// trying to go from faces to dodecahedra
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function shared_vertices(f1, f2) {
return f1.nodes.filter((f) => f2.nodes.includes(f));
}
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function adjacent_faces(f1, f2) {
// adjacent faces which share an edge, not just a vertex
const intersect = shared_vertices(f1, f2);
if( intersect.length < 2 ) {
return false;
}
if( intersect.length > 2 ) {
console.log(`warning: faces ${f1.id} and ${f2.id} have too many common vertices`);
}
return true;
}
function find_adjacent_faces(faces, face) {
const neighbours = faces.filter((f) => f.id !== face.id && adjacent_faces(f, face));
return neighbours;
}
function find_dodeca_mutuals(faces, f1, f2) {
// for any two adjacent faces, find their common neighbours where
// all three share exactly one vertex (this, I think, guarantees that
// all are on the same dodecahedron)
const n1 = find_adjacent_faces(faces, f1);
const n2 = find_adjacent_faces(faces, f2);
const common = n1.filter((f1) => n2.filter((f2) => f1.id === f2.id).length > 0 );
// there's one extra here - the third which has two nodes in common with
// both f1 and f2 - filter it out
const mutuals = common.filter((cf) => {
const shared = cf.nodes.filter((n) => f1.nodes.includes(n) && f2.nodes.includes(n));
return shared.length === 1
});
return mutuals;
}
function find_dodeca_next(faces, dodeca, f1, f2) {
// of a pair of mutuals, return the one we haven't already got
const m = find_dodeca_mutuals(faces, f1, f2);
if( dodeca.filter((f) => f.id === m[0].id ).length > 0 ) {
m.shift();
}
return m[0];
}
// from any two mutual faces, return all the faces in their dodecahedron
function make_dodecahedron(faces, f1, f2) {
const dodecahedron = [ f1, f2 ];
// take f1 as the 'center', get the other four around it from f2
const fs = find_dodeca_mutuals(faces, f1, f2);
const f3 = fs[0];
const f6 = fs[1];
dodecahedron.push(f3);
const f4 = find_dodeca_next(faces, dodecahedron, f1, f3);
dodecahedron.push(f4);
const f5 = find_dodeca_next(faces, dodecahedron, f1, f4);
dodecahedron.push(f5);
dodecahedron.push(f6);
// get the next ring
const f7 = find_dodeca_next(faces, dodecahedron, f6, f2);
dodecahedron.push(f7);
const f8 = find_dodeca_next(faces, dodecahedron, f2, f3);
dodecahedron.push(f8);
const f9 = find_dodeca_next(faces, dodecahedron, f3, f4);
dodecahedron.push(f9);
const f10 = find_dodeca_next(faces, dodecahedron, f4, f5);
dodecahedron.push(f10);
const f11 = find_dodeca_next(faces, dodecahedron, f5, f6);
dodecahedron.push(f11);
// get the last
const f12 = find_dodeca_next(faces, dodecahedron, f7, f8);
dodecahedron.push(f12);
return dodecahedron;
}
// for a face, pick an edge, and then find the other two faces which
// share this edge. These can be used as the starting points for the
// first face's two dodecahedra
function find_edge_neighbours(faces, face) {
const n1 = face.nodes[0];
const n2 = face.nodes[1];
return faces.filter((f) => f.id !== face.id && f.nodes.includes(n1) && f.nodes.includes(n2));
}
// each face is in two dodecahedra: this returns them both
function face_to_dodecahedra(faces, f) {
const edge_friends = find_edge_neighbours(faces, f);
const d1 = make_dodecahedron(faces, f, edge_friends[0]);
const d2 = make_dodecahedron(faces, f, edge_friends[1]);
return [ d1, d2 ];
}
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// brute-force calculation of all dodecahedra
function dd_fingerprint(dodecahedron) {
const ids = dodecahedron.map((face) => face.id);
ids.sort()
return ids.join(',');
}
function make_120cell_cells(faces) {
const dodecas = [];
const seen = {};
for( const face of faces ) {
const dds = face_to_dodecahedra(faces, face);
for( const dd of dds ) {
const fp = dd_fingerprint(dd);
if( ! (fp in seen) ) {
console.log(`added dodeca ${fp}`);
dodecas.push(dd);
seen[fp] = 1;
}
}
}
return dodecas;
}
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
}
}
}
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const nodes = make_120cell_vertices();
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const links = auto_detect_edges(nodes, 4);
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const faces = auto_120cell_faces(links);