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4D to 3D transformation

feature-big-polytopes
Mike Lynch 2023-07-22 16:59:48 +10:00
parent 7a02e5039a
commit 161abcfd0f
2 changed files with 124 additions and 28 deletions
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11
TODO.md
View File

@ -12,4 +12,13 @@ To-do:
* algorithm for 4d -> 3d transform
* 4D shape -> 3D projection -> wireframe -> three.js
--DONE
* 4D shape -> 3D projection -> wireframe -> three.js
--DONE
Next:
how to do this efficiently so that we can rotate the shape in 4d and have
this animate in 3d?

141
main.js
View File

@ -3,6 +3,72 @@ import * as THREE from 'three';
const NODE_SIZE = 0.07;
const LINK_SIZE = 0.02;
const HYPERPLANE = 4;
const r5 = Math.sqrt(5);
const CELL5 = {
nodes: [
{id:1, x: 1, y: 1, z: 1, w: -1 / r5 },
{id:2, x: 1, y: -1, z: -1, w: -1 / r5 },
{id:3, x: -1, y: 1, z: -1, w: -1 / r5 },
{id:4, x: -1, y: -1, z: 1, w: -1 / r5 },
{id:5, x: 0, y: 0, z: 0, w: 4 / 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},
]
};
const CELL16 = {
nodes: [
{ id: 1, x: 0, y: -1, z: 0, w: 0 },
{ id: 2, x: 0, y: 0, z: -1, w: 0 },
{ id: 3, x: -1, y: 0, z: 0, w: 0 },
{ id: 4, x: 0, y: 0, z: 1, w: 0 },
{ id: 5, x: 1, y: 0, z: 0, w: 0 },
{ id: 6, x: 0, y: 1, z: 0, w: 0 },
{ id: 7, x: 0, y: 0, z: 0, w: -1 },
{ id: 8, x: 0, y: 0, z: 0, w: 1 },
],
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: 3, target: 4 },
{ id: 7, source: 4, target: 5 },
{ id: 8, source: 5, target: 2 },
{ id: 9, source: 2, target: 6 },
{ id: 10, source: 3, target: 6 },
{ id: 11, source: 4, target: 6 },
{ id: 12, source: 5, target: 6 },
{ id: 13, source: 1, target: 7 },
{ id: 14, source: 1, target: 8 },
{ id: 15, source: 2, target: 7 },
{ id: 16, source: 2, target: 8 },
{ id: 17, source: 3, target: 7 },
{ id: 18, source: 3, target: 8 },
{ id: 19, source: 4, target: 7 },
{ id: 20, source: 4, target: 8 },
{ id: 21, source: 5, target: 7 },
{ id: 22, source: 5, target: 8 },
{ id: 23, source: 6, target: 7 },
{ id: 25, source: 6, target: 8 },
]
};
function makeLink(link_m, n1, n2) {
const length = n1.distanceTo(n2);
@ -21,10 +87,10 @@ function makeLink(link_m, n1, n2) {
function makeWireFrame(node_m, link_m, graph) {
function makeWireFrame(node_m, link_m, graph3) {
const nodeids = {}
const group = new THREE.Group();
for ( const n of graph.nodes ) {
for ( const n of graph3.nodes ) {
const v3 = new THREE.Vector3(n.x, n.y, n.z);
nodeids[n.id] = v3.clone();
const geometry = new THREE.SphereGeometry(NODE_SIZE);
@ -32,7 +98,7 @@ function makeWireFrame(node_m, link_m, graph) {
sphere.position.copy(v3);
group.add(sphere);
}
for ( const l of graph.links ) {
for ( const l of graph3.links ) {
const link = makeLink(link_m, nodeids[l.source], nodeids[l.target]);
group.add(link);
}
@ -40,6 +106,44 @@ function makeWireFrame(node_m, link_m, graph) {
}
function fourDtoV3(x, y, z, w) {
const k = HYPERPLANE / (HYPERPLANE + w);
return new THREE.Vector3(x * k, y * k, z * k);
}
function nodes4tonodes3(graph4) {
return graph4.map((n) => {
return { id: n.id, v3: fourDtoV3(n.x, n.y, n.z, n.w) }
})
}
// TODO - turn W into a parameter for the node size
function makeShape4D(node_m, link_m, graph4) {
const nodes3 = nodes4tonodes3(graph4.nodes);
const nodeids = {}
const group = new THREE.Group();
for ( const n of nodes3 ) {
nodeids[n.id] = n.v3;
const geometry = new THREE.SphereGeometry(NODE_SIZE);
const sphere = new THREE.Mesh(geometry, node_m);
sphere.position.copy(n.v3);
group.add(sphere);
}
for ( const l of graph4.links ) {
const link = makeLink(link_m, nodeids[l.source], nodeids[l.target]);
group.add(link);
}
return group;
}
const scene = new THREE.Scene();
const camera = new THREE.PerspectiveCamera( 75, window.innerWidth / window.innerHeight, 0.1, 1000 );
@ -68,31 +172,12 @@ const link_m = new THREE.MeshStandardMaterial(
link_m.metalness = 0.4;
link_m.roughness = 0.0;
link_m.transparent = true;
link_m.opacity = 0.3;
const shape = makeWireFrame(node_m, link_m, {
nodes: [
{ id: 1, x: 0, y: -1, z: 0 },
{ id: 2, x: 0, y: 0, z: -1 },
{ id: 3, x: -1, y: 0, z: 0 },
{ id: 4, x: 0, y: 0, z: 1 },
{ id: 5, x: 1, y: 0, z: 0 },
{ id: 6, x: 0, y: 1, z: 0 },
],
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: 3, target: 4 },
{ id: 7, source: 4, target: 5 },
{ id: 8, source: 5, target: 2 },
{ id: 9, source: 2, target: 6 },
{ id: 10, source: 3, target: 6 },
{ id: 11, source: 4, target: 6 },
{ id: 12, source: 5, target: 6 },
]
});
const shape = makeShape4D(node_m, link_m, CELL5);
@ -105,6 +190,8 @@ camera.position.z = 3;
let tick = 0;
// note: for 4d stuff we'll need to redraw the whole thing I think
function animate() {
requestAnimationFrame( animate );