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bombinans:feature-3d-shapes
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bombinans:feature-120-cell-index
bombinans:feature-faces
bombinans:feature-big-polytopes

1 Commits
main ... feature-3d

Author SHA1 Message Date
Mike Lynch
c8ce499b22 Added dodecahedron with compound of five cubes, refactored the 
inscribed polytopes into one function
 2023-09-16 17:05:07 +10:00
19 changed files with 600 additions and 3159 deletions
Show Stats Expand all files Collapse all files

17
CHANGELOG.md
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@ -1,17 +0,0 @@
CHANGELOG
=========
## v1.1 - 1/1/2026
The 120-cell now includes a visualisation of its inscribed 5-cells, which honestly
looks like less of a mess than I expected it to.
## v1.0 - 16/11/2025
It's been [two years](https://mikelynch.org/2023/Sep/02/120-cell/)</a> since
I first made this, and I haven't updated it in a while, but I got tapered links to
work without too much performance overhead, so that seemed worth a version.
The results flicker a bit at low opacities but otherwise I'm pretty happy with
it.
`

26
NOTES.md
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@ -1,26 +0,0 @@
# NOTES
New approach for the 5-cells:
Pick a tetrahedron of an inscribed 600-cell with vertices A, B, C, D
This gives pairs of vertices:
AB
AC
AD
BC
BD
CD
Each of these gives rise to seven pairs of 5-cells which are on neighboring vertices
of the 5 600-cells.
Try enumerating these and inspecting them to find one or more coherent sets of four
5-cells which lie on one tetrahedron from each of the 600-cells.
(I expect there to be more than one, like how there are two ways to partition the
120-cell vertices into 600-cells)

1038
cellindex.js
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File diff suppressed because it is too large Load Diff

23
colours.js
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@ -1,21 +1,14 @@
import ColorScheme from 'color-scheme';
import Color from 'color';
export const get_colours = (basis) => {
const basis_c = Color(basis);
const hslb = basis_c.hsl();
const hue = hslb['color'][0];
const saturation = hslb['color'][1];
const luminance = hslb['color'][2];
const scheme = new ColorScheme;
scheme.from_hue(hue).scheme("tetrade").distance(0.75);
const colours = scheme.colors().slice(1, 9);
colours.reverse();
const hsl = colours.map((c) => Color("#" + c).hsl());
const resaturated = hsl.map((hslc) => hslc.saturationl(saturation).rgbNumber());
resaturated.unshift(basis);
console.log(resaturated);
return resaturated;
const hexbasis = basis.toString(16).padStart(6, "0");
scheme.from_hex(hexbasis).scheme("tetrade").variation("hard").distance(0.5);
const colours = scheme.colors().map((cs) => parseInt('0x' + cs));
const set = colours.slice(1, 6);
set.reverse();
set.unshift(colours[0]);
return set;
}
// basic colours where 0 = blue
@ -35,4 +28,4 @@ export const get_plain_colours = (basis) => {
0xff9900,
0x000000,
]
}
}

1
explore_120
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@ -1 +0,0 @@

492
explore_120cell.js
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@ -1,492 +0,0 @@
import * as POLYTOPES from './polytopes.js';
// exploring more inscriptions of the 120-cell
function choice(a) {
const r = Math.floor(Math.random() * a.length);
return a[r];
}
export function nodes_links(links, nodeid) {
return links.filter((l) => l.source === nodeid || l.target === nodeid);
}
export function linked(links, n1, n2) {
const ls = nodes_links(nodes_links(links, n1), n2);
if( ls.length ) {
return ls[0]
} else {
return false;
}
}
function fingerprint(ids) {
const sids = [...ids];
sids.sort();
return sids.join(',');
}
export function dist(n1, n2) {
return Math.sqrt((n1.x - n2.x) ** 2 + (n1.y - n2.y) ** 2 + (n1.z - n2.z) ** 2 + (n1.w - n2.w) ** 2);
}
export function make_120cell() {
const nodes = POLYTOPES.make_120cell_vertices();
const links = POLYTOPES.auto_detect_edges(nodes, 4);
return {
nodes: nodes,
links: links
}
}
function round_dist(raw) {
return Math.floor(raw * 100000) / 100000;
}
export function distance_groups(cell120) {
// get list of other nodes by distance
// sort them and dump them out
const dists = {};
cell120.nodes.map((n) => {
const draw = dist(cell120.nodes[0], n);
const dtrunc = round_dist(draw);
if( !(dtrunc in dists) ) {
dists[dtrunc] = [];
}
dists[dtrunc].push(n);
});
return dists;
}
function distance_group(cell120, n0, chord) {
const nodes = []
cell120.nodes.map((n) => {
const d = round_dist(dist(n0, n));
if( d == chord ) {
nodes.push(n);
}
});
// filter and return those whose chord is also the same
const equidistant = [];
for( const n1 of nodes ) {
for( const n2 of nodes ) {
if( n2.id > n1.id ) {
if( round_dist(dist(n1, n2)) == chord ) {
equidistant.push([n1, n2]);
}
}
}
}
return equidistant;
}
export function chord_survey() {
const cell120 = POLYTOPES.cell120_inscribed();
const dgroups = distance_groups(cell120);
const dists = Object.keys(dgroups);
dists.sort();
for( const d of dists ) {
const g0 = dgroups[d][0];
dgroups[d].map((g) => {
console.log(`${g0.id}-${g.id}: ${round_dist(dist(g0, g))}`);
});
}
}
function overlap(c1, c2) {
for( const l in c1 ) {
if( c1[l] === c2[l] ) {
return true;
}
}
return false;
}
function c5match(c1, c2) {
for( const l in c1 ) {
if( c1[l] != c2[l] ) {
return false;
}
}
return true;
}
export function gather_5cells(cell120) {
const CHORD5 = round_dist(Math.sqrt(2.5));
const bins = [];
const all = [];
cell120.nodes.filter((n) => n.label === 1).map((n) => {
const cells = [ ];
const g = distance_group(cell120, n, CHORD5);
for( const pair of g ) {
let seen = false;
for( const cell of cells ) {
const c = Object.values(cell);
if( c.includes(pair[0].id) || c.includes(pair[1].id) ) {
if( !c.includes(pair[0].id) ) {
cell[pair[0].label] = pair[0].id;
}
if( !c.includes(pair[1].id) ) {
cell[pair[1].label] = pair[1].id;
}
seen = true;
break;
}
}
if( !seen ) {
const cell = {};
cell[1]= n.id;
cell[pair[0].label] = pair[0].id;
cell[pair[1].label] = pair[1].id;
cells.push(cell);
}
}
all.push(...cells);
});
return all;
}
function audit_5cells(cells) {
// this verifies that for each label (a 600-cell set), each of its
// vertices is in exactly 7 5-cells. It checks out.
['1','2','3','4','5'].map((l) => {
const sets = {};
for( const cell of cells ) {
const lv = cell[l];
if( !(lv in sets) ) {
sets[lv] = [];
}
sets[lv].push(cell);
}
for( const lv in sets ) {
const ok = ( sets[lv].length === 7 ) ? 'ok' : 'miss';
console.log(`${l},${lv},${sets[lv].length},${ok}`);
}
});
}
function try_120_5_cells_fails(cell120, cells, l) {
// iterate over every vertex in the 600-cell defined by label l,
// get all 7 5-cells including that vertex, and add them if they are
// disjoint with what we already have
// this always runs out of disjoint nodes early
const vertices = cell120.nodes.filter((n) => n.label === l);
const cellset = [];
for( const v of vertices ) {
console.log(`Vertex ${v.id}`);
const vcells = cells.filter((c) => c[l] === v.id);
const overlap_any = (cs, c) => {
for( const seen of cs ) {
if( overlap(seen, c) ) {
console.log("overlap");
console.log(c);
return true;
}
}
return false;
}
const disjoint = vcells.filter((c) => ! overlap_any(cellset, c));
console.log(`Found ${disjoint.length} disjoint cells`);
if( disjoint.length > 0 ) {
cellset.push(choice(disjoint));
}
}
console.log(`Found total of ${cellset.length} disjoint cells`);
//console.log(cellset);
}
function overlap_any(cs, c) {
for( const seen of cs ) {
if( overlap(seen, c) ) {
return true;
}
}
return false;
}
function explore_disjoint(cell120, all5, l) {
const a = all5[0];
const overlaps = all5.filter((c) => overlap(c, a));
console.log(a);
console.log(overlaps.length);
console.log(overlaps);
}
// select a five-cell from a starting vertex v
// find a neighbor of v vn on its 600 cell, find all of the 5-cells which include
// vn. Then see if we can find any from that set which are similiar neighbours to
// the other four vertices in the first 5-cell
// the idea is that the 600-cells are a guide to finding the right subset of
// 5-cells
function neighbours600(cell120, vid) {
const v = cell120.nodes.filter((node) => node.id === vid)[0];
const label = v.label;
const links = cell120.links.filter((l) => {
return l.label === v.label && (l.source === v.id || l.target == v.id );
});
const nodes = links.map((l) => {
if( l.source === v.id ) {
return l.target;
} else {
return l.source;
}
});
return nodes;
}
function cell120node(cell120, nid) {
return cell120.nodes.filter((n) => n.id === nid)[0];
}
function node_dist(cell120, aid, bid) {
const a = cell120node(cell120, aid);
const b = cell120node(cell120, bid);
return dist(a, b);
}
function print_row(v1, v2, p, v5) {
console.log(`${v1.id},${v2.id},${p},${v5[1]},${v5[2]},${v5[3]},${v5[4]},${v5[5]}`);
}
// for a pair of vertices which are on the same inscribed 600 cell,
// this returns all 7 pairs of 5-cells which contain v1 and v2 and
// which are also evenly spaced (ie every pair of vertices on the
// same 600-cell is one edge apart)
function find_adjoining_5cells(cell120, all5, v1, v2) {
const DIST600 = round_dist(node_dist(cell120, v1.id, v2.id));
const v15s = all5.filter((c5) => c5[v1.label] === v1.id);
const v25s = all5.filter((c5) => c5[v2.label] === v2.id);
let p = 0;
const c5pairs = [];
for( const v5a of v15s ) {
for( const v5b of v25s ) {
let match = true;
const d = {};
for( const label in v5a ) {
d[label] = round_dist(node_dist(cell120, v5a[label], v5b[label]));
if( d[label] != DIST600 ) {
match = false;
}
}
if( match ) {
c5pairs.push([ v5a, v5b ]);
}
}
}
return c5pairs;
}
function tetras(cell120, v) {
// given a vertex v, find all of the 600-cell tetras it's on
const n600s = neighbours600(cell120, v.id);
// need to find all sets of three neighbours which are neighbours: there
// should be 20 of these because they're faces of an icosahedron
const tetras = new Set;
for( const v2id of n600s ) {
// find mutual neighbours of the first two
const n2600s = neighbours600(cell120, v2id);
const mutuals = n2600s.filter((nid) => {
return nid != v2id && nid != v.id && n600s.includes(nid)
});
for( const nm of mutuals ) {
const nnms = neighbours600(cell120, nm);
const mutuals2 = nnms.filter((nid) => {
return nid != nm && nid != v2id && nid != v.id && mutuals.includes(nid)
});
for( const m2 of mutuals2 ) {
const t = [ v.id, v2id, nm, m2 ];
t.sort((a, b) => a - b);
const tstr = t.join(',');
tetras.add(tstr);
}
}
}
const tarray = [];
for( const t of tetras ) {
const ta = t.split(',').map((v) => Number(v));
tarray.push(ta);
}
return tarray;
}
function vertices(hedra) {
const v = new Set;
for ( const h of hedra) {
for( const p of h ) {
v.add(p);
}
}
return Array.from(v);
}
function str5cell(c5) {
return ["1","2","3","4","5"].map((l) => String(c5[l]).padStart(3, '0')).join('-');
}
function tetra_sets(cell120, all5, tetra) {
// given a tetrahedron on a 600-cell, find the sets of adjacent 5-cells on
// all of the pairs
// this is ass-backwards. Need to find tetras on the other 4 vertices of a 5-cell
const vs = tetra.map((tid) => cell120node(cell120, tid));
const pairs = [[0,1], [0,2], [0, 3], [1, 2], [1, 3], [2, 3]];
for( const p of pairs ) {
const v1 = vs[p[0]];
const v2 = vs[p[1]];
const c5pairs = find_adjoining_5cells(cell120, all5, v1, v2);
console.log(v1.id, v2.id);
console.log(c5pairs.map((p) => str5cell(p[0]) + " " + str5cell(p[1])));
}
}
function cell5_neighbourhoods(cell120, all5, c5) {
const neighbours = {}
for( const l in c5 ) {
const v = cell120node(cell120, c5[l]);
neighbours[l] = vertices(tetras(cell120, v));
}
// now take the set of all 5-cells and filter it to only those whose vertices
// are in the neighour sets. On first inspection there are 13?
const n5cells = all5.filter((c5) => {
for( const l in c5 ) {
if( ! neighbours[l].includes(c5[l]) ) {
return false;
}
}
return true;
});
return n5cells;
}
function cell5_tetras(cell120, all5, c5) {
const nb = cell5_neighbourhoods(cell120, all5, c5);
const v1 = cell120node(cell120, c5["1"]);
const ts = tetras(cell120, v1);
const c5s = [];
for( const t of ts ) {
const nt = nb.filter((n) => {
for( const l in n ) {
if( t.includes(n[l]) ) {
return true;
}
}
return false
});
for( const nc5 of nt ) {
const exact = c5s.filter((c) => c5match(c, nc5));
if( exact.length === 0 ) {
const o = c5s.filter((c) => overlap(c, nc5));
if( o.length > 0 ) {
console.log("Overlap", c5, o);
} else {
c5s.push(nc5);
}
}
}
}
return c5s;
}
function coherent_5cells_r(cell120, all5, c5s, c50) {
// Find next set of c5s, see if there are any we haven't seen,
// recurse into those ones
const c5ns = cell5_tetras(cell120, all5, c50);
const c5unseen = c5ns.filter((c5) => {
const matched = c5s.filter((c5b) => c5match(c5b, c5));
return matched.length === 0;
});
for( const c5u of c5unseen ) {
c5s.push(c5u);
}
for( const c5u of c5unseen ) {
coherent_5cells_r(cell120, all5, c5s, c5u);
}
}
function coherent_5cells(cell120, all5) {
// pick a starting point, collect coherent 5_cells, continue till
// there aren't any new ones
const c5set = [];
let c5 = all5[0];
const c5s = [];
coherent_5cells_r(cell120, all5, c5s, c5);
return c5s;
}
const cell120 = POLYTOPES.cell120_inscribed();
const all5 = gather_5cells(cell120);
const c5s = coherent_5cells(cell120, all5);
const celli = c5s.map((c5) => [ "1", "2", "3", "4", "5" ].map((l) => c5[l]));
// check it because I don't believe it yet
const vertex_check = {};
for( const c5 of celli ) {
for( const l in c5 ) {
const v = c5[l];
if( v in vertex_check ) {
console.log(`Double count vertex ${v}`);
}
vertex_check[v] = 1;
}
}
for( let i = 1; i < 601; i++ ) {
if( !vertex_check[i] ) {
console.log(`v ${i} missing`);
}
}
const idict = {};
for( let i = 1; i < 121; i++ ) {
idict[i] = celli[i - 1];
}
console.log(JSON.stringify(idict, null, 2));

