322 lines
5.7 KiB
JavaScript
322 lines
5.7 KiB
JavaScript
|
|
import * as PERMUTE from './permute.js';
|
|
|
|
function index_nodes(nodes, scale) {
|
|
let i = 1;
|
|
for( const n of nodes ) {
|
|
n["id"] = i;
|
|
i++;
|
|
}
|
|
}
|
|
|
|
function scale_nodes(nodes, scale) {
|
|
for( const n of nodes ) {
|
|
for( const a of [ 'x', 'y', 'z', 'w' ] ) {
|
|
n[a] = scale * n[a];
|
|
}
|
|
}
|
|
}
|
|
|
|
function dist2(n1, n2) {
|
|
return (n1.x - n2.x) ** 2 + (n1.y - n2.y) ** 2 + (n1.z - n2.z) ** 2 + (n1.w - n2.w) ** 2;
|
|
}
|
|
|
|
function auto_detect_edges(nodes, neighbours, debug=false) {
|
|
const seen = {};
|
|
const nnodes = nodes.length;
|
|
const links = [];
|
|
let id = 1;
|
|
for( const n1 of nodes ) {
|
|
const d2 = [];
|
|
for( const n2 of nodes ) {
|
|
d2.push({ d2: dist2(n1, n2), id: n2.id });
|
|
}
|
|
d2.sort((a, b) => a.d2 - b.d2);
|
|
const closest = d2.slice(1, neighbours + 1);
|
|
if( debug ) {
|
|
console.log(`closest = ${closest.length}`);
|
|
console.log(closest);
|
|
}
|
|
for( const e of closest ) {
|
|
const ids = [ n1.id, e.id ];
|
|
ids.sort();
|
|
const fp = ids.join(',');
|
|
if( !seen[fp] ) {
|
|
seen[fp] = true;
|
|
links.push({ id: id, label: 0, source: n1.id, target: e.id });
|
|
id++;
|
|
}
|
|
}
|
|
}
|
|
if( debug ) {
|
|
console.log(`Found ${links.length} edges`)
|
|
}
|
|
return links;
|
|
}
|
|
|
|
// too small and simple to calculate
|
|
|
|
export const cell5 = () => {
|
|
const r5 = Math.sqrt(5);
|
|
const r2 = Math.sqrt(2) / 2;
|
|
return {
|
|
nodes: [
|
|
{id:1, x: r2, y: r2, z: r2, w: -r2 / r5 },
|
|
{id:2, x: r2, y: -r2, z: -r2, w: -r2 / r5 },
|
|
{id:3, x: -r2, y: r2, z: -r2, w: -r2 / r5 },
|
|
{id:4, x: -r2, y: -r2, z: r2, w: -r2 / r5 },
|
|
{id:5, x: 0, y: 0, z: 0, w: 4 * r2 / r5 },
|
|
],
|
|
links: [
|
|
{ id:1, source:1, target: 2},
|
|
{ id:2, source:1, target: 3},
|
|
{ id:3, source:1, target: 4},
|
|
{ id:4, source:1, target: 5},
|
|
{ id:5, source:2, target: 3},
|
|
{ id:6, source:2, target: 4},
|
|
{ id:7, source:2, target: 5},
|
|
{ id:8, source:3, target: 4},
|
|
{ id:9, source:3, target: 5},
|
|
{ id:10, source:4, target: 5},
|
|
],
|
|
geometry: {
|
|
node_size: 0.02,
|
|
link_size: 0.02
|
|
}
|
|
};
|
|
};
|
|
|
|
|
|
export const cell16 = () => {
|
|
let nodes = PERMUTE.coordinates([1, 1, 1, 1], 0);
|
|
nodes = nodes.filter((n) => n.x * n.y * n.z * n.w > 0);
|
|
index_nodes(nodes);
|
|
scale_nodes(nodes, 0.75);
|
|
const links = auto_detect_edges(nodes, 6);
|
|
|
|
return {
|
|
nodes: nodes,
|
|
links: links,
|
|
geometry: {
|
|
node_size: 0.02,
|
|
link_size: 0.02
|
|
}
|
|
};
|
|
};
|
|
|
|
|
|
|
|
export const tesseract = () => {
|
|
const nodes = PERMUTE.coordinates([1, 1, 1, 1], 0);
|
|
index_nodes(nodes);
|
|
scale_nodes(nodes, Math.sqrt(2) / 2);
|
|
const links = auto_detect_edges(nodes, 4);
|
|
|
|
return {
|
|
nodes: nodes,
|
|
links: links,
|
|
geometry: {
|
|
node_size: 0.02,
|
|
link_size: 0.02
|
|
}
|
|
};
|
|
}
|
|
|
|
|
|
|
|
|
|
export const cell24 = () => {
|
|
const nodes = PERMUTE.coordinates([0, 0, 1, 1], 0);
|
|
index_nodes(nodes);
|
|
const links = auto_detect_edges(nodes, 6);
|
|
|
|
return {
|
|
nodes: nodes,
|
|
links: links,
|
|
geometry: {
|
|
node_size: 0.02,
|
|
link_size: 0.02
|
|
}
|
|
};
|
|
}
|
|
|
|
|
|
|
|
|
|
function make_120cell_vertices() {
|
|
const phi = 0.5 * (1 + Math.sqrt(5));
|
|
const r5 = Math.sqrt(5);
|
|
