bombinans
/
fourdjs
1
1
Fork 0
Code Issues 11 Pull Requests Packages Projects Releases Wiki Activity

Broken 120-cell

feature-big-polytopes
Mike Lynch 2023-07-27 19:23:26 +10:00
parent c986b7cbfb
commit 3ba81a2f83
4 changed files with 141 additions and 27 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

2
fourDShape.js
View File

@ -3,7 +3,7 @@ import * as THREE from 'three';
const HYPERPLANE = 2;
const NODE_SIZE = 0.08;
const NODE_SIZE = 0.02;
const LINK_SIZE = 0.02;

4
main.js
View File

@ -7,7 +7,7 @@ import { FourDShape } from './fourDShape.js';
import { GUI } from 'lil-gui';
const DEFAULT_SHAPE = '16-cell';
const DEFAULT_SHAPE = '120-cell';
// hacky stuff for 4d rotations
@ -120,7 +120,7 @@ const LINK_OPACITY = 0.7;
// 2 M 2 (0-2) B
const node_ms = [
new THREE.MeshStandardMaterial( { color: 0x707070 } ),
new THREE.MeshStandardMaterial( { color: 0xc0c0c0 } ),
new THREE.MeshStandardMaterial( { color: 0x20dddd } ),
new THREE.MeshStandardMaterial( { color: 0xdddd20 } ),
new THREE.MeshStandardMaterial( { color: 0xdd20dd } ),

80
permute.js
View File

@ -86,14 +86,14 @@ function permutations_even(a) {
// [ [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) {
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({x: xv, y:yv, z:zv, w:wv});
expanded.push({label: label, x: xv, y:yv, z:zv, w:wv});
}
}
}
@ -102,14 +102,86 @@ function expand_sign(a) {
}
export function coordinates(a, even=false) {
export 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);
const expanded = expand_sign(p, 0);
coords.push(...expanded);
}
return coords;
}
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 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([2, 2, 0, 0], 0),
coordinates([r5, 1, 1, 1], 1),
coordinates([phi, phi, phi, phi2inv], 2),
coordinates([phi, phiinv, phiinv, phiinv], 0),
coordinates([phi2, phi2inv, 1, 0], 1, true),
coordinates([r5, phiinv, phi, 0], 2, true),
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( let i = 0; i < nnodes - 1; i++ ) {
const d2 = [];
for( let j = 0; j < nnodes; j++ ) {
d2.push({ d2: dist2(nodes[i], nodes[j]), id: j });
}
d2.sort((a, b) => b.d2 - a.d2);
const closest = d2.slice(1, 4);
for( const e in closest ) {
const ids = [ nodes[i].id, e.id ];
ids.sort();
const fp = ids.join(',');
if( !seen[fp] ) {
seen[fp] = true;
links.push({ id: id, label: 0, source: nodes[i].id, target: e.id });
id++;
}
}
}
return links;
}
const nodes = make_120cell_vertices();
const links = make_120cell_edges(nodes);
console.log(links);

82
polytopes.js
View File

@ -1,6 +1,19 @@
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;
@ -232,38 +245,67 @@ export const cell24 = () => {
function make_120cell_vertices() {
const phi = 0.5 * (1 + Math.sqrt(5)); 3
const r5 = Math.sqrt(5); 5
const phi2 = phi * phi; 4
const phiinv = 1 / phi; 6
const phi2inv = 1 / phi2; 7
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([2, 2, 0, 0]),
PERMUTE.coordinates([r5, 1, 1, 1]),
PERMUTE.coordinates([phi, phi, phi, phi2inv]),
PERMUTE.coordinates([phi, phiinv, phiinv, phiinv]),
PERMUTE.coordinates([2, 2, 0, 0], 0),
PERMUTE.coordinates([r5, 1, 1, 1], 1),
PERMUTE.coordinates([phi, phi, phi, phi2inv], 2),
PERMUTE.coordinates([phi, phiinv, phiinv, phiinv], 0),
PERMUTE.coordinates([phi2, phi2inv, 1, 0], true),
PERMUTE.coordinates([r5, phiinv, phi, 0], true),
PERMUTE.coordinates([2, 1, phi, phiinv], true),
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();
let i = 1;
for( const n of nodes ) {
n["id"] = i;
i++;
}
return nodes;
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: links
}
}
const nodes = cell120();