fourdjs/polytopes.js

495 lines
9.1 KiB
JavaScript

import * as PERMUTE from './permute.js';
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
export const cell5 = () => {
const r5 = Math.sqrt(5);
const r2 = Math.sqrt(2) / 2;
return {
nodes: [
{id:1, label: 0, x: r2, y: r2, z: r2, w: -r2 / r5 },
{id:2, label: 1, x: r2, y: -r2, z: -r2, w: -r2 / r5 },
{id:3, label: 2, x: -r2, y: r2, z: -r2, w: -r2 / r5 },
{id:4, label: 3, x: -r2, y: -r2, z: r2, w: -r2 / r5 },
{id:5, label: 4, 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);
nodes[0].label = 0;
nodes[3].label = 1;
nodes[5].label = 2;
nodes[6].label = 3;
nodes[7].label = 0;
nodes[4].label = 1;
nodes[2].label = 2;
nodes[1].label = 3;
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
}
};
};
export const tesseract = () => {
const nodes = PERMUTE.coordinates([1, 1, 1, 1], 0);
index_nodes(nodes);
for( const n of nodes ) {
if( n.x * n.y * n.z * n.w > 0 ) {
n.label = 1;
}
}
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_INDEXING = {
x: { y: 0, z: 2, w: 1 },
y: { z: 1, w: 2 },
z: { w: 0 }
};
export const cell24 = () => {
const nodes = PERMUTE.coordinates([0, 0, 1, 1], 0);
for( const n of nodes ) {
const axes = ['x', 'y', 'z', 'w'].filter((a) => n[a] !== 0);
n.label = CELL24_INDEXING[axes[0]][axes[1]];
}
index_nodes(nodes);
const links = auto_detect_edges(nodes, 8);
return {
nodes: nodes,
links: links,
geometry: {
node_size: 0.02,
link_size: 0.02
}
};
}
// notes on coherent indexing
// see table in https://en.wikipedia.org/wiki/120-cell - maybe adapt the
// unit radius table
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();
index_nodes(nodes);
scale_nodes(nodes, 0.5);
return nodes;
}
function label_nodes(nodes, ids, label) {
nodes.filter((n) => ids.includes(n.id)).map((n) => n.label = label);
}
export const cell120 = () => {
const nodes = make_120cell_vertices();
const links = auto_detect_edges(nodes, 4);
naive_label_120cell(nodes, links);
return {
nodes: nodes,
links: links,
geometry: {
node_size: 0.02,
link_size: 0.02
}
}
}
// Schoute's partition via https://arxiv.org/abs/1010.4353
const partition600 = {
"2,0,0,0": 1,
"0,2,0,0": 1,
"0,0,2,0": 1,
"0,0,0,2": 1,
"1,1,1,1": 1,
"1,1,-1,-1": 1,
"1,-1,1,-1": 1,
"1,-1,-1,1": 1,
"1,-1,-1,-1": 1,
"1,-1,1,1": 1,
"1,1,-1,1": 1,
"1,1,1,-1": 1,
"k,0,-t,-1": 2,
"0,k,1,-t": 2,
"t,-1,k,0": 2,
"1,t,0,k": 2,
"t,k,0,-1": 2,
"1,0,k,t": 2,
"k,-t,-1,0": 2,
"0,1,-t,k": 2,
"1,k,t,0": 2,
"t,0,-1,k": 2,
"0,t,-k,-1": 2,
"k,-1,0,-t": 2,
"t,0,1,k": 3,
"0,t,-k,1": 3,
"1,-k,-t,0": 3,
"k,1,0,-t": 3,
"0,k,1,t": 3,
"t,1,-k,0": 3,
"k,0,t,-1": 3,
"1,-t,0,k": 3,
"t,-k,0,-1": 3,
"0,1,-t,-k": 3,
"1,0,-k,t": 3,
"k,t,1,0": 3,
"t,0,-1,-k": 4,
"0,t,k,-1": 4,
"1,-k,t,0": 4,
"k,1,0,t": 4,
"t,1,k,0": 4,
"0,k,-1,-t": 4,
"1,-t,0,-k": 4,
"k,0,-t,1": 4,
"0,1,t,k": 4,
"t,-k,0,1": 4,
"k,t,-1,0": 4,
"1,0,k,-t": 4,
"k,0,t,1": 5,
"0,k,-1,t": 5,
"t,-1,-k,0": 5,
"1,t,0,-k": 5,
"1,0,-k,-t": 5,
"t,k,0,1": 5,
"0,1,t,-k": 5,
"k,-t,1,0": 5,
"t,0,1,-k": 5,
"1,k,-t,0": 5,
"k,-1,0,t": 5,
"0,t,k,1": 5
};
function partition_coord(i, coords, invert) {
const j = invert ? -i : i;
if( j >= 0 ) {
return coords[j];
}
return "-" + coords[-j];
}