104
fourDShape.js
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@ -1,10 +1,7 @@
import * as THREE from 'three';
import { TaperedLink } from './taperedLink.js';
const HYPERPLANE = 2.0;
const W_FORESHORTENING = 0.04;
class FourDShape extends THREE.Group {
@ -18,10 +15,11 @@ class FourDShape extends THREE.Group {
this.nodes3 = {};
this.links = structure.links;
this.faces = ( "faces" in structure ) ? structure.faces : [];
this.node_size = structure.geometry.node_size;
this.link_size = structure.geometry.link_size;
this.node_scale = 1;
this.link_scale = 1;
this.hyperplane = HYPERPLANE;
this.foreshortening = W_FORESHORTENING;
this.initShapes();
}
@ -29,15 +27,15 @@ class FourDShape extends THREE.Group {
// if a node/link has no label, use the 0th material
getMaterialLabel(entity) {
if( "label" in entity ) {
return entity.label
} else {
return 0;
}
getMaterial(entity, materials) {
if( "label" in entity ) {
return materials[entity.label];
} else {
return materials[0];
}
}
makeNode(material, v3, scale) {
makeNode(material, v3) {
const geometry = new THREE.SphereGeometry(this.node_size);
const sphere = new THREE.Mesh(geometry, material);
sphere.position.copy(v3);
@ -45,24 +43,34 @@ class FourDShape extends THREE.Group {
return sphere;
}
makeLink(materialLabel, link) {
const n1 = this.nodes3[link.source];
const n2 = this.nodes3[link.target];
const s1 = this.link_scale * n1.scale;
const s2 = this.link_scale * n2.scale;
const basematerial = this.link_ms[materialLabel];
const edge = new TaperedLink(basematerial, materialLabel, n1, n2, s1, s2);
this.add( edge );
makeLink(material, link) {
const n1 = this.nodes3[link.source].v3;
const n2 = this.nodes3[link.target].v3;
const length = n1.distanceTo(n2);
const centre = new THREE.Vector3();
centre.lerpVectors(n1, n2, 0.5);
const geometry = new THREE.CylinderGeometry(this.link_size, this.link_size, 1);
const cyl = new THREE.Mesh(geometry, material);
const edge = new THREE.Group();
edge.add(cyl);
edge.position.copy(centre);
edge.scale.copy(new THREE.Vector3(1, 1, length));
edge.lookAt(n2);
cyl.rotation.x = Math.PI / 2.0;
this.add(edge);
return edge;
}
updateLink(link, links_show) {
const n1 = this.nodes3[link.source];
const n2 = this.nodes3[link.target];
const s1 = this.link_scale * n1.scale;
const s2 = this.link_scale * n2.scale;
link.object.update(n1, n2, s1, s2);
link.object.visible = (!links_show || links_show.includes(link.label));
updateLink(link) {
const n1 = this.nodes3[link.source].v3;
const n2 = this.nodes3[link.target].v3;
const length = n1.distanceTo(n2);
const centre = new THREE.Vector3();
centre.lerpVectors(n1, n2, 0.5);
link.object.scale.copy(new THREE.Vector3(this.link_scale, this.link_scale, length));
link.object.position.copy(centre);
link.object.lookAt(n2);
link.object.children[0].rotation.x = Math.PI / 2.0;
}
@ -91,62 +99,47 @@ class FourDShape extends THREE.Group {
}
fourDscale(w) {
return this.hyperplane / ( this.hyperplane + w );
}
fourDrotate(x, y, z, w, rotations) {
fourDtoV3(x, y, z, w, rotations) {
const v4 = new THREE.Vector4(x, y, z, w);
for ( const m4 of rotations ) {
v4.applyMatrix4(m4);
}
return v4;
const k = this.hyperplane / (this.hyperplane + v4.w);
return new THREE.Vector3(v4.x * k, v4.y * k, v4.z * k);
}
fourDtoV3(v4) {
const k = this.fourDscale(v4.w);
return new THREE.Vector3(v4.x * k, v4.y * k, v4.z * k);
}
initShapes() {
for( const n of this.nodes4 ) {
const k = this.fourDscale(n.w);
const v3 = new THREE.Vector3(n.x * k, n.y * k, n.z * k);
const material = this.node_ms[this.getMaterialLabel(n)];
const v3 = this.fourDtoV3(n.x, n.y, n.z, n.w, []);
const material = this.getMaterial(n, this.node_ms);
this.nodes3[n.id] = {
v3: v3,
scale: k,
label: n.label,
object: this.makeNode(material, v3, k)
object: this.makeNode(material, v3)
};
}
for( const l of this.links ) {
const mLabel = this.getMaterialLabel(l);
l.object = this.makeLink(mLabel, l);
const material = this.getMaterial(l, this.link_ms);
l.object = this.makeLink(material, l);
}
for( const f of this.faces ) {
const material = this.face_ms(this.getMaterialLabel(f));
const material = this.getMaterial(f, this.face_ms);
f.object = this.makeFace(material, f);
}
}
render3(rotations, nodes_show, links_show) {
render3(rotations) {
this.scalev3 = new THREE.Vector3(this.node_scale, this.node_scale, this.node_scale);
for( const n of this.nodes4 ) {
const v4 = this.fourDrotate(n.x, n.y, n.z, n.w, rotations);
const k = this.fourDscale(v4.w);
const v3 = new THREE.Vector3(v4.x * k, v4.y * k, v4.z * k);
const s4 = k * this.node_scale * this.foreshortening;
const s3 = new THREE.Vector3(s4, s4, s4);
const v3 = this.fourDtoV3(n.x, n.y, n.z, n.w, rotations);
this.nodes3[n.id].v3 = v3;
this.nodes3[n.id].scale = k * this.foreshortening;
this.nodes3[n.id].object.position.copy(v3);
this.nodes3[n.id].object.scale.copy(s3);
this.nodes3[n.id].object.visible = ( !nodes_show || nodes_show.includes(n.label) );
this.nodes3[n.id].object.scale.copy(this.scalev3);
}
for( const l of this.links ) {
this.updateLink(l, links_show);
this.updateLink(l);
}
for( const f of this.faces ) {
@ -154,6 +147,7 @@ class FourDShape extends THREE.Group {
}
}
}
export { FourDShape };

127
gui.js
View File

@ -1,26 +1,20 @@
import { GUI } from 'lil-gui';
const DEFAULTS = {
nodesize: 0.6,
nodeopacity: 1,
linksize: 1.0,
linkopacity: 0.75,
shape: '120-cell',
link2opacity: 0.75,
option: 'none',
visibility: 5,
thickness: 0.25,
nodesize: 1.25,
linkopacity: 0.5,
link2opacity: 0.5,
shape: 'five-cubes',
inscribed: false,
inscribe_all: false,
color: 0x3293a9,
background: 0xd4d4d4,
hyperplane: 0.93,
zoom: 1,
xRotate: 'YZ',
yRotate: 'XZ',
hyperplane: 2,
rotation: 'rigid',
dtheta: 0,
damping: false,
captions: true,
dpsi: 0,
}
@ -28,86 +22,50 @@ const DEFAULTS = {
class FourDGUI {
constructor(funcs) {
this.shapes = funcs.shapes;
constructor(changeShape, setColor, setBackground, setLinkOpacity) {
this.gui = new GUI();
const SHAPE_NAMES = this.shapes.map((s) => s.name);
this.parseLinkParams();
const guiObj = this;
this.params = {
shape: this.link['shape'],
option: this.link['option'],
inscribed: this.link['inscribed'],
inscribe_all: this.link['inscribe_all'],
linksize: this.link['linksize'],
thickness: this.link['thickness'],
linkopacity: this.link['linkopacity'],
link2opacity: this.link['link2opacity'],
link2opacity: this.link['linkopacity'],
nodesize: this.link['nodesize'],
nodeopacity: this.link['nodeopacity'],
depth: this.link['depth'],
color: this.link['color'],
background: this.link['background'],
hyperplane: this.link['hyperplane'],
zoom: this.link['zoom'],
xRotate: this.link['xRotate'],
yRotate: this.link['yRotate'],
rotation: this.link['rotation'],
damping: false,
captions: true,
dtheta: this.link['dtheta'],
dpsi: this.link['dpsi'],
"copy link": function () { guiObj.copyUrl() },
"copy link": function () { guiObj.copyUrl() }
};
if( funcs.extras ) {
for( const label in funcs.extras ) {
console.log(label);
console.log(funcs.extras[label]);
this.params[label] = funcs.extras[label];
}
}
let options_ctrl;
this.gui.add(this.params, 'shape', SHAPE_NAMES).onChange((shape) => {
const options = this.getShapeOptions(shape);
options_ctrl = options_ctrl.options(options).onChange((option) => {
funcs.setVisibility(option)
});
options_ctrl.setValue(options[0])
funcs.changeShape(shape)
});
const options = this.getShapeOptions(this.params['shape']);
options_ctrl = this.gui.add(this.params, 'option').options(options).onChange((option) => {
funcs.setVisibility(option)
});
this.gui.add(this.params, 'hyperplane', 0.5, 1 / 0.8);
this.gui.add(this.params, 'zoom', 0.1, 2.0);
this.gui.add(this.params, 'nodesize', 0, 1.5);
this.gui.add(this.params, 'nodeopacity', 0, 1).onChange(funcs.setNodeOpacity);
this.gui.add(this.params, 'linksize', 0, 2);
console.log(funcs.setLinkOpacity);
this.gui.add(this.params, 'linkopacity', 0, 1).onChange((v) => funcs.setLinkOpacity(v, true));
this.gui.add(this.params, 'link2opacity', 0, 1).onChange((v) => funcs.setLinkOpacity(v, false));
this.gui.addColor(this.params, 'color').onChange(funcs.setColor);
this.gui.addColor(this.params, 'background').onChange(funcs.setBackground);
this.gui.add(this.params, 'xRotate', [ 'YW', 'YZ', 'ZW' ]);
this.gui.add(this.params, 'yRotate', [ 'XZ', 'XY', 'XW' ]);
this.gui.add(this.params, 'captions').onChange(this.showDocs);
this.gui.add(this.params, 'shape',
[ 'dodecahedron', 'five-cubes', '5-cell', '16-cell', 'tesseract',
'24-cell', '600-cell', '120-cell' ]
).onChange(changeShape)
this.gui.add(this.params, 'inscribed').onChange(changeShape);
this.gui.add(this.params, 'inscribe_all').onChange(changeShape);
this.gui.add(this.params, 'hyperplane', 1.5, 2.25);
this.gui.add(this.params, 'thickness', 0.1, 2);
this.gui.add(this.params, 'linkopacity', 0, 1).onChange(
(v) => setLinkOpacity(v, true)
);
this.gui.add(this.params, 'link2opacity', 0, 1).onChange(
(v) => setLinkOpacity(v, false)
);
this.gui.add(this.params, 'nodesize', 0.1, 4);
this.gui.addColor(this.params, 'color').onChange(setColor);
this.gui.addColor(this.params, 'background').onChange(setBackground);
this.gui.add(this.params, 'rotation', [ 'rigid', 'tumbling', 'inside-out', 'axisymmetrical' ]);
this.gui.add(this.params, 'damping');
this.gui.add(this.params, 'copy link');
if( funcs.extras ) {
for( const label in funcs.extras ) {
this.gui.add(this.params, label);
}
}
}
getShapeOptions(shape) {
const spec = this.shapes.filter((s) => s.name === shape);
if( spec && spec[0].options ) {
return spec[0].options.map((o) => o.name);
} else {
return [];
}
}
}
numParam(param, parser) {
@ -137,7 +95,7 @@ class FourDGUI {
const guiObj = this;
this.urlParams = this.linkUrl.searchParams;
for( const param of [ "shape", "xRotate", "yRotate", "option" ]) {
for( const param of [ "shape", "rotation" ]) {
const value = this.urlParams.get(param);
if( value ) {
this.link[param] = value;
@ -149,12 +107,10 @@ class FourDGUI {
this.link[param] = ( this.urlParams.get(param) === 'y' );
}
this.link['hyperplane'] = this.numParam('hyperplane', parseFloat);
this.link['zoom'] = this.numParam('zoom', parseFloat);
this.link['linksize'] = this.numParam('linksize', parseFloat);
this.link['thickness'] = this.numParam('thickness', parseFloat);
this.link['linkopacity'] = this.numParam('linkopacity', parseFloat);
this.link['link2opacity'] = this.numParam('link2opacity', parseFloat);
this.link['nodesize'] = this.numParam('nodesize', parseFloat);
this.link['nodeopacity'] = this.numParam('nodeopacity', parseFloat);
this.link['color'] = this.numParam('color', (s) => guiObj.stringToHex(s));
this.link['background'] = this.numParam('background', (s) => guiObj.stringToHex(s));
this.link['dpsi'] = this.numParam('dpsi', parseFloat);
@ -165,19 +121,16 @@ class FourDGUI {
copyUrl() {
const url = new URL(this.linkUrl.origin + this.linkUrl.pathname);
url.searchParams.append("shape", this.params.shape);
url.searchParams.append("option", this.params.option);
url.searchParams.append("inscribed", this.params.inscribed ? 'y': 'n');
url.searchParams.append("inscribe_all", this.params.inscribe_all ? 'y': 'n');
url.searchParams.append("linksize", this.params.linksize.toString());
url.searchParams.append("thickness", this.params.thickness.toString());
url.searchParams.append("nodesize", this.params.nodesize.toString());
url.searchParams.append("nodeopacity", this.params.nodesize.toString());
url.searchParams.append("linkopacity", this.params.nodeopacity.toString());
url.searchParams.append("linkopacity", this.params.thickness.toString());
url.searchParams.append("link2opacity", this.params.nodesize.toString());
url.searchParams.append("color", this.hexToString(this.params.color));
url.searchParams.append("background", this.hexToString(this.params.background));
url.searchParams.append("hyperplane", this.params.hyperplane.toString());
url.searchParams.append("zoom", this.params.zoom.toString());
url.searchParams.append("xRotate", this.params.xRotate);
url.searchParams.append("yRotate", this.params.yRotate);
url.searchParams.append("rotation", this.params.rotation);
url.searchParams.append("dtheta", this.params.dtheta.toString());
url.searchParams.append("dpsi", this.params.dpsi.toString());
this.copyTextToClipboard(url);
@ -225,4 +178,4 @@ class FourDGUI {
}
export { FourDGUI, DEFAULTS };
export { FourDGUI, DEFAULTS };