const phi2 = phi * phi;
|
|
const phiinv = 1 / phi;
|
|
const phi2inv = 1 / phi2;
|
|
|
|
const nodes = [
|
|
PERMUTE.coordinates([0, 0, 2, 2], 0),
|
|
PERMUTE.coordinates([1, 1, 1, r5], 0),
|
|
PERMUTE.coordinates([phi, phi, phi, phi2inv], 0),
|
|
PERMUTE.coordinates([phiinv, phiinv, phiinv, phi2], 0),
|
|
|
|
PERMUTE.coordinates([phi2, phi2inv, 1, 0], 0, true),
|
|
PERMUTE.coordinates([r5, phiinv, phi, 0], 0, true),
|
|
PERMUTE.coordinates([2, 1, phi, phiinv], 0, true),
|
|
].flat();
|
|
index_nodes(nodes);
|
|
scale_nodes(nodes, 0.5);
|
|
return nodes;
|
|
}
|
|
|
|
|
|
export const cell120 = () => {
|
|
const nodes = make_120cell_vertices();
|
|
const links = auto_detect_edges(nodes, 4);
|
|
return {
|
|
nodes: nodes,
|
|
links: links,
|
|
geometry: {
|
|
node_size: 0.02,
|
|
link_size: 0.02
|
|
}
|
|
|
|
}
|
|
}
|
|
|
|
// Schoute's partition via https://arxiv.org/abs/1010.4353
|
|
|
|
const partition600 = {
|
|
|
|
"2,0,0,0": 1,
|
|
"0,2,0,0": 1,
|
|
"0,0,2,0": 1,
|
|
"0,0,0,2": 1,
|
|
"1,1,1,1": 1,
|
|
"1,1,-1,-1": 1,
|
|
"1,-1,1,-1": 1,
|
|
"1,-1,-1,1": 1,
|
|
"1,-1,-1,-1": 1,
|
|
"1,-1,1,1": 1,
|
|
"1,1,-1,1": 1,
|
|
"1,1,1,-1": 1,
|
|
|
|
"k,0,-t,-1": 2,
|
|
"0,k,1,-t": 2,
|
|
"t,-1,k,0": 2,
|
|
"1,t,0,k": 2,
|
|
"t,k,0,-1": 2,
|
|
"1,0,k,t": 2,
|
|
"k,-t,-1,0": 2,
|
|
"0,1,-t,k": 2,
|
|
"1,k,t,0": 2,
|
|
"t,0,-1,k": 2,
|
|
"0,t,-k,-1": 2,
|
|
"k,-1,0,-t": 2,
|
|
|
|
"t,0,1,k": 3,
|
|
"0,t,-k,1": 3,
|
|
"1,-k,-t,0": 3,
|
|
"k,1,0,-t": 3,
|
|
"0,k,1,t": 3,
|
|
"t,1,-k,0": 3,
|
|
"k,0,t,-1": 3,
|
|
"1,-t,0,k": 3,
|
|
"t,-k,0,-1": 3,
|
|
"0,1,-t,-k": 3,
|
|
"1,0,-k,t": 3,
|
|
"k,t,1,0": 3,
|
|
|
|
"t,0,-1,k": 4,
|
|
"0,t,k,-1": 4,
|
|
"1,-k,t,0": 4,
|
|
"k,1,0,t": 4,
|
|
"t,1,k,0": 4,
|
|
"0,k,-1,-t": 4,
|
|
"1,-t,0,-k": 4,
|
|
"k,0,-t,1": 4,
|
|
"0,1,t,k": 4,
|
|
"t,-k,0,1": 4,
|
|
"k,t,-1,0": 4,
|
|
"1,0,k,-t": 4,
|
|
|
|
"k,0,t,1": 5,
|
|
"0,k,-1,t": 5,
|
|
"t,-1,-k,0": 5,
|
|
"1,t,0,-k": 5,
|
|
"1,0,-k,-t": 5,
|
|
"t,k,0,1": 5,
|
|
"0,1,t,-k": 5,
|
|
"k,-t,1,0": 5,
|
|
"t,0,1,-k": 5,
|
|
"1,k,-t,0": 5,
|
|
"k,-1,0,t": 5,
|
|
"0,t,k,1": 5
|
|
};
|
|
|
|
|
|
|
|
// permute unique indices ->
|
|
// use these to label nodes ->
|
|
// assign actual values to indices ->
|
|
|
|
function map_coord(i, coords, values) {
|
|
if( i >= 0 ) {
|
|
return values[coords[i]];
|
|
}
|
|
return -values[coords[-i]];
|
|
}
|
|
|
|
|
|
function make_600cell_vertices() {
|
|
const coords = {
|
|
0: '0',
|
|
1: '1',
|
|
2: '2',
|
|
3: 't',
|
|
4: 'k'
|
|
};
|
|
const t = 0.5 * (1 + Math.sqrt(5));
|
|
const values = {
|
|
'0': 0,
|
|
'1': 1,
|
|
'2': 2,
|
|
't': t,
|
|
'k': 1 / t
|
|
};
|
|
|
|
const nodes = [
|
|
PERMUTE.coordinates([0, 0, 0, 2], ),
|
|
PERMUTE.coordinates([1, 1, 1, 1], 0),
|
|
|
|
PERMUTE.coordinates([3, 1, 4, 0], 1, true)
|
|
].flat();
|
|
|
|
for( const n of nodes ) {
|
|
for( const a of [ 'x', 'y', 'z', 'w'] ) {
|
|
n[a] = map_coord(n[a], coords, values);
|
|
}
|
|
}
|
|
|
|
index_nodes(nodes);
|
|
//const groups = partition_nodes_by_distance(nodes, 2);
|
|
scale_nodes(nodes, 0.75);
|
|
return nodes;
|
|
}
|
|
|
|
|
|
|
|
|
|
export const cell600 = () => {
|
|
const nodes = make_600cell_vertices();
|
|
const links = auto_detect_edges(nodes, 12);
|
|
return {
|
|
nodes: nodes,
|
|
links: links,
|
|
geometry: {
|
|
node_size: 0.08,
|
|
link_size: 0.02
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
|
|
|