function partition_fingerprint(n, coords, invert) {
const p = ['x','y','z','w'].map((a) => partition_coord(n[a], coords, invert));
const fp = p.join(',');
return fp;
}
function label_vertex(n, coords, partition) {
const fp = partition_fingerprint(n, coords, false);
if( fp in partition ) {
return partition[fp];
} else {
const ifp = partition_fingerprint(n, coords, true);
if( ifp in partition ) {
return partition[ifp];
}
console.log(`Map for ${fp} ${ifp} not found`);
return 0;
}
}
function map_coord(i, coords, values) {
if( i >= 0 ) {
return values[coords[i]];
}
return -values[coords[-i]];
}
function make_600cell_vertices() {
const coords = {
0: '0',
1: '1',
2: '2',
3: 't',
4: 'k'
};
const t = 0.5 * (1 + Math.sqrt(5));
const values = {
'0': 0,
'1': 1,
'2': 2,
't': t,
'k': 1 / t
};
const nodes = [
PERMUTE.coordinates([0, 0, 0, 2], 0),
PERMUTE.coordinates([1, 1, 1, 1], 0),
PERMUTE.coordinates([3, 1, 4, 0], 0, true)
].flat();
for( const n of nodes ) {
n.label = label_vertex(n, coords, partition600) - 1;
}
for( const n of nodes ) {
for( const a of [ 'x', 'y', 'z', 'w'] ) {
n[a] = map_coord(n[a], coords, values);
}
}
index_nodes(nodes);
scale_nodes(nodes, 0.75);
return nodes;
}
function get_node(nodes, id) {
const ns = nodes.filter((n) => n.id === id);
if( ns ) {
return ns[0]
} else {
return undefined;
}
}
function audit_link_labels(nodes, links) {
console.log("Link audit");
for( const l of links ) {
const n1 = get_node(nodes, l.source);
const n2 = get_node(nodes, l.target);
if( n1.label === n2.label ) {
console.log(`link ${l.id} joins ${n1.id} ${n2.id} with label ${n2.label}`);
}
}
}
function find_edges(links, nid) {
return links.filter((l) => l.source === nid || l.target === nid );
}
function find_adjacent(links, nid) {
return find_edges(links, nid).map((l) => {
if( l.source === nid ) {
return l.target;
} else {
return l.source;
}
});
}
function iterate_graph(nodes, links, n, fn) {
const queue = [];
const seen = {};
const nodes_id = {};
nodes.map((n) => nodes_id[n.id] = n);
queue.push(n.id);
seen[n.id] = true;
fn(n);
while( queue.length > 0 ) {
const v = queue.shift();
find_adjacent(links, v).map((aid) => {
if( !(aid in seen) ) {
seen[aid] = true;
queue.push(aid);
fn(nodes_id[aid]);
}
})
}
}
function dumb_label_120cell(nodes, links) {
let l = 0;
iterate_graph(nodes, links, nodes[0], (n) => {
n.label = l;
console.log(`Labelled ${n.id} ${n.label}`);
l++;
if( l > 2 ) {
l = 0;
}
})
}
// stupid tetrahedral labelling
function naive_label_120cell(nodes, links, n) {
const nodes_id = {};
nodes.map((n) => nodes_id[n.id] = n);
iterate_graph(nodes, links, nodes[0], (n) => {
const cols = new Set();
const nbors = find_adjacent(links, n.id);
for( const nb of nbors ) {
if( nodes_id[nb].label > 0 ) {
cols.add(nodes_id[nb].label);
}
for( const nb2 of find_adjacent(links, nb) ) {
if( nb2 !== n.id && nodes_id[nb].label > 0 ) {
cols.add(nodes_id[nb2].label);
}
}
}
const pcols = [ 1, 2, 3, 4, 5 ].filter((c) => !cols.has(c));
if( pcols.length < 1 ) {
console.log(`Got stuck, no options at ${n.id}`);
} else {
n.label = pcols[0];
console.log(`applied ${pcols[0]} to node ${n.id}`);
}
}
}
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
}
}
}