28
index.html
View File

@ -5,24 +5,6 @@
<title>FourD</title>
<style>
body { margin: 0; }
div#description {
position: fixed;
top: 0;
left: 0;
width: 20%;
z-index: 2;
font-family: sans-serif;
padding: 1em;
}
div#release_notes {
position: fixed;
top: 0;
left: 0;
width: 20%;
z-index: 2;
padding: 1em;
font-family: sans-serif;
}
div#info {
position: fixed;
bottom:0;
@ -34,11 +16,7 @@
</head>
<body>
<script type="module" src="/main.js"></script>
<div id="description"></div>
<div id="release_notes"></div>
<div id="info"><a href="#" id="show_notes">release 1.1</a> |
by <a target="_blank" href="https://mikelynch.org/">Mike Lynch</a> |
<a target="_blank" href="https://git.tilde.town/bombinans/fourdjs">source</a></div>
<div id="info">by <a target="_blank" href="https://mikelynch.org/">Mike Lynch</a> -
<a target="_blank" href="https://github.com/spikelynch/fourdjs">source</a></div>
</body>
</html>
</html>

173
layer600cell.js
View File

@ -1,173 +0,0 @@
import * as POLYTOPES from './polytopes.js';
// face detection for the 600-cell
export function nodes_links(links, nodeid) {
return links.filter((l) => l.source === nodeid || l.target === nodeid);
}
export function linked(links, n1, n2) {
const ls = nodes_links(nodes_links(links, n1), n2);
if( ls.length ) {
return ls[0]
} else {
return false;
}
}
function fingerprint(ids) {
const sids = [...ids];
sids.sort();
return sids.join(',');
}
export function make_600cell() {
const nodes = POLYTOPES.make_600cell_vertices();
const links = POLYTOPES.auto_detect_edges(nodes, 12);
return {
nodes: nodes,
links: links
}
}
export function link_to_tetras(nodes, links, link) {
const n1 = link.source;
const n2 = link.target;
const nl1 = nodes_links(links, n1).filter((l) => l.id !== link.id);
const nl2 = nodes_links(links, n2).filter((l) => l.id !== link.id);
const p1 = new Set();
const p = new Set();
for( const nl of nl1 ) {
if( nl.source !== n1 ) {
p1.add(nl.source);
}
if( nl.target !== n1 ) {
p1.add(nl.target);
}
}
for( const nl of nl2 ) {
if( nl.source !== n2 && p1.has(nl.source) ) {
p.add(nl.source);
}
if( nl.target !== n2 && p1.has(nl.target) ) {
p.add(nl.target);
}
}
const lp = Array.from(p);
const seen = {};
const tetras = [];
for( const p1 of lp ) {
for( const p2 of lp ) {
if( p1 != p2 ) {
if( linked(links, p1, p2) ) {
const fp = fingerprint([n1, n2, p1, p2]);
if( !seen[fp] ) {
seen[fp] = true;
tetras.push({fingerprint: fp, nodes: [n1, n2, p1, p2]})
}
}
}
}
}
return tetras;
}
export function auto_600cell_cells(nodes, links) {
const seen = {};
const tetras = [];
links.map((link) => {
link_to_tetras(nodes, links, link).map((lt) => {
if( !seen[lt.fingerprint] ) {
seen[lt.fingerprint] = true;
tetras.push(lt.nodes);
}
})
});
return tetras;
}
function node_by_id(nodes, nid) {
const ns = nodes.filter((n) => n.id === nid);
return ns[0];
}
export function tetra_w(nodes, tetra) {
let w = 0;
for( const nid of tetra ) {
const node = node_by_id(nodes, nid);
w += node.w;
}
return w / 4;
}
export function sorted_600cells() {
const cell600 = make_600cell();
const tetras = auto_600cell_cells(cell600.nodes, cell600.links);
const layers = tetras.map((t) => { return { "nodes": t, w: tetra_w(cell600.nodes, t) } });
layers.sort((a, b) => b.w - a.w);
return layers;
}
// const cell600 = make_600cell();
// const layers = sorted_600cells(cell600.nodes, cell600.links);
// for( const cell of layers ) {
// // const fp = fingerprint(cell.nodes);
// console.log(`${cell.w} ${cell.nodes}`);
// }
export function make_layered_600cell() {
const tetras = sorted_600cells()
const LAYERS = [
[ "00", 20 ],
[ "01", 20 ],
[ "02", 30 ],
[ "03", 60 ],
[ "04", 60 ],
[ "05", 60 ],
[ "06", 20 ],
[ "07", 60 ],
[ "08", 20 ],
[ "09", 60 ],
[ "10", 60 ],
[ "11", 60 ],
[ "12", 30 ],
[ "13", 20 ],
[ "14", 20 ]
];
const vertices = {};
const seen = {};
let i = 0;
for( const layer of LAYERS ) {
const label = layer[0];
const n = layer[1];
vertices[label] = [];
console.log(`Layer ${label} starting at ${i}`);
for( const t of tetras.slice(i, i + n) ) {
console.log(t);
for( const n of t.nodes ) {
if( !seen[n] ) {
vertices[label].push(n);
seen[n] = true;
}
}
}
i += n;
}
return JSON.stringify(vertices);
}

119
linktest.js
View File

@ -1,119 +0,0 @@
import * as THREE from 'three';
import { OrbitControls } from 'three/addons/controls/OrbitControls.js';
import { GUI } from 'lil-gui';
import { TaperedLink } from './taperedLink.js';
const FACE_OPACITY = 0.3;
const CAMERA_K = 5;
// scene, lights and camera
const scene = new THREE.Scene();
const camera = new THREE.PerspectiveCamera( 75, window.innerWidth / window.innerHeight, 0.1, 1000 );
const light = new THREE.PointLight(0xffffff, 2);
light.position.set(10, 10, 10);
scene.add(light);
const light2 = new THREE.PointLight(0xffffff, 2);
light2.position.set(-10, 5, 10);
scene.add(light);
const amblight = new THREE.AmbientLight(0xffffff, 0.5);
scene.add(amblight);
camera.position.set(0, 0, CAMERA_K / 2);
camera.lookAt(0, 0, 0);
camera.position.z = 8;
const renderer = new THREE.WebGLRenderer({antialias: true});
renderer.setSize( window.innerWidth, window.innerHeight );
renderer.localClippingEnabled = true;
const controls = new OrbitControls( camera, renderer.domElement );
controls.autoRotate = true;
document.body.appendChild( renderer.domElement );
const NODEC = 0x3293a9;
const LINKC = 0x00ff88;
const BACKGROUNDC = 0xd4d4d4;
scene.background = new THREE.Color(BACKGROUNDC);
const material = new THREE.MeshStandardMaterial({ color: LINKC });
material.transparent = true;
material.opacity = 0.7;
const node_mat = new THREE.MeshStandardMaterial({ color: NODEC });
node_mat.transparent = true;
node_mat.opacity = 0.5;
const params = {
r1: 0.5,
r2: 0.6,
sync: false,
l: 9,
rotx: 1,
roty: 0,
rotz: 0,
};
const gui = new GUI();
gui.add(params, "r1", 0.01, 1.5);
gui.add(params, "r2", 0.01, 1.5);
gui.add(params, "sync");
gui.add(params, "l", 0, 10);
gui.add(params, "rotx", 0, 4);
gui.add(params, "roty", 0, 4);
gui.add(params, "rotz", 0, 4);
function makeNode(material, pos, r) {
const geometry = new THREE.SphereGeometry(1);
const sphere = new THREE.Mesh(geometry, material);
const node = {
v3: pos,
object: sphere
};
updateNode(node, pos, r);
return node;
}
function updateNode(node, pos, r) {
node.v3 = pos;
node.object.scale.copy(new THREE.Vector3(r, r, r));
node.object.position.copy(pos);
}
const n1 = makeNode(node_mat, new THREE.Vector3(-params["l"], -1, -1), params["r1"]);
const n2 = makeNode(node_mat, new THREE.Vector3(params["l"], 1, 1), params["r2"]);
const tl = new TaperedLink(material, n1, n2, params["r1"], params["r2"]);
scene.add(n1.object);
scene.add(n2.object);
scene.add(tl);
function animate() {
requestAnimationFrame(animate);
const r1 = params["r1"];
const r2 = params["sync"] ? r1 : params["r2"]
updateNode(n1, new THREE.Vector3(- params["l"], -1, -1), r1);
updateNode(n2, new THREE.Vector3(params["l"], 1, 1), r2);
tl.update(n1, n2, r1, r2, params["rotx"], params["roty"], params["rotz"]);
controls.update();
renderer.render(scene, camera);
}
animate();

224
main.js
View File

@ -1,31 +1,14 @@
import * as THREE from 'three';
const RELEASE_NOTES = `
<p><b>v1.1 - 1/1/2026</b></p>
<p>The 120-cell now includes a visualisation of its inscribed 5-cells, which honestly
looks like less of a mess than I expected it to.</p>
<p><b>v1.0 - 16/11/2025</b></p>
<p>It's been <a target="_blank" href="https://mikelynch.org/2023/Sep/02/120-cell/">two years</a> since
I first made this, and I haven't updated it in a while, but I got tapered links to
work without too much performance overhead, so that seemed worth a version.</p>
<p>The results flicker a bit at low opacities but otherwise I'm pretty happy with
it.</p>
`;
import * as POLYTOPES from './polytopes.js';
import { rotfn } from './rotation.js';
import { get_rotation } from './rotation.js';
import { FourDGUI, DEFAULTS } from './gui.js';
import { FourDShape } from './fourDShape.js';
import { get_colours } from './colours.js';
const FACE_OPACITY = 0.3;
const CAMERA_K = 5;
// scene, lights and camera
@ -40,44 +23,34 @@ scene.add(light);
const amblight = new THREE.AmbientLight(0xffffff, 0.5);
scene.add(amblight);
camera.position.set(0, 0, CAMERA_K / 2);
camera.lookAt(0, 0, 0);
//camera.position.z = 4;
camera.position.z = 4;
const renderer = new THREE.WebGLRenderer({antialias: true});
renderer.setSize( window.innerWidth, window.innerHeight );
renderer.localClippingEnabled = true;
document.body.appendChild( renderer.domElement );
// set up colours and materials for gui callbacks
scene.background = new THREE.Color(DEFAULTS.background);
const material = new THREE.MeshStandardMaterial({ color: DEFAULTS.color });
const node_colours = get_colours(DEFAULTS.color);
material.transparent = true;
material.opacity = 0.5;
const node_ms = node_colours.map((c) => new THREE.MeshStandardMaterial({color: c}));
const link_ms = node_colours.map((c) => new THREE.MeshStandardMaterial({color: c}));
node_ms.map((m) => {
m.transparent = true;
m.opacity = 1.0;
}
);
link_ms.map((m) => {
m.transparent = true;
m.opacity = 0.5;
}
);
console.log("link_ms", link_ms);
)
const face_ms = [
new THREE.MeshStandardMaterial( { color: 0x44ff44 } )
new THREE.MeshLambertMaterial( { color: 0x44ff44 } )
];
for( const face_m of face_ms ) {
@ -86,140 +59,92 @@ for( const face_m of face_ms ) {
}
const STRUCTURES = POLYTOPES.build_all();
const STRUCTURES = {
'5-cell': POLYTOPES.cell5(),
'16-cell': POLYTOPES.cell16(),
'tesseract': POLYTOPES.tesseract(),
'24-cell': POLYTOPES.cell24(),
'dodecahedron': POLYTOPES.dodecahedron(),
'five-cubes': POLYTOPES.five_cubes(),
'120-cell': POLYTOPES.cell120(),
'600-cell': POLYTOPES.cell600(),
};
const STRUCTURES_BY_NAME = {};
const INSCRIBED = {
'tesseract': POLYTOPES.tesseract_inscribed(),
'24-cell': POLYTOPES.cell24_inscribed(),
'120-cell': POLYTOPES.cell120_inscribed(),
'600-cell': POLYTOPES.cell600_inscribed(),
'dodecahedron': POLYTOPES.dodecahedron_inscribed(),
'five-cubes': POLYTOPES.five_cubes_inscribed(),
};
STRUCTURES.map((s) => STRUCTURES_BY_NAME[s.name] = s);
const ALL_INSCRIBED = {
'tesseract': POLYTOPES.tesseract_all_inscribed(),
'24-cell': POLYTOPES.cell24_all_inscribed(),
'120-cell': POLYTOPES.cell120_all_inscribed(),
'600-cell': POLYTOPES.cell600_all_inscribed(),
'dodecahedron': POLYTOPES.dodecahedron_all_inscribed(),
'five-cubes': POLYTOPES.five_cubes_all_inscribed(),
}
let shape = false;
let structure = false;
let node_show = [];
let link_show = [];
function createShape(name, option) {
function createShape(name, inscribed, all) {
if( shape ) {
scene.remove(shape);
}
structure = STRUCTURES_BY_NAME[name];
let structure = STRUCTURES[name];
if( inscribed ) {
if( name in INSCRIBED ) {
if( all ) {
structure = ALL_INSCRIBED[name];
} else {
structure = INSCRIBED[name];
}
}
}
shape = new FourDShape(node_ms, link_ms, face_ms, structure);
scene.add(shape);
setVisibility(option ? option : structure.options[0].name);
}
function displayDocs(name) {
const docdiv = document.getElementById("description");
const description = STRUCTURES_BY_NAME[name].description;
if( description ) {
docdiv.innerHTML =`<p>${name}</p><p>${description}</p>`;
} else {
docdiv.innerHTML =`<p>${name}</p>`;
}
}
function showDocs(visible) {
const docdiv = document.getElementById("description");
if( visible ) {
docdiv.style.display = '';
} else {
docdiv.style.display = 'none';
}
}
function releaseNotes() {
showDocs(false);
const reldiv = document.getElementById("release_notes");
reldiv.style.display = '';
reldiv.innerHTML = RELEASE_NOTES + '<p><a id="no_notes" href="#">[hide]</a>';
const goaway = document.getElementById("no_notes");
goaway.addEventListener('click', noNotes);
}
function noNotes() {
const reldiv = document.getElementById("release_notes");
reldiv.style.display = 'none';
}
const relnotes = document.getElementById('show_notes');
relnotes.addEventListener('click', releaseNotes);
// initialise gui and read params from URL
// callbacks to do things which are triggered by controls: reset the shape,
// change the colors. Otherwise we just read stuff from gui.params.
function setColors(c) {
const nc = get_colours(c);
for( let i = 0; i < node_ms.length; i++ ) {
node_ms[i].color = new THREE.Color(nc[i]);
link_ms[i].color = new THREE.Color(nc[i]);
}
if( shape ) {
// taperedLink.set_color updates according to the link index
shape.links.map((l) => l.object.set_color(nc));
}
const nc = get_colours(c);
for( let i = 0; i < node_ms.length; i++ ) {
node_ms[i].color = new THREE.Color(nc[i]);
link_ms[i].color = new THREE.Color(nc[i]);
}
material.color = new THREE.Color(c);
}
function setBackground(c) {
scene.background = new THREE.Color(c)
}
// taperedLinks have their own materials so we have to set opacity
// on them individually. And also set the base materials as they
// will get updated from it when the shape changes
function setLinkOpacity(o, primary) {
link_ms.map((lm) => lm.opacity = o);
if( shape ) {
shape.links.map((l) => {
if( (primary && l.label == 0) || (!primary && l.label !== 0) ) {
l.object.material.opacity = o
}
});
}
}
function setNodeOpacity(o) {
node_ms.map((nm) => nm.opacity = o);
}
let gui;
function changeShape() {
createShape(gui.params.shape);
displayDocs(gui.params.shape);
}
function setVisibility(option_name) {
console.log("setVisibility", option_name);
console.log(structure.options);
const option = structure.options.filter((o) => o.name === option_name);
if( option.length ) {
node_show = option[0].nodes;
link_show = option[0].links;
if( primary ) {
link_ms[0].opacity = o;
} else {
console.log(`Error: option '${option_name}' not found`);
for( const lm of link_ms.slice(1) ) {
lm.opacity = o;
}
}
}
let gui; //
gui = new FourDGUI(
{
shapes: STRUCTURES,
changeShape: changeShape,
setColors: setColors,
setBackground: setBackground,
setNodeOpacity: setNodeOpacity,
setLinkOpacity: setLinkOpacity,
setVisibility: setVisibility,
showDocs: showDocs,
}
);
function changeShape() {
console.log("change shape!")
createShape(gui.params.shape, gui.params.inscribed, gui.params.inscribe_all);
}
gui = new FourDGUI(changeShape, setColors, setBackground, setLinkOpacity);
// these are here to pick up colour settings from the URL params
setColors(gui.params.color);
@ -262,8 +187,7 @@ renderer.domElement.addEventListener("pointerup", (event) => {
dragging = false;
})
createShape(gui.params.shape, gui.params.option);
displayDocs(gui.params.shape);
createShape(gui.params.shape, gui.params.inscribed, gui.params.inscribe_all);
function animate() {
requestAnimationFrame( animate );
@ -277,18 +201,12 @@ function animate() {
}
}
const rotations = [
rotfn[gui.params.xRotate](theta),
rotfn[gui.params.yRotate](psi)
];
shape.hyperplane = 1 / gui.params.hyperplane;
camera.position.set(0, 0, gui.params.zoom * CAMERA_K * gui.params.hyperplane);
const rotations = get_rotation(gui.params.rotation, theta, psi);
shape.hyperplane = gui.params.hyperplane;
shape.link_scale = gui.params.thickness;
shape.node_scale = gui.params.nodesize;
shape.link_scale = gui.params.linksize * gui.params.nodesize * 0.5;
shape.render3(rotations, node_show, link_show);
shape.render3(rotations);
renderer.render( scene, camera );
}

