Effective 4D rotations and a tesseract model

feature-big-polytopes
Mike Lynch 2023-07-23 18:16:02 +10:00
parent 3fbdf3dd41
commit e3fedbba32
2 changed files with 84 additions and 15 deletions

View File

@ -2,7 +2,7 @@
<html>
<head lang="en">
<meta charset="utf-8">
<title>Wack ass 3d</title>
<title>FourD</title>
<style>
body { margin: 0; }
</style>

97
main.js
View File

@ -72,6 +72,67 @@ const CELL16 = {
]
};
const TESSERACT = {
nodes: [
{ id: 1, x: -1, y: -1, z: -1, w: -1 },
{ id: 2, x: 1, y: -1, z: -1, w: -1 },
{ id: 3, x: -1, y: 1, z: -1, w: -1 },
{ id: 4, x: 1, y: 1, z: -1, w: -1 },
{ id: 5, x: -1, y: -1, z: 1, w: -1 },
{ id: 6, x: 1, y: -1, z: 1, w: -1 },
{ id: 7, x: -1, y: 1, z: 1, w: -1 },
{ id: 8, x: 1, y: 1, z: 1, w: -1 },
{ id: 9, x: -1, y: -1, z: -1, w: 1 },
{ id: 10, x: 1, y: -1, z: -1, w: 1 },
{ id: 11, x: -1, y: 1, z: -1, w: 1 },
{ id: 12, x: 1, y: 1, z: -1, w: 1 },
{ id: 13, x: -1, y: -1, z: 1, w: 1 },
{ id: 14, x: 1, y: -1, z: 1, w: 1 },
{ id: 15, x: -1, y: 1, z: 1, w: 1 },
{ id: 16, x: 1, y: 1, z: 1, w: 1 },
],
links: [
{ id: 1, source: 1, target: 2 },
{ id: 2, source: 2, target: 4 },
{ id: 3, source: 4, target: 3 },
{ id: 4, source: 3, target: 1 },
{ id: 5, source: 5, target: 6 },
{ id: 6, source: 6, target: 8 },
{ id: 7, source: 8, target: 7 },
{ id: 8, source: 7, target: 5 },
{ id: 9, source: 1, target: 5 },
{ id: 10, source: 2, target: 6 },
{ id: 11, source: 3, target: 7 },
{ id: 12, source: 4, target: 8 },
{ id: 13, source: 9, target: 10 },
{ id: 14, source: 10, target: 12 },
{ id: 15, source: 12, target: 11 },
{ id: 16, source: 11, target: 9 },
{ id: 17, source: 13, target: 14 },
{ id: 18, source: 14, target: 16 },
{ id: 19, source: 16, target: 15 },
{ id: 20, source: 15, target: 13 },
{ id: 21, source: 9, target: 13 },
{ id: 22, source: 10, target: 14 },
{ id: 23, source: 11, target: 15 },
{ id: 24, source: 12, target: 16 },
{ id: 25, source: 1, target: 9 },
{ id: 26, source: 2, target: 10 },
{ id: 27, source: 3, target: 11 },
{ id: 28, source: 4, target: 12 },
{ id: 29, source: 5, target: 13 },
{ id: 30, source: 6, target: 14 },
{ id: 31, source: 7, target: 15 },
{ id: 32, source: 8, target: 16 },
]
};
// hacky stuff for 4d rotations
// see https://math.stackexchange.com/questions/1402362/can-rotations-in-4d-be-given-an-explicit-matrix-form#1402376
@ -147,9 +208,11 @@ function rotXY(theta) {
// putting rotation here first - it's a matrix4
function fourDtoV3(x, y, z, w, m4) {
function fourDtoV3(x, y, z, w, rotations) {
const v4 = new THREE.Vector4(x, y, z, w);
v4.applyMatrix4(m4);
for ( const m4 of rotations ) {
v4.applyMatrix4(m4);
}
const k = HYPERPLANE / (HYPERPLANE + v4.w);
return new THREE.Vector3(v4.x * k, v4.y * k, v4.z * k);
}
@ -167,7 +230,6 @@ class FourDShape extends THREE.Group {
this.initShapes();
}
makeNode(v3) {
const geometry = new THREE.SphereGeometry(NODE_SIZE);
const sphere = new THREE.Mesh(geometry, this.node_m);
@ -187,8 +249,8 @@ class FourDShape extends THREE.Group {
const edge = new THREE.Group();
edge.add(cyl);
edge.position.copy(centre);
edge.scale.copy(new THREE.Vector3(1, 1, length));
edge.lookAt(n2);
edge.scale.copy(new THREE.Vector3(1, length, 1));
cyl.rotation.x = Math.PI / 2.0;
this.add(edge);
return edge;
@ -200,14 +262,15 @@ class FourDShape extends THREE.Group {
const length = n1.distanceTo(n2);
const centre = new THREE.Vector3();
centre.lerpVectors(n1, n2, 0.5);
link.object.scale.copy(new THREE.Vector3(1, 1, length));
link.object.position.copy(centre);
link.object.lookAt(n2);
link.object.scale.copy(new THREE.Vector3(1, 1, length));
link.object.children[0].rotation.x = Math.PI / 2.0;
}
initShapes() {
for( const n of this.nodes4 ) {
const v3 = fourDtoV3(n.x, n.y, n.z, n.w, new THREE.Matrix4());
const v3 = fourDtoV3(n.x, n.y, n.z, n.w, []);
this.nodes3[n.id] = {
v3: v3,
object: this.makeNode(v3)
@ -218,18 +281,20 @@ class FourDShape extends THREE.Group {
}
}
update(m4) {
render3(rotations) {
for( const n of this.nodes4 ) {
const v3 = fourDtoV3(n.x, n.y, n.z, n.w, m4);
const v3 = fourDtoV3(n.x, n.y, n.z, n.w, rotations);
this.nodes3[n.id].v3 = v3;
this.nodes3[n.id].object.position.copy(v3);
// could do scaling here
}
for( const l of this.links ) {
this.updateLink(l);
}
}
}
@ -250,7 +315,8 @@ scene.add(amblight);
scene.background = new THREE.Color(0xdddddd);
const renderer = new THREE.WebGLRenderer();
const renderer = new THREE.WebGLRenderer({antialias: true});
//renderer.physicallyCorrectLights = true;
renderer.setSize( window.innerWidth, window.innerHeight );
document.body.appendChild( renderer.domElement );
@ -260,17 +326,17 @@ const node_m = new THREE.MeshStandardMaterial(
node_m.roughness = 0.2;
const link_m = new THREE.MeshStandardMaterial(
{ color: 0xf0f0f0 } );
{ color: 0xb0b0b0 } );
link_m.metalness = 0.4;
link_m.roughness = 0.0;
link_m.transparent = true;
link_m.opacity = 0.3;
link_m.opacity = 0.5;
const shape = new FourDShape(node_m, link_m, CELL5);
const shape = new FourDShape(node_m, link_m, TESSERACT);
scene.add(shape);
@ -285,9 +351,12 @@ const rotation = new THREE.Matrix4();
function animate() {
requestAnimationFrame( animate );
theta += 0.02;
theta += 0.01;
const rotations = [rotXY(theta * 0.5), rotXW(theta)];
shape.render3(rotations);
shape.update(rotXY(theta));
renderer.render( scene, camera );
}
animate();