270
package-lock.json generated
View File

@ -4,11 +4,9 @@
"requires": true,
"packages": {
"": {
"name": "fourdjs",
"dependencies": {
"color": "^4.2.3",
"color-scheme": "^1.0.1",
"lil-gui": "^0.19.0",
"lil-gui": "^0.18.2",
"three": "^0.154.0"
},
"devDependencies": {
@ -16,9 +14,9 @@
}
},
"node_modules/@esbuild/android-arm": {
"version": "0.18.20",
"resolved": "https://registry.npmjs.org/@esbuild/android-arm/-/android-arm-0.18.20.tgz",
"integrity": "sha512-fyi7TDI/ijKKNZTUJAQqiG5T7YjJXgnzkURqmGj13C6dCqckZBLdl4h7bkhHt/t0WP+zO9/zwroDvANaOqO5Sw==",
"version": "0.18.15",
"resolved": "https://registry.npmjs.org/@esbuild/android-arm/-/android-arm-0.18.15.tgz",
"integrity": "sha512-wlkQBWb79/jeEEoRmrxt/yhn5T1lU236OCNpnfRzaCJHZ/5gf82uYx1qmADTBWE0AR/v7FiozE1auk2riyQd3w==",
"cpu": [
"arm"
],
@ -32,9 +30,9 @@
}
},
"node_modules/@esbuild/android-arm64": {
"version": "0.18.20",
"resolved": "https://registry.npmjs.org/@esbuild/android-arm64/-/android-arm64-0.18.20.tgz",
"integrity": "sha512-Nz4rJcchGDtENV0eMKUNa6L12zz2zBDXuhj/Vjh18zGqB44Bi7MBMSXjgunJgjRhCmKOjnPuZp4Mb6OKqtMHLQ==",
"version": "0.18.15",
"resolved": "https://registry.npmjs.org/@esbuild/android-arm64/-/android-arm64-0.18.15.tgz",
"integrity": "sha512-NI/gnWcMl2kXt1HJKOn2H69SYn4YNheKo6NZt1hyfKWdMbaGadxjZIkcj4Gjk/WPxnbFXs9/3HjGHaknCqjrww==",
"cpu": [
"arm64"
],
@ -48,9 +46,9 @@
}
},
"node_modules/@esbuild/android-x64": {
"version": "0.18.20",
"resolved": "https://registry.npmjs.org/@esbuild/android-x64/-/android-x64-0.18.20.tgz",
"integrity": "sha512-8GDdlePJA8D6zlZYJV/jnrRAi6rOiNaCC/JclcXpB+KIuvfBN4owLtgzY2bsxnx666XjJx2kDPUmnTtR8qKQUg==",
"version": "0.18.15",
"resolved": "https://registry.npmjs.org/@esbuild/android-x64/-/android-x64-0.18.15.tgz",
"integrity": "sha512-FM9NQamSaEm/IZIhegF76aiLnng1kEsZl2eve/emxDeReVfRuRNmvT28l6hoFD9TsCxpK+i4v8LPpEj74T7yjA==",
"cpu": [
"x64"
],
@ -64,9 +62,9 @@
}
},
"node_modules/@esbuild/darwin-arm64": {
"version": "0.18.20",
"resolved": "https://registry.npmjs.org/@esbuild/darwin-arm64/-/darwin-arm64-0.18.20.tgz",
"integrity": "sha512-bxRHW5kHU38zS2lPTPOyuyTm+S+eobPUnTNkdJEfAddYgEcll4xkT8DB9d2008DtTbl7uJag2HuE5NZAZgnNEA==",
"version": "0.18.15",
"resolved": "https://registry.npmjs.org/@esbuild/darwin-arm64/-/darwin-arm64-0.18.15.tgz",
"integrity": "sha512-XmrFwEOYauKte9QjS6hz60FpOCnw4zaPAb7XV7O4lx1r39XjJhTN7ZpXqJh4sN6q60zbP6QwAVVA8N/wUyBH/w==",
"cpu": [
"arm64"
],
@ -80,9 +78,9 @@
}
},
"node_modules/@esbuild/darwin-x64": {
"version": "0.18.20",
"resolved": "https://registry.npmjs.org/@esbuild/darwin-x64/-/darwin-x64-0.18.20.tgz",
"integrity": "sha512-pc5gxlMDxzm513qPGbCbDukOdsGtKhfxD1zJKXjCCcU7ju50O7MeAZ8c4krSJcOIJGFR+qx21yMMVYwiQvyTyQ==",
"version": "0.18.15",
"resolved": "https://registry.npmjs.org/@esbuild/darwin-x64/-/darwin-x64-0.18.15.tgz",
"integrity": "sha512-bMqBmpw1e//7Fh5GLetSZaeo9zSC4/CMtrVFdj+bqKPGJuKyfNJ5Nf2m3LknKZTS+Q4oyPiON+v3eaJ59sLB5A==",
"cpu": [
"x64"
],
@ -96,9 +94,9 @@
}
},
"node_modules/@esbuild/freebsd-arm64": {
"version": "0.18.20",
"resolved": "https://registry.npmjs.org/@esbuild/freebsd-arm64/-/freebsd-arm64-0.18.20.tgz",
"integrity": "sha512-yqDQHy4QHevpMAaxhhIwYPMv1NECwOvIpGCZkECn8w2WFHXjEwrBn3CeNIYsibZ/iZEUemj++M26W3cNR5h+Tw==",
"version": "0.18.15",
"resolved": "https://registry.npmjs.org/@esbuild/freebsd-arm64/-/freebsd-arm64-0.18.15.tgz",
"integrity": "sha512-LoTK5N3bOmNI9zVLCeTgnk5Rk0WdUTrr9dyDAQGVMrNTh9EAPuNwSTCgaKOKiDpverOa0htPcO9NwslSE5xuLA==",
"cpu": [
"arm64"
],
@ -112,9 +110,9 @@
}
},
"node_modules/@esbuild/freebsd-x64": {
"version": "0.18.20",
"resolved": "https://registry.npmjs.org/@esbuild/freebsd-x64/-/freebsd-x64-0.18.20.tgz",
"integrity": "sha512-tgWRPPuQsd3RmBZwarGVHZQvtzfEBOreNuxEMKFcd5DaDn2PbBxfwLcj4+aenoh7ctXcbXmOQIn8HI6mCSw5MQ==",
"version": "0.18.15",
"resolved": "https://registry.npmjs.org/@esbuild/freebsd-x64/-/freebsd-x64-0.18.15.tgz",
"integrity": "sha512-62jX5n30VzgrjAjOk5orYeHFq6sqjvsIj1QesXvn5OZtdt5Gdj0vUNJy9NIpjfdNdqr76jjtzBJKf+h2uzYuTQ==",
"cpu": [
"x64"
],
@ -128,9 +126,9 @@
}
},
"node_modules/@esbuild/linux-arm": {
"version": "0.18.20",
"resolved": "https://registry.npmjs.org/@esbuild/linux-arm/-/linux-arm-0.18.20.tgz",
"integrity": "sha512-/5bHkMWnq1EgKr1V+Ybz3s1hWXok7mDFUMQ4cG10AfW3wL02PSZi5kFpYKrptDsgb2WAJIvRcDm+qIvXf/apvg==",
"version": "0.18.15",
"resolved": "https://registry.npmjs.org/@esbuild/linux-arm/-/linux-arm-0.18.15.tgz",
"integrity": "sha512-dT4URUv6ir45ZkBqhwZwyFV6cH61k8MttIwhThp2BGiVtagYvCToF+Bggyx2VI57RG4Fbt21f9TmXaYx0DeUJg==",
"cpu": [
"arm"
],
@ -144,9 +142,9 @@
}
},
"node_modules/@esbuild/linux-arm64": {
"version": "0.18.20",
"resolved": "https://registry.npmjs.org/@esbuild/linux-arm64/-/linux-arm64-0.18.20.tgz",
"integrity": "sha512-2YbscF+UL7SQAVIpnWvYwM+3LskyDmPhe31pE7/aoTMFKKzIc9lLbyGUpmmb8a8AixOL61sQ/mFh3jEjHYFvdA==",
"version": "0.18.15",
"resolved": "https://registry.npmjs.org/@esbuild/linux-arm64/-/linux-arm64-0.18.15.tgz",
"integrity": "sha512-BWncQeuWDgYv0jTNzJjaNgleduV4tMbQjmk/zpPh/lUdMcNEAxy+jvneDJ6RJkrqloG7tB9S9rCrtfk/kuplsQ==",
"cpu": [
"arm64"
],
@ -160,9 +158,9 @@
}
},
"node_modules/@esbuild/linux-ia32": {
"version": "0.18.20",
"resolved": "https://registry.npmjs.org/@esbuild/linux-ia32/-/linux-ia32-0.18.20.tgz",
"integrity": "sha512-P4etWwq6IsReT0E1KHU40bOnzMHoH73aXp96Fs8TIT6z9Hu8G6+0SHSw9i2isWrD2nbx2qo5yUqACgdfVGx7TA==",
"version": "0.18.15",
"resolved": "https://registry.npmjs.org/@esbuild/linux-ia32/-/linux-ia32-0.18.15.tgz",
"integrity": "sha512-JPXORvgHRHITqfms1dWT/GbEY89u848dC08o0yK3fNskhp0t2TuNUnsrrSgOdH28ceb1hJuwyr8R/1RnyPwocw==",
"cpu": [
"ia32"
],
@ -176,9 +174,9 @@
}
},
"node_modules/@esbuild/linux-loong64": {
"version": "0.18.20",
"resolved": "https://registry.npmjs.org/@esbuild/linux-loong64/-/linux-loong64-0.18.20.tgz",
"integrity": "sha512-nXW8nqBTrOpDLPgPY9uV+/1DjxoQ7DoB2N8eocyq8I9XuqJ7BiAMDMf9n1xZM9TgW0J8zrquIb/A7s3BJv7rjg==",
"version": "0.18.15",
"resolved": "https://registry.npmjs.org/@esbuild/linux-loong64/-/linux-loong64-0.18.15.tgz",
"integrity": "sha512-kArPI0DopjJCEplsVj/H+2Qgzz7vdFSacHNsgoAKpPS6W/Ndh8Oe24HRDQ5QCu4jHgN6XOtfFfLpRx3TXv/mEg==",
"cpu": [
"loong64"
],
@ -192,9 +190,9 @@
}
},
"node_modules/@esbuild/linux-mips64el": {
"version": "0.18.20",
"resolved": "https://registry.npmjs.org/@esbuild/linux-mips64el/-/linux-mips64el-0.18.20.tgz",
"integrity": "sha512-d5NeaXZcHp8PzYy5VnXV3VSd2D328Zb+9dEq5HE6bw6+N86JVPExrA6O68OPwobntbNJ0pzCpUFZTo3w0GyetQ==",
"version": "0.18.15",
"resolved": "https://registry.npmjs.org/@esbuild/linux-mips64el/-/linux-mips64el-0.18.15.tgz",
"integrity": "sha512-b/tmngUfO02E00c1XnNTw/0DmloKjb6XQeqxaYuzGwHe0fHVgx5/D6CWi+XH1DvkszjBUkK9BX7n1ARTOst59w==",
"cpu": [
"mips64el"
],
@ -208,9 +206,9 @@
}
},
"node_modules/@esbuild/linux-ppc64": {
"version": "0.18.20",
"resolved": "https://registry.npmjs.org/@esbuild/linux-ppc64/-/linux-ppc64-0.18.20.tgz",
"integrity": "sha512-WHPyeScRNcmANnLQkq6AfyXRFr5D6N2sKgkFo2FqguP44Nw2eyDlbTdZwd9GYk98DZG9QItIiTlFLHJHjxP3FA==",
"version": "0.18.15",
"resolved": "https://registry.npmjs.org/@esbuild/linux-ppc64/-/linux-ppc64-0.18.15.tgz",
"integrity": "sha512-KXPY69MWw79QJkyvUYb2ex/OgnN/8N/Aw5UDPlgoRtoEfcBqfeLodPr42UojV3NdkoO4u10NXQdamWm1YEzSKw==",
"cpu": [
"ppc64"
],
@ -224,9 +222,9 @@
}
},
"node_modules/@esbuild/linux-riscv64": {
"version": "0.18.20",
"resolved": "https://registry.npmjs.org/@esbuild/linux-riscv64/-/linux-riscv64-0.18.20.tgz",
"integrity": "sha512-WSxo6h5ecI5XH34KC7w5veNnKkju3zBRLEQNY7mv5mtBmrP/MjNBCAlsM2u5hDBlS3NGcTQpoBvRzqBcRtpq1A==",
"version": "0.18.15",
"resolved": "https://registry.npmjs.org/@esbuild/linux-riscv64/-/linux-riscv64-0.18.15.tgz",
"integrity": "sha512-komK3NEAeeGRnvFEjX1SfVg6EmkfIi5aKzevdvJqMydYr9N+pRQK0PGJXk+bhoPZwOUgLO4l99FZmLGk/L1jWg==",
"cpu": [
"riscv64"
],
@ -240,9 +238,9 @@
}
},
"node_modules/@esbuild/linux-s390x": {
"version": "0.18.20",
"resolved": "https://registry.npmjs.org/@esbuild/linux-s390x/-/linux-s390x-0.18.20.tgz",
"integrity": "sha512-+8231GMs3mAEth6Ja1iK0a1sQ3ohfcpzpRLH8uuc5/KVDFneH6jtAJLFGafpzpMRO6DzJ6AvXKze9LfFMrIHVQ==",
"version": "0.18.15",
"resolved": "https://registry.npmjs.org/@esbuild/linux-s390x/-/linux-s390x-0.18.15.tgz",
"integrity": "sha512-632T5Ts6gQ2WiMLWRRyeflPAm44u2E/s/TJvn+BP6M5mnHSk93cieaypj3VSMYO2ePTCRqAFXtuYi1yv8uZJNA==",
"cpu": [
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],
@ -256,9 +254,9 @@
}
},
"node_modules/@esbuild/linux-x64": {
"version": "0.18.20",
"resolved": "https://registry.npmjs.org/@esbuild/linux-x64/-/linux-x64-0.18.20.tgz",
"integrity": "sha512-UYqiqemphJcNsFEskc73jQ7B9jgwjWrSayxawS6UVFZGWrAAtkzjxSqnoclCXxWtfwLdzU+vTpcNYhpn43uP1w==",
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"integrity": "sha512-MsHtX0NgvRHsoOtYkuxyk4Vkmvk3PLRWfA4okK7c+6dT0Fu4SUqXAr9y4Q3d8vUf1VWWb6YutpL4XNe400iQ1g==",
"cpu": [
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],
@ -272,9 +270,9 @@
}
},
"node_modules/@esbuild/netbsd-x64": {
"version": "0.18.20",
"resolved": "https://registry.npmjs.org/@esbuild/netbsd-x64/-/netbsd-x64-0.18.20.tgz",
"integrity": "sha512-iO1c++VP6xUBUmltHZoMtCUdPlnPGdBom6IrO4gyKPFFVBKioIImVooR5I83nTew5UOYrk3gIJhbZh8X44y06A==",
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"resolved": "https://registry.npmjs.org/@esbuild/netbsd-x64/-/netbsd-x64-0.18.15.tgz",
"integrity": "sha512-djST6s+jQiwxMIVQ5rlt24JFIAr4uwUnzceuFL7BQT4CbrRtqBPueS4GjXSiIpmwVri1Icj/9pFRJ7/aScvT+A==",
"cpu": [
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],
@ -288,9 +286,9 @@
}
},
"node_modules/@esbuild/openbsd-x64": {
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"resolved": "https://registry.npmjs.org/@esbuild/openbsd-x64/-/openbsd-x64-0.18.20.tgz",
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],
@ -304,9 +302,9 @@
}
},
"node_modules/@esbuild/sunos-x64": {
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"cpu": [
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],
@ -320,9 +318,9 @@
}
},
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@ -336,9 +334,9 @@
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@ -352,9 +350,9 @@
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"integrity": "sha512-kTdfRcSiDfQca/y9QIkng02avJ+NCaQvrMejlsB3RRv5sE9rRoeBPISaZpKxHELzRxZyLvNts1P27W3wV+8geQ==",
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@ -367,52 +365,15 @@
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"color-convert": "^2.0.1",
"color-string": "^1.9.0"
},
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"resolved": "https://registry.npmjs.org/color-string/-/color-string-1.9.1.tgz",
"integrity": "sha512-shrVawQFojnZv6xM40anx4CkoDP+fZsw/ZerEMsW/pyzsRbElpsL/DBVW7q3ExxwusdNXI3lXpuhEZkzs8p5Eg==",
"dependencies": {
"color-name": "^1.0.0",
"simple-swizzle": "^0.2.2"
}
},
"node_modules/esbuild": {
"version": "0.18.20",
"resolved": "https://registry.npmjs.org/esbuild/-/esbuild-0.18.20.tgz",
"integrity": "sha512-ceqxoedUrcayh7Y7ZX6NdbbDzGROiyVBgC4PriJThBKSVPWnnFHZAkfI1lJT8QFkOwH4qOS2SJkS4wvpGl8BpA==",
"version": "0.18.15",
"resolved": "https://registry.npmjs.org/esbuild/-/esbuild-0.18.15.tgz",
"integrity": "sha512-3WOOLhrvuTGPRzQPU6waSDWrDTnQriia72McWcn6UCi43GhCHrXH4S59hKMeez+IITmdUuUyvbU9JIp+t3xlPQ==",
"dev": true,
"hasInstallScript": true,
"bin": {
@ -422,34 +383,34 @@
"node": ">=12"
},
"optionalDependencies": {
"@esbuild/android-arm": "0.18.20",
"@esbuild/android-arm64": "0.18.20",
"@esbuild/android-x64": "0.18.20",
"@esbuild/darwin-arm64": "0.18.20",
"@esbuild/darwin-x64": "0.18.20",
"@esbuild/freebsd-arm64": "0.18.20",
"@esbuild/freebsd-x64": "0.18.20",
"@esbuild/linux-arm": "0.18.20",
"@esbuild/linux-arm64": "0.18.20",
"@esbuild/linux-ia32": "0.18.20",
"@esbuild/linux-loong64": "0.18.20",
"@esbuild/linux-mips64el": "0.18.20",
"@esbuild/linux-ppc64": "0.18.20",
"@esbuild/linux-riscv64": "0.18.20",
"@esbuild/linux-s390x": "0.18.20",
"@esbuild/linux-x64": "0.18.20",
"@esbuild/netbsd-x64": "0.18.20",
"@esbuild/openbsd-x64": "0.18.20",
"@esbuild/sunos-x64": "0.18.20",
"@esbuild/win32-arm64": "0.18.20",
"@esbuild/win32-ia32": "0.18.20",
"@esbuild/win32-x64": "0.18.20"
"@esbuild/android-arm": "0.18.15",
"@esbuild/android-arm64": "0.18.15",
"@esbuild/android-x64": "0.18.15",
"@esbuild/darwin-arm64": "0.18.15",
"@esbuild/darwin-x64": "0.18.15",
"@esbuild/freebsd-arm64": "0.18.15",
"@esbuild/freebsd-x64": "0.18.15",
"@esbuild/linux-arm": "0.18.15",
"@esbuild/linux-arm64": "0.18.15",
"@esbuild/linux-ia32": "0.18.15",
"@esbuild/linux-loong64": "0.18.15",
"@esbuild/linux-mips64el": "0.18.15",
"@esbuild/linux-ppc64": "0.18.15",
"@esbuild/linux-riscv64": "0.18.15",
"@esbuild/linux-s390x": "0.18.15",
"@esbuild/linux-x64": "0.18.15",
"@esbuild/netbsd-x64": "0.18.15",
"@esbuild/openbsd-x64": "0.18.15",
"@esbuild/sunos-x64": "0.18.15",
"@esbuild/win32-arm64": "0.18.15",
"@esbuild/win32-ia32": "0.18.15",
"@esbuild/win32-x64": "0.18.15"
}
},
"node_modules/fsevents": {
"version": "2.3.3",
"resolved": "https://registry.npmjs.org/fsevents/-/fsevents-2.3.3.tgz",
"integrity": "sha512-5xoDfX+fL7faATnagmWPpbFtwh/R77WmMMqqHGS65C3vvB0YHrgF+B1YmZ3441tMj5n63k0212XNoJwzlhffQw==",
"version": "2.3.2",
"resolved": "https://registry.npmjs.org/fsevents/-/fsevents-2.3.2.tgz",
"integrity": "sha512-xiqMQR4xAeHTuB9uWm+fFRcIOgKBMiOBP+eXiyT7jsgVCq1bkVygt00oASowB7EdtpOHaaPgKt812P9ab+DDKA==",
"dev": true,
"hasInstallScript": true,
"optional": true,
@ -460,15 +421,10 @@
"node": "^8.16.0 || ^10.6.0 || >=11.0.0"
}
},
"node_modules/is-arrayish": {
"version": "0.3.2",
"resolved": "https://registry.npmjs.org/is-arrayish/-/is-arrayish-0.3.2.tgz",
"integrity": "sha512-eVRqCvVlZbuw3GrM63ovNSNAeA1K16kaR/LRY/92w0zxQ5/1YzwblUX652i4Xs9RwAGjW9d9y6X88t8OaAJfWQ=="
},
"node_modules/lil-gui": {
"version": "0.19.0",
"resolved": "https://registry.npmjs.org/lil-gui/-/lil-gui-0.19.0.tgz",
"integrity": "sha512-02/Z7rPng3GXWFwkQVj1hQaJYo2fIEYctqe0ima5uI/N2HEagB9ZGCQKkVWr3UuKfTr0arto3Q9prTB8sxtJJw=="
"version": "0.18.2",
"resolved": "https://registry.npmjs.org/lil-gui/-/lil-gui-0.18.2.tgz",
"integrity": "sha512-DgdrLy3/KGC0PiQLKgOcJMPItP4xY4iWgJ9+91Zaxfr8GCTmMps05QS9w9jW7yspILlbscbquwjOwxmWnSx5Uw=="
},
"node_modules/nanoid": {
"version": "3.3.6",
@ -495,9 +451,9 @@
"dev": true
},
"node_modules/postcss": {
"version": "8.4.31",
"resolved": "https://registry.npmjs.org/postcss/-/postcss-8.4.31.tgz",
"integrity": "sha512-PS08Iboia9mts/2ygV3eLpY5ghnUcfLV/EXTOW1E2qYxJKGGBUtNjN76FYHnMs36RmARn41bC0AZmn+rR0OVpQ==",
"version": "8.4.27",
"resolved": "https://registry.npmjs.org/postcss/-/postcss-8.4.27.tgz",
"integrity": "sha512-gY/ACJtJPSmUFPDCHtX78+01fHa64FaU4zaaWfuh1MhGJISufJAH4cun6k/8fwsHYeK4UQmENQK+tRLCFJE8JQ==",
"dev": true,
"funding": [
{
@ -523,9 +479,9 @@
}
},
"node_modules/rollup": {
"version": "3.29.4",
"resolved": "https://registry.npmjs.org/rollup/-/rollup-3.29.4.tgz",
"integrity": "sha512-oWzmBZwvYrU0iJHtDmhsm662rC15FRXmcjCk1xD771dFDx5jJ02ufAQQTn0etB2emNk4J9EZg/yWKpsn9BWGRw==",
"version": "3.26.3",
"resolved": "https://registry.npmjs.org/rollup/-/rollup-3.26.3.tgz",
"integrity": "sha512-7Tin0C8l86TkpcMtXvQu6saWH93nhG3dGQ1/+l5V2TDMceTxO7kDiK6GzbfLWNNxqJXm591PcEZUozZm51ogwQ==",
"dev": true,
"bin": {
"rollup": "dist/bin/rollup"
@ -538,14 +494,6 @@
"fsevents": "~2.3.2"
}
},
"node_modules/simple-swizzle": {
"version": "0.2.2",
"resolved": "https://registry.npmjs.org/simple-swizzle/-/simple-swizzle-0.2.2.tgz",
"integrity": "sha512-JA//kQgZtbuY83m+xT+tXJkmJncGMTFT+C+g2h2R9uxkYIrE2yy9sgmcLhCnw57/WSD+Eh3J97FPEDFnbXnDUg==",
"dependencies": {
"is-arrayish": "^0.3.1"
}
},
"node_modules/source-map-js": {
"version": "1.0.2",
"resolved": "https://registry.npmjs.org/source-map-js/-/source-map-js-1.0.2.tgz",
@ -561,14 +509,14 @@
"integrity": "sha512-Uzz8C/5GesJzv8i+Y2prEMYUwodwZySPcNhuJUdsVMH2Yn4Nm8qlbQe6qRN5fOhg55XB0WiLfTPBxVHxpE60ug=="
},
"node_modules/vite": {
"version": "4.5.3",
"resolved": "https://registry.npmjs.org/vite/-/vite-4.5.3.tgz",
"integrity": "sha512-kQL23kMeX92v3ph7IauVkXkikdDRsYMGTVl5KY2E9OY4ONLvkHf04MDTbnfo6NKxZiDLWzVpP5oTa8hQD8U3dg==",
"version": "4.4.6",
"resolved": "https://registry.npmjs.org/vite/-/vite-4.4.6.tgz",
"integrity": "sha512-EY6Mm8vJ++S3D4tNAckaZfw3JwG3wa794Vt70M6cNJ6NxT87yhq7EC8Rcap3ahyHdo8AhCmV9PTk+vG1HiYn1A==",
"dev": true,
"dependencies": {
"esbuild": "^0.18.10",
"postcss": "^8.4.27",
"rollup": "^3.27.1"
"postcss": "^8.4.26",
"rollup": "^3.25.2"
},
"bin": {
"vite": "bin/vite.js"

3
package.json
View File

@ -1,8 +1,7 @@
{
"dependencies": {
"color": "^4.2.3",
"color-scheme": "^1.0.1",
"lil-gui": "^0.19.0",
"lil-gui": "^0.18.2",
"three": "^0.154.0"
},
"devDependencies": {

692
polytopes.js
View File

@ -1,6 +1,6 @@
import * as PERMUTE from './permute.js';
import * as CELLINDEX from './cellindex.js';
import * as CELL120 from './cellindex.js';
function index_nodes(nodes, scale) {
let i = 1;
@ -22,7 +22,7 @@ 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;
}
export function auto_detect_edges(nodes, neighbours, debug=false) {
function auto_detect_edges(nodes, neighbours, debug=false) {
const seen = {};
const nnodes = nodes.length;
const links = [];
@ -55,38 +55,18 @@ export function auto_detect_edges(nodes, neighbours, debug=false) {
return links;
}
export const linkTest = () => {
return {
name: 'linky',
nodes: [
{ id:1, label: 1, x: -1, y: -1, z:-1, w: 0 },
{ id:2, label: 2, x: 1, y: 1, z: 1, w: 0 },
],
links: [
{ id: 1, source: 1, target: 2 }
],
options: [ { name: '--' }],
description: `link`,
}
};
// too small and simple to calculate
export const cell5 = () => {
const c1 = Math.sqrt(5) / 4;
const r5 = Math.sqrt(5);
const r2 = Math.sqrt(2) / 2;
return {
name: '5-cell',
nodes: [
{id:1, label: 1, x: c1, y: c1, z: c1, w: -0.25 },
{id:2, label: 2, x: c1, y: -c1, z: -c1, w: -0.25 },
{id:3, label: 3, x: -c1, y: c1, z: -c1, w: -0.25 },
{id:4, label: 4, x: -c1, y: -c1, z: c1, w: -0.25 },
{id:5, label: 5, x: 0, y: 0, z: 0, w: 1 },
{id:1, label: 1, x: r2, y: r2, z: r2, w: -r2 / r5 },
{id:2, label: 2, x: r2, y: -r2, z: -r2, w: -r2 / r5 },
{id:3, label: 3, x: -r2, y: r2, z: -r2, w: -r2 / r5 },
{id:4, label: 4, x: -r2, y: -r2, z: r2, w: -r2 / r5 },
{id:5, label: 5, x: 0, y: 0, z: 0, w: 4 * r2 / r5 },
],
links: [
{ id:1, source:1, target: 2},
@ -100,12 +80,10 @@ export const cell5 = () => {
{ id:9, source:3, target: 5},
{ id:10, source:4, target: 5},
],
options: [ { name: '--' }],
description: `Five tetrahedra joined at ten faces with three
tetrahedra around each edge. The 5-cell is the simplest regular
four-D polytope and the four-dimensional analogue of the tetrahedron.
A corresponding polytope, or simplex, exists for every n-dimensional
space.`,
geometry: {
node_size: 0.02,
link_size: 0.02
}
};
};
@ -124,18 +102,16 @@ export const cell16 = () => {
nodes[1].label = 4;
index_nodes(nodes);
scale_nodes(nodes, 0.5);
scale_nodes(nodes, 0.75);
const links = auto_detect_edges(nodes, 6);
return {
name: '16-cell',
nodes: nodes,
links: links,
options: [ { name: '--' }],
description: `Sixteen tetrahedra joined at 32 faces with four
tetrahedra around each edge. The 16-cell is the four-dimensional
analogue of the octahedron and is dual to the tesseract. Every
n-dimensional space has a corresponding polytope in this family.`,
geometry: {
node_size: 0.02,
link_size: 0.02
}
};
};
@ -153,37 +129,41 @@ export const tesseract = () => {
}
}
scale_nodes(nodes, 0.5);
scale_nodes(nodes, Math.sqrt(2) / 2);
const links = auto_detect_edges(nodes, 4);
links.map((l) => { l.label = 0 });
for( const p of [ 1, 2 ] ) {
const nodes16 = nodes.filter((n) => n.label === p);
const links16 = auto_detect_edges(nodes16, 6);
links16.map((l) => l.label = p);
links.push(...links16);
}
return {
name: 'Tesseract',
nodes: nodes,
links: links,
options: [
{ name: 'none', links: [ 0 ] },
{ name: 'one 16-cell', links: [ 0, 1 ] },
{ name: 'both 16-cells', links: [ 0, 1, 2 ] },
],
description: `The most well-known four-dimensional shape, the
tesseract is analogous to the cube, and is constructed by placing two
cubes in parallel hyperplanes and joining their corresponding
vertices. It consists of eight cubes joined at 32 face with three
cubes around each edge, and is dual to the 16-cell. Every
n-dimensional space has a cube analogue or measure polytope.`,
geometry: {
node_size: 0.02,
link_size: 0.02
}
};
}
const tesseract_some_inscribed = (ps) => {
const t = tesseract();
const i_links = [];
for( const p of ps ) {
const nodes16 = t.nodes.filter((n) => n.label === p);
const links16 = auto_detect_edges(nodes16, 6);
links16.map((l) => l.label = p);
i_links.push(...links16);
}
t.links.push(...i_links);
return t;
}
export const tesseract_inscribed = () => tesseract_some_inscribed([1]);
export const tesseract_all_inscribed = () => tesseract_some_inscribed([1,2]);
const CELL24_INDEXING = {
x: { y: 1, z: 3, w: 2 },
y: { z: 2, w: 3 },
@ -205,17 +185,9 @@ export const cell24 = () => {
n.label = CELL24_INDEXING[axes[0]][axes[1]];
}
scale_nodes(nodes, Math.sqrt(2) / 2);
index_nodes(nodes);
const links = auto_detect_edges(nodes, 8);
links.map((l) => l.label = 0);
for( const p of [ 1, 2, 3 ] ) {
const nodes16 = nodes.filter((n) => n.label === p);
const links16 = auto_detect_edges(nodes16, 6);
links16.map((l) => l.label = p);
links.push(...links16);
}
// links.map((l) => {
// const ls = [ l.source, l.target ].map((nid) => node_by_id(nodes, nid).label);
// for ( const c of [1, 2, 3] ) {
@ -226,23 +198,35 @@ export const cell24 = () => {
// });
return {
name: '24-cell',
nodes: nodes,
links: links,
base: {},
options: [
{ name: 'none', links: [ 0 ] },
{ name: 'one 16-cell', links: [ 0, 1 ] },
{ name: 'three 16-cells', links: [ 0, 1, 2, 3 ] }
],
description: `A unique object without an exact analogue in higher
or lower dimensions, the 24-cell is made of twenty-four octahedra
joined at 96 faces, with three around each edge. The 24-cell is
self-dual.`,
geometry: {
node_size: 0.02,
link_size: 0.02
}
};
}
const cell24_some_inscribed = (ps) => {
const t = cell24();
const i_links = [];
for( const p of ps ) {
const nodes16 = t.nodes.filter((n) => n.label === p);
const links16 = auto_detect_edges(nodes16, 6);
links16.map((l) => l.label = p);
i_links.push(...links16);
}
t.links.push(...i_links);
return t;
}
export const cell24_inscribed = () => cell24_some_inscribed([1]);
export const cell24_all_inscribed = () => cell24_some_inscribed([1,2,3]);
@ -324,7 +308,7 @@ function auto_120cell_faces(links) {
export function make_120cell_vertices() {
function make_120cell_vertices() {
const phi = 0.5 * (1 + Math.sqrt(5));
const r5 = Math.sqrt(5);
const phi2 = phi * phi;
@ -342,14 +326,14 @@ export function make_120cell_vertices() {
PERMUTE.coordinates([2, 1, phi, phiinv], 0, true),
].flat();
index_nodes(nodes);
scale_nodes(nodes, 0.25 * Math.sqrt(2));
scale_nodes(nodes, 0.5);
label_120cell(nodes);
return nodes;
}
function label_nodes(nodes, ids, label) {
nodes.filter((n) => ids.includes(n.id)).map((n) => n.label = label);
}
@ -357,8 +341,16 @@ function label_nodes(nodes, ids, label) {
function label_faces_120cell(nodes, faces, cfaces, label) {
const ns = new Set();
console.log(`label faces from ${cfaces}`);
for( const fid of cfaces ) {
const face = faces.filter((f)=> f.id === fid );
if( face.length > 0 ) {
@ -371,6 +363,33 @@ function label_faces_120cell(nodes, faces, cfaces, label) {
}
function basic_auto_label_120cell(nodes, links) {
const faces = auto_120cell_faces(links);
const dodecas = DODECAHEDRA.DODECAHEDRA;
//const cfaces = [ 1, 2, 4, 145, 169 ];
let colour = 1;
for( const dd of dodecas ) {
label_faces_120cell(nodes, faces, dd, colour);
colour++;
if( colour > 8 ) {
colour = 1;
}
}
}
function label_120cell(nodes) {
for( const cstr in CELL120.INDEX ) {
label_nodes(nodes, CELL120.INDEX[cstr], Number(cstr));
}
}
function link_labels(nodes, link) {
const n1 = nodes.filter((n) => n.id === link.source);
const n2 = nodes.filter((n) => n.id === link.target);
@ -378,124 +397,126 @@ function link_labels(nodes, link) {
}
// version of the 120-cell where nodes are partitioned by
// layer and the links follow that
export const cell120_layered = (max) => {
export const cell120 = () => {
const nodes = make_120cell_vertices();
const links = auto_detect_edges(nodes, 4);
nodes.map((n) => n.label = 9); // make all invisible by default
for (const cstr in CELLINDEX.LAYERS120 ) {
label_nodes(nodes, CELLINDEX.LAYERS120[cstr], Number(cstr));
}
links.map((l) => {
const labels = link_labels(nodes, l);
if( labels[0] >= labels[1] ) {
l.label = labels[0];
} else {
l.label = labels[1];
}
});
const options = [];
const layers = [];
for( const i of [ 0, 1, 2, 3, 4, 5, 6, 7 ] ) {
layers.push(i);
options.push({
name: CELLINDEX.LAYER_NAMES[i],
links: [...layers],
nodes: [...layers]
})
}
label_120cell(nodes);
return {
name: '120-cell layered',
nodes: nodes,
links: links,
nolink2opacity: true,
options: options,
description: `This version of the 120-cell lets you explore its
structure by building each layer from the 'north pole' onwards.`,
geometry: {
node_size: 0.02,
link_size: 0.02
},
}
}
const inscribed_polytope = (vertex_fn, edges, inscr_edges, parts) => {
const nodes = vertex_fn();
const links = auto_detect_edges(nodes, edges);
const all_links = links;
all_links.map((l) => l.label = 0);
export const cell120_inscribed = () => {
const nodes = make_120cell_vertices();
const links = auto_detect_edges(nodes, 4);
for( const cstr in CELLINDEX.INDEX120 ) {
label_nodes(nodes, CELLINDEX.INDEX120[cstr], Number(cstr));
for( const p of parts ) {
const nodes_in = nodes.filter((n) => n.label === p);
const links_in = auto_detect_edges(nodes_in, inscr_edges);
links_in.map((l) => l.label = p);
all_links.push(...links_in);
}
links.map((l) => l.label = 0);
for( const p of [ 1, 2, 3, 4, 5 ]) {
const nodes600 = nodes.filter((n) => n.label === p);
const links600 = auto_detect_edges(nodes600, 12);
links600.map((l) => l.label = p);
links.push(...links600);
}
const CELL5S = CELLINDEX.CELL120_CELL5.cell5s;
for( const c5 in CELL5S ) {
const nodes5 = nodes.filter((n) => CELL5S[c5].includes(n.id));
const links5 = auto_detect_edges(nodes5, 5);
links5.map((l) => l.label = 8);
links.push(...links5);
}
return {
name: '120-cell',
nodes: nodes,
links: links,
options: [
{ name: "none", links: [ 0 ]},
{ name: "one inscribed 600-cell", links: [ 0, 1 ] },
{ name: "five inscribed 600-cells", links: [ 0, 1, 2, 3, 4, 5 ] },
{ name: "120 inscribed 5-cells", links: [ 0, 8 ] },
],
description: `The 120-cell is the four-dimensional analogue of the
dodecahedron, and consists of 120 dodecahedra joined at 720 faces,
with three dodecahedra around each edge. It is dual to the 600-cell,
and five 600-cells can be inscribed in its vertices. The converse
of this allows 120 5-cells (each of which has one vertex in each
of the 5 600-cells) to be inscribed in the 120-cell.`,
links: all_links,
geometry: {
node_size: 0.02,
link_size: 0.02
},
}
}
export const cell120_inscribed_cell5 = () => {
const nodes = make_120cell_vertices();
const links = auto_detect_edges(nodes, 4);
for( const cstr in CELLINDEX.INDEX120 ) {
label_nodes(nodes, CELLINDEX.INDEX120[cstr], Number(cstr));
}
links.map((l) => l.label = 0);
export const cell120_inscribed = () => inscribed_polytope(
make_120cell_vertices, 4, 12, [1]
);
export const cell120_all_inscribed = () => inscribed_polytope(
make_120cell_vertices, 4, 12, [1,2,3,4,5]
);
// Schoute's partition via https://arxiv.org/abs/1010.4353
const partition600 = {
return {
name: '120-cell-5-cell',
nodes: nodes,
links: links,
options: [
{ name: "5-cells", links: [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] },
],
description: `The 120-cell with one of its 5-cells.`,
}
}
"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
};
@ -537,7 +558,7 @@ function map_coord(i, coords, values) {
}
export function make_600cell_vertices() {
function make_600cell_vertices() {
const coords = {
0: '0',
1: '1',
@ -561,7 +582,7 @@ export function make_600cell_vertices() {
].flat();
for( const n of nodes ) {
n.label = label_vertex(n, coords, CELLINDEX.PARTITION600);
n.label = label_vertex(n, coords, partition600);
}
for( const n of nodes ) {
@ -572,7 +593,7 @@ export function make_600cell_vertices() {
index_nodes(nodes);
scale_nodes(nodes, 0.5);
scale_nodes(nodes, 0.75);
return nodes;
}
@ -586,6 +607,7 @@ function get_node(nodes, id) {
}
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);
@ -601,108 +623,22 @@ export const cell600 = () => {
const nodes = make_600cell_vertices();
const links = auto_detect_edges(nodes, 12);
links.map((l) => l.label = 0);
for( const p of [1, 2, 3, 4, 5]) {
const nodes24 = nodes.filter((n) => n.label === p);
const links24 = auto_detect_edges(nodes24, 8);
links24.map((l) => l.label = p);
links.push(...links24);
}
return {
name: '600-cell',
nodes: nodes,
links: links,
options: [
{ name: "none", links: [ 0 ]},
{ name: "one 24-cell", links: [ 0, 1 ] },
{ name: "five 24-cells", links: [ 0, 1, 2, 3, 4, 5 ] }
],
description: `The 600-cell is the four-dimensional analogue of the
icosahedron, and consists of 600 tetrahedra joined at 1200 faces
with five tetrahedra around each edge. It is dual to the 120-cell.
Its 120 vertices can be partitioned into five sets which form the
vertices of five inscribed 24-cells.`,
}
}
export const cell600_layered = () => {
const nodes = make_600cell_vertices();
const links = auto_detect_edges(nodes, 12);
nodes.map((n) => n.label = 9); // make all invisible by default
for (const cstr in CELLINDEX.LAYERS600 ) {
label_nodes(nodes, CELLINDEX.LAYERS600[cstr], Number(cstr));
}
links.map((l) => {
const labels = link_labels(nodes, l);
if( labels[0] >= labels[1] ) {
l.label = labels[0];
} else {
l.label = labels[1];
geometry: {
node_size: 0.02,
link_size: 0.02
}
});
const options = [];
const layers = [];
for( const i of [ 0, 1, 2, 3, 4, 5, 6, 7 ] ) {
layers.push(i);
options.push({
name: CELLINDEX.LAYER_NAMES[i],
links: [...layers],
nodes: [...layers]
})
}
return {
name: '600-cell layered',
nodes: nodes,
links: links,
nolink2opacity: true,
options: options,
description: `This version of the 600-cell lets you explore its
structure by building each layer from the 'north pole' onwards.`,
}
}
export const snub24cell = () => {
const nodes600 = make_600cell_vertices();
const links600 = auto_detect_edges(nodes600, 12);
const nodes = nodes600.filter((n) => n.label != 1);
const links = links600.filter((l) => {
const sn = node_by_id(nodes, l.source);
const tn = node_by_id(nodes, l.target);
return sn && tn;
});
links.map((l) => l.label = 0);
return {
name: 'Snub 24-cell',
nodes: nodes,
links: links,
options: [ { name: "--" } ],
description: `The snub 24-cell is a semiregular polytope which
connects the 24-cell with the 600-cell. It consists of 24 icosahedra
and 120 tetrahedra, and is constructed by removing one of the
five inscribed 24-cells from a 600-cell.`
}
}
export const cell600_inscribed = () => inscribed_polytope(
make_600cell_vertices, 12, 8, [1]
);
export const cell600_all_inscribed = () => inscribed_polytope(
make_600cell_vertices, 12, 8, [1,2,3,4,5]
);
function make_dodecahedron_vertices() {
@ -735,7 +671,6 @@ function make_dodecahedron_vertices() {
{ x: -phi, y: phiinv, z:0, w: 0 , label: 4},
{ x: -phi, y: -phiinv, z:0, w: 0 , label: 2},
];
scale_nodes(nodes, 1 / Math.sqrt(3));
index_nodes(nodes);
return nodes;
}
@ -743,180 +678,65 @@ function make_dodecahedron_vertices() {
export const dodecahedron = () => {
const nodes = make_dodecahedron_vertices();
const links = auto_detect_edges(nodes, 3);
links.map((l) => l.label = 0);
for( const p of [ 1, 2, 3, 4, 5 ]) {
const tetran = nodes.filter((n) => n.label === p);
const tetral = auto_detect_edges(tetran, 3);
tetral.map((l) => l.label = p);
links.push(...tetral);
}
return {
name: 'Dodecahedron',
nodes: nodes,
links: links,
options: [
{ name: "none", links: [ 0 ]},
{ name: "one tetrahedron", links: [ 0, 1 ] },
{ name: "five tetrahedra", links: [ 0, 1, 2, 3, 4, 5 ] }
],
description: `The dodecahedron is a three-dimensional polyhedron
which is included here so that you can see the partition of its
vertices into five interlocked tetrahedra. This structure is the
basis for the partition of the 120-cell's vertices into five
600-cells.`
geometry: {
node_size: 0.02,
link_size: 0.02
}
}
}
export const dodecahedron_inscribed = () => inscribed_polytope(
make_dodecahedron_vertices, 3, 3, [1]
);
export const dodecahedron_all_inscribed = () => inscribed_polytope(
make_dodecahedron_vertices, 3, 3, [1,2,3,4,5]
);
export const tetrahedron = () => {
const r2 = Math.sqrt(2);
const r3 = Math.sqrt(3);
return {
name: 'Tetrahedron',
nodes: [
{id:1, label: 1, x: 2 * r2 / 3, y: 0, z: -1/3, w: 0 },
{id:2, label: 2, x: -r2 / 3, y: r2 / r3, z: -1/3, w: 0 },
{id:3, label: 3, x: -r2 / 3, y: -r2 / r3, z: -1/3, w: 0 },
{id:4, label: 4, x: 0, y: 0, z: 1, w: 0 },
],
links: [
{ id:1, source:1, target: 2},
{ id:2, source:1, target: 3},
{ id:3, source:1, target: 4},
{ id:4, source:2, target: 3},
{ id:5, source:2, target: 4},
{ id:6, source:3, target: 4},
],
options: [ { name: '--' }],
description: `The simplest three-dimensional polytope, consisting of four triangles joined at six edges. The 5-cell is its four-dimensional analogue.`,
};
};
export const octahedron = () => {
const nodes = [
{id: 1, label: 1, x: 1, y: 0, z: 0, w: 0},
{id: 2, label: 1, x: -1, y: 0, z: 0, w: 0},
{id: 3, label: 2, x: 0, y: 1, z: 0, w: 0},
{id: 4, label: 2, x: 0, y: -1, z: 0, w: 0},
{id: 5, label: 3, x: 0, y: 0, z: 1, w: 0},
{id: 6, label: 3, x: 0, y: 0, z: -1, w: 0},
];
const links = [
{id:1, source: 1, target: 3},
{id:2, source: 1, target: 4},
{id:3, source: 1, target: 5},
{id:4, source: 1, target: 6},
{id:5, source: 2, target: 3},
{id:6, source: 2, target: 4},
{id:7, source: 2, target: 5},
{id:8, source: 2, target: 6},
{id:9, source: 3, target: 5},
{id:10, source: 3, target: 6},
{id:11, source: 4, target: 5},
{id:12, source: 4, target: 6},
]
links.map((l) => { l.label = 0 });
return {
name: 'Octahedron',
nodes: nodes,
links: links,
options: [ { name: '--' }],
description: `The three-dimensional cross-polytope, the 16-cell is its four-dimensional analogue.`,
};
// this can't be done with inscribed_polytope because each vertex
// belongs to two cubes
}
export const cube = () => {
const nodes = [
{id: 1, label: 1, x: 1, y: 1, z: 1, w: 0},
{id: 2, label: 2, x: -1, y: 1, z: 1, w: 0},
{id: 3, label: 2, x: 1, y: -1, z: 1, w: 0},
{id: 4, label: 1, x: -1, y: -1, z: 1, w: 0},
{id: 5, label: 2, x: 1, y: 1, z: -1, w: 0},
{id: 6, label: 1, x: -1, y: 1, z: -1, w: 0},
{id: 7, label: 1, x: 1, y: -1, z: -1, w: 0},
{id: 8, label: 2, x: -1, y: -1, z: -1, w: 0},
];
scale_nodes(nodes, 1/Math.sqrt(3));
export const dodecahedron_five_cubes = (parts) => {
const nodes = make_dodecahedron_vertices();
const links = auto_detect_edges(nodes, 3);
links.map((l) => { l.label = 0 });
return {
name: 'Cube',
nodes: nodes,
links: links,
options: [ { name: '--' }],
description: `The three-dimensional measure polytope, the tesseract is its four-dimensional analogue.`,
const all_links = links;
all_links.map((l) => l.label = 0);
const CUBES = {
1: [ 1, 2, 3, 4, 5, 6, 7, 8 ],
2: [ 4, 5, 10, 11, 13, 16, 17, 20],
3: [ 2, 7, 9, 12, 13, 16, 18, 19],
4: [ 1, 8, 10, 11, 14, 15, 18, 19],
5: [ 3, 6, 9, 12, 14, 15, 17, 20]
};
}
function make_icosahedron_vertices() {
const phi = 0.5 * (1 + Math.sqrt(5));
const nodes = [
{ x: 0, y: 1, z: phi, w: 0, label: 1 },
{ x: 0, y: -1, z: phi, w: 0, label: 1 },
{ x: 0, y: 1, z: -phi, w: 0, label: 1 },
{ x: 0, y: -1, z: -phi, w: 0, label: 1 },
{ x: 1, y: phi, z: 0, w: 0, label: 2 },
{ x: -1, y: phi, z: 0, w: 0, label: 2 },
{ x: 1, y: -phi, z: 0, w: 0, label: 2 },
{ x: -1, y: -phi, z: 0, w: 0, label: 2 },
{ x: phi, y: 0, z: 1, w: 0, label: 3},
{ x: phi, y: 0, z: -1, w: 0, label: 3},
{ x: -phi, y: 0, z: 1, w: 0, label: 3},
{ x: -phi, y: 0, z: -1, w: 0, label: 3},
];
scale_nodes(nodes, 1/Math.sqrt((5 + Math.sqrt(5)) / 2));
index_nodes(nodes);
return nodes;
}
export const icosahedron = () => {
const nodes = make_icosahedron_vertices();
const links = auto_detect_edges(nodes, 5);
links.map((l) => l.label = 0);
if( parts.length > 0 ) {
// console.log(parts);
//console.log(parts.map(String));
//nodes.map((n) => n.label = 0);
for( const label of parts.map(String) ) {
console.log(`label = ${label}`);
const cube = nodes.filter((n) => CUBES[label].includes(n.id));
const cubel = auto_detect_edges(cube, 3);
cubel.map((l) => l.label = Number(label));
all_links.push(...cubel);
}
}
return {
name: 'Icosahedron',
nodes: nodes,
links: links,
options: [
{ name: "--"},
],
description: `The icosahedron is a twenty-sided polyhedron and is dual to the dodecahedron. Its four-dimensional analogue is the 600-cell.`
links: all_links,
geometry: {
node_size: 0.02,
link_size: 0.02
}
}
}
export const five_cubes = () => dodecahedron_five_cubes([]);
export const five_cubes_inscribed = () => dodecahedron_five_cubes([1]);
export const five_cubes_all_inscribed = () => dodecahedron_five_cubes([1,2,3,4,5]);
export const build_all = () => {
return [
tetrahedron(),
octahedron(),
cube(),
icosahedron(),
dodecahedron(),
cell5(),
cell16(),
tesseract(),
cell24(),
snub24cell(),
cell600(),
cell600_layered(),
cell120_inscribed(),
cell120_layered()
];
}
export const radii = (shape) => {
return shape.nodes.map(n => Math.sqrt(n.x * n.x + n.y * n.y + n.z * n.z + n.w * n.w))
}

19
rotation.js
View File

@ -81,5 +81,24 @@ export const rotfn = {
ZW: rotZW,
};
const rotMode = {
'rigid': [ rotYW, rotXW ],
'tumbling': [ rotYW, rotXZ ],
'inside-out': [ rotYW, rotXY ],
'axisymmetrical': [ rotZW, rotXY ]
};
export const get_rotation = (mode, theta, psi) => {
const fns = rotMode[mode];
return [ fns[0](theta), fns[1](psi) ];
}
// [
// rotfn[gui.params.xRotate](theta),
// rotfn[gui.params.yRotate](psi)
// ];

66
taperedLink.js
View File

@ -1,66 +0,0 @@
import * as THREE from 'three';
const EPSILON = 0.001;
class TaperedLink extends THREE.Group {
constructor(baseMaterial, color_i, n1, n2, r1, r2) {
super();
const geometry = new THREE.ConeGeometry( 1, 1, 16, true );
const cplane = new THREE.Plane(new THREE.Vector3(0, -1, 0), 0.5);
this.color_i = color_i;
this.material = baseMaterial.clone();
this.material.clippingPlanes = [ cplane ];
this.object = new THREE.Mesh( geometry, this.material );
this.add( this.object );
this.update(n1, n2, r1, r2);
}
update(n1, n2, r1, r2) {
const kraw = r1 - r2;
let k = ( Math.abs(kraw) < EPSILON ) ? EPSILON : kraw;
let nbase = n1.v3;
let napex = n2.v3;
let rbase = r1;
let rapex = r2;
if( k < 0 ) {
nbase = n2.v3;
napex = n1.v3;
rbase = r2;
rapex = r1;
k = -k;
}
const l = nbase.distanceTo(napex);
const lapex = l * rapex / k;
const h = l + lapex;
this.scale.copy(new THREE.Vector3(rbase, rbase, h));
const h_offset = 0.5 * h / l;
const pos = new THREE.Vector3();
pos.lerpVectors(nbase, napex, h_offset);
this.position.copy(pos); // the group, not the cone!!
this.lookAt(nbase);
this.children[0].rotation.x = 3 * Math.PI / 2.0;
this.visible = true;
const clipnorm = new THREE.Vector3();
clipnorm.copy(napex);
clipnorm.sub(nbase);
clipnorm.negate();
clipnorm.normalize();
this.material.clippingPlanes[0].setFromNormalAndCoplanarPoint(
clipnorm, napex
);
}
set_color(colors) {
this.material.color = new THREE.Color(colors[this.color_i]);
}
}
export { TaperedLink };

326
label120cell.js → testbed.js
View File

@ -1,8 +1,7 @@
// code for generating the 120-cell labels
// has some overlap with permute - FIXME
//testbed for playing with stuff in node repl
const THREE = require('three');
const THREE =require('three');
function pandita(a) {
const n = a.length;
@ -134,7 +133,7 @@ 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;
}
export function auto_detect_edges(nodes, neighbours, debug=false) {
function auto_detect_edges(nodes, neighbours, debug=false) {
const seen = {};
const nnodes = nodes.length;
const links = [];
@ -169,7 +168,7 @@ export function auto_detect_edges(nodes, neighbours, debug=false) {
export function make_120cell_vertices() {
function make_120cell_vertices() {
const phi = 0.5 * (1 + Math.sqrt(5));
const r5 = Math.sqrt(5);
const phi2 = phi * phi;
@ -231,7 +230,7 @@ function fingerprint(ids) {
export function auto_120cell_faces(links) {
function auto_120cell_faces(links) {
const faces = [];
const seen = {};
let id = 1;
@ -487,7 +486,7 @@ function colour_next_dodeca_maybe(nodes, links, faces, colours, dd, nextf, nextd
const nextvs = dodecahedron_vertices(nextdd);
// get the initial colour permutations from the existing labels;
const p = [];
for( let i = 0; i < 5; i ++ ) {
for( i = 0; i < 5; i ++ ) {
p[i] = colours[nextvs[i]];
}
const nlabels = colour_dodecahedron_from_face(nextdd, p);
@ -530,33 +529,6 @@ function meridian(nodes, links, faces, startf, startn, dir=11, max=10) {
}
function meridian_bump(nodes, links, faces, startf, startn, bumpdir=6) {
const o = face_plus_to_dodecahedron(faces, startf, startn);
const dir = 11;
const max = 10;
const colours = colour_dodecahedron_from_face(o, [ 1, 2, 3, 4, 5 ] );
const dds = follow_meridian(nodes, links, faces, colours, o, dir, max);
const dd4 = dds[4];
const nextf = dd4[bumpdir];
const bump = follow_face_to_dodeca(faces, dd4, nextf);
const ncolours = colour_next_dodeca_maybe(nodes, links, faces, colours, dd4, nextf, bump);
add_colours(colours, ncolours);
const labels = { 1: [], 2:[], 3:[], 4:[], 5:[] };
for( const vstr in colours ) {
labels[colours[vstr]].push(Number(vstr));
}
return { dodecahedra: dds, labels: labels };
}
function all_meridians(nodes, links, faces, startf, startn) {
const o = face_plus_to_dodecahedron(faces, startf, startn);
@ -696,9 +668,8 @@ function arctic(nodes, links, faces, startf, startn, max) {
// this is the final one that works for the whole 120-cell
export function label_120cell(nodes, links, faces, startf, startn) {
function arctic_two(nodes, links, faces, startf, startn) {
const pole = face_plus_to_dodecahedron(faces, startf, startn);
const dds = [ pole ];
@ -717,6 +688,10 @@ export function label_120cell(nodes, links, faces, startf, startn) {
seen[dd_fingerprint(nextdd)] = true;
}
// go around all of the arctic circle and grow all faces
// 1, 12, 20, 12, 30 = 75
// 0 1 13, 33, 45
for( const a of dds.slice(1, 13) ) {
for( const i of [ 6, 7, 8, 9, 10 ] ) {
@ -747,8 +722,6 @@ export function label_120cell(nodes, links, faces, startf, startn) {
}
// the 30 equatorials?
for( const a of dds.slice(13, 46) ) {
for( const i of [ 6, 7, 8, 9, 10 ] ) {
const [ nextdd, ncolours ] = follow_and_colour(
@ -777,10 +750,7 @@ export function label_120cell(nodes, links, faces, startf, startn) {
}
}
// this should get the rest or explode!
for( const a of dds ) {
for( const i of [ 6, 7, 8, 9, 10 ] ) {
const [ nextdd, ncolours ] = follow_and_colour(
@ -808,124 +778,6 @@ export function label_120cell(nodes, links, faces, startf, startn) {
export function cell120_layers(nodes, links, faces, startf, startn, max_layer) {
const pole = face_plus_to_dodecahedron(faces, startf, startn);
const dds = [ pole ];
const dd_families = { "0": [ pole ] }
const seen = {};
seen[dd_fingerprint(pole)] = true;
const colours = colour_dodecahedron_from_face(dds[0], [ 1, 2, 3, 4, 5 ] );
const vs = dodecahedron_vertices(dds[0]);
// arctic
if( max_layer > 0 ) {
dd_families["1"] = [];
for( const face of pole ) {
const [ nextdd, ncolours ] = follow_and_colour(
nodes, links, faces, colours, pole, face
);
add_colours(colours, ncolours);
dds.push(nextdd);
dd_families["1"].push(nextdd);
seen[dd_fingerprint(nextdd)] = true;
}
}
// subarctic - interstitial
if( max_layer > 1 ) {
dd_families["2"] = [];
for( const a of dd_families["1"] ) {
for( const i of [ 6, 7, 8, 9, 10 ] ) {
const [ nextdd, ncolours ] = follow_and_colour(
nodes, links, faces, colours, a, a[i]
);
const fp = dd_fingerprint(nextdd);
if( !(fp in seen) ) {
add_colours(colours, ncolours);
dds.push(nextdd);
dd_families["2"].push(nextdd);
seen[fp] = true;
}
}
}
}
// tropic of cancer
if( max_layer > 2 ) {
dd_families["3"] = [];
for( const a of dd_families["1"] ) {
const [ nextdd, ncolours ] = follow_and_colour(
nodes, links, faces, colours, a, a[11]
);
const fp = dd_fingerprint(nextdd);
if( !(fp in seen) ) {
add_colours(colours, ncolours);
dds.push(nextdd);
dd_families["3"].push(nextdd);
seen[fp] = true;
}
}
}
if( max_layer > 3 ) {
// equator
dd_families["4"] = [];
for( const a of dds.slice(13, 46) ) {
for( const i of [ 6, 7, 8, 9, 10 ] ) {
const [ nextdd, ncolours ] = follow_and_colour(
nodes, links, faces, colours, a, a[i]
);
const fp = dd_fingerprint(nextdd);
if( !(fp in seen) ) {
add_colours(colours, ncolours);
dd_families["4"].push(nextdd);
dds.push(nextdd);
seen[fp] = true;
}
}
}
}
if( max_layer > 4 ) {
dd_families["5"] = [];
for( const a of dd_families["4"] ) {
for( const i of [ 6, 7, 8, 9, 10 ] ) {
const [ nextdd, ncolours ] = follow_and_colour(
nodes, links, faces, colours, a, a[i]
);
const fp = dd_fingerprint(nextdd);
if( !(fp in seen) ) {
add_colours(colours, ncolours);
dds.push(nextdd);
dd_families["5"].push(nextdd);
seen[fp] = true;
}
}
}
}
const labels = { 1: [], 2:[], 3:[], 4:[], 5:[] };
for( const vstr in colours ) {
labels[colours[vstr]].push(Number(vstr));
}
return { dodecahedra: dds, labels: labels, families: dd_families };
}
// 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
@ -963,6 +815,7 @@ function make_120cell_cells(faces) {
for( const dd of dds ) {
const fp = dd_fingerprint(dd);
if( ! (fp in seen) ) {
//console.log(`added dodeca ${fp}`);
const d = {
id: i,
faces: dd,
@ -1042,7 +895,7 @@ function meridian_label_120cell(nodes) {
//label_nodes(nodes, [313], 6);
}
1
function check_120cell_nodes(nodes) {
nodes.map((n) => {
const vs = find_adjacent_labels(nodes, links, n.id);
@ -1060,134 +913,39 @@ function make_dodecahedron_vertices() {
const phiinv = 1 / phi;
const nodes = [
{ x: 1, y: 1, z: 1, w: 0 },
{ x: 1, y: 1, z: -1, w: 0 },
{ x: 1, y: -1, z: 1, w: 0 },
{ x: 1, y: -1, z: -1, w: 0 },
{ x: -1, y: 1, z: 1, w: 0 },
{ x: -1, y: 1, z: -1, w: 0 },
{ x: -1, y: -1, z: 1, w: 0 },
{ x: -1, y: -1, z: -1, w: 0 }
].flat();
scale_nodes(nodes, 0.5);
{ x: 1, y: 1, z: 1, w: 0, label: 4 },
{ x: 1, y: 1, z: -1, w: 0, label: 3 },
{ x: 1, y: -1, z: 1, w: 0, label: 3 },
{ x: 1, y: -1, z: -1, w: 0, label: 2 },
{ x: -1, y: 1, z: 1, w: 0, label: 3 },
{ x: -1, y: 1, z: -1, w: 0, label: 1 },
{ x: -1, y: -1, z: 1, w: 0, label: 5 },
{ x: -1, y: -1, z: -1, w: 0, label: 3 },
{ x: 0, y: phi, z: phiinv, w: 0, label: 5 },
{ x: 0, y: phi, z: -phiinv, w: 0 , label: 2 },
{ x: 0, y: -phi, z: phiinv, w: 0, label: 4 },
{ x: 0, y: -phi, z: -phiinv, w: 0 , label: 1 },
{ x: phiinv, y: 0, z: phi, w: 0 , label: 2},
{ x: phiinv, y: 0, z: -phi, w: 0 , label: 4},
{ x: -phiinv, y: 0, z: phi, w: 0 , label: 1},
{ x: -phiinv, y: 0, z: -phi, w: 0 , label: 5},
{ x: phi, y: phiinv, z:0, w: 0 , label: 1},
{ x: phi, y: -phiinv, z:0, w: 0 , label: 5},
{ x: -phi, y: phiinv, z:0, w: 0 , label: 4},
{ x: -phi, y: -phiinv, z:0, w: 0 , label: 2},
];
index_nodes(nodes);
return nodes;
}
// this one does the coherent indexing / partition into 600-cells
export function make_labelled_120cell() {
const nodes = make_120cell_vertices();
const links = auto_detect_edges(nodes, 4);
const faces = auto_120cell_faces(links);
const labelled = label_120cell(nodes, links, faces, faces[0], 341);
return labelled;
}
// calculate the w-distance of a dodecahedron's centroid
export function dd_w_distance(nodes, dd) {
const vertices = new Set();
dd.map((f) => f.nodes.map((n) => vertices.add(n)));
let w = 0;
for( const nid of vertices ) {
const node = node_by_id(nodes, nid);
w += node.w;
}
return w / 20;
}
export function sort_dds_w(nodes, dds) {
dds.sort((a, b) => {
return dd_w_distance(nodes, a) - dd_w_distance(nodes, b)
})
}
export function find_antipode_dd(nodes, links, dd) {
}
// notes because I'm too sick to continue working on this today
// the vertices which aren't counted by the layers are showing
// up in the visualisation because they are labelled "0" by default -
// for this to work better there needs to be a value which is never
// displayed.
// in the current layer algorithm, layer '5' (the one after the equator)
// is too greedy
export function make_layered_120cell(max_layer) {
const nodes = make_120cell_vertices();
const links = auto_detect_edges(nodes, 4);
const faces = auto_120cell_faces(links);
const labelled = label_120cell(nodes, links, faces, faces[628], 250, max_layer);
// get layers from sorted w-distance order
const dds = labelled.dodecahedra;
dds.sort((a, b) => dd_w_distance(nodes, b) - dd_w_distance(nodes, a));
const LAYERS = [
[ "0", 1 ],
[ "1", 12 ],
[ "2", 20 ],
[ "3", 12 ],
[ "4", 30 ],
[ "5", 12 ],
[ "6", 20 ],
[ "7", 12 ],
[ "8", 1]
];
const layer_dds = labelled["families"];
const vertices_layers = {};
const seen = {};
let i = 0;
for( const layer of LAYERS ) {
const label = layer[0];
const n = layer[1];
vertices_layers[label] = [];
console.log(`Layer ${label} starting at ${i}`);
for( const dd of dds.slice(i, i + n) ) {
console.log(dd_w_distance(nodes, dd));
for( const face of dd ) {
for( const n of face.nodes ) {
if( !seen[n] ) {
vertices_layers[label].push(n);
seen[n] = true;
}
}
}
}
i += n;
}
return JSON.stringify(vertices_layers);
}
export function make_meridians(bumpdir) {
const nodes = make_120cell_vertices();
const links = auto_detect_edges(nodes, 4);
const faces = auto_120cell_faces(links);
const mbs ={}
for( const bumpdir of [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 ] ) {
mbs[bumpdir] = meridian_bump(nodes, links, faces, faces[0], 341, bumpdir)
}
return mbs;
//
}
// const nodes = make_120cell_vertices();
// const links = auto_detect_edges(nodes, 4);
// const faces = auto_120cell_faces(links);
// console.log("Calculating 120-cell colours")

11
vite.config.js
View File

@ -3,14 +3,5 @@
import { defineConfig, loadEnv } from 'vite';
export default defineConfig({
base: '/fourjs/',
build: {
rollupOptions: {
output: {
manualChunks: {
threejs: [ 'three' ]
}
}
}
}
base: '/fourjs/'
})