Effective 4D rotations and a tesseract model
Mike Lynch
parent
3fbdf3dd41
commit
e3fedbba32
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@ -2,7 +2,7 @@
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<html>
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<head lang="en">
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<meta charset="utf-8">
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<title>Wack ass 3d</title>
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<title>FourD</title>
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<style>
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body { margin: 0; }
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</style>
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95
main.js
95
main.js
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@ -72,6 +72,67 @@ const CELL16 = {
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]
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};
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const TESSERACT = {
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nodes: [
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{ id: 1, x: -1, y: -1, z: -1, w: -1 },
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{ id: 2, x: 1, y: -1, z: -1, w: -1 },
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{ id: 3, x: -1, y: 1, z: -1, w: -1 },
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{ id: 4, x: 1, y: 1, z: -1, w: -1 },
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{ id: 5, x: -1, y: -1, z: 1, w: -1 },
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{ id: 6, x: 1, y: -1, z: 1, w: -1 },
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{ id: 7, x: -1, y: 1, z: 1, w: -1 },
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{ id: 8, x: 1, y: 1, z: 1, w: -1 },
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{ id: 9, x: -1, y: -1, z: -1, w: 1 },
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{ id: 10, x: 1, y: -1, z: -1, w: 1 },
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{ id: 11, x: -1, y: 1, z: -1, w: 1 },
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{ id: 12, x: 1, y: 1, z: -1, w: 1 },
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{ id: 13, x: -1, y: -1, z: 1, w: 1 },
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{ id: 14, x: 1, y: -1, z: 1, w: 1 },
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{ id: 15, x: -1, y: 1, z: 1, w: 1 },
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{ id: 16, x: 1, y: 1, z: 1, w: 1 },
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],
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links: [
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{ id: 1, source: 1, target: 2 },
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{ id: 2, source: 2, target: 4 },
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{ id: 3, source: 4, target: 3 },
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{ id: 4, source: 3, target: 1 },
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{ id: 5, source: 5, target: 6 },
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{ id: 6, source: 6, target: 8 },
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{ id: 7, source: 8, target: 7 },
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{ id: 8, source: 7, target: 5 },
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{ id: 9, source: 1, target: 5 },
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{ id: 10, source: 2, target: 6 },
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{ id: 11, source: 3, target: 7 },
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{ id: 12, source: 4, target: 8 },
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{ id: 13, source: 9, target: 10 },
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{ id: 14, source: 10, target: 12 },
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{ id: 15, source: 12, target: 11 },
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{ id: 16, source: 11, target: 9 },
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{ id: 17, source: 13, target: 14 },
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{ id: 18, source: 14, target: 16 },
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{ id: 19, source: 16, target: 15 },
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{ id: 20, source: 15, target: 13 },
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{ id: 21, source: 9, target: 13 },
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{ id: 22, source: 10, target: 14 },
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{ id: 23, source: 11, target: 15 },
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{ id: 24, source: 12, target: 16 },
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{ id: 25, source: 1, target: 9 },
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{ id: 26, source: 2, target: 10 },
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{ id: 27, source: 3, target: 11 },
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{ id: 28, source: 4, target: 12 },
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{ id: 29, source: 5, target: 13 },
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{ id: 30, source: 6, target: 14 },
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{ id: 31, source: 7, target: 15 },
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{ id: 32, source: 8, target: 16 },
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]
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};
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// hacky stuff for 4d rotations
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// see https://math.stackexchange.com/questions/1402362/can-rotations-in-4d-be-given-an-explicit-matrix-form#1402376
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@ -147,9 +208,11 @@ function rotXY(theta) {
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// putting rotation here first - it's a matrix4
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function fourDtoV3(x, y, z, w, m4) {
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function fourDtoV3(x, y, z, w, rotations) {
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const v4 = new THREE.Vector4(x, y, z, w);
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for ( const m4 of rotations ) {
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v4.applyMatrix4(m4);
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}
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const k = HYPERPLANE / (HYPERPLANE + v4.w);
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return new THREE.Vector3(v4.x * k, v4.y * k, v4.z * k);
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}
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@ -167,7 +230,6 @@ class FourDShape extends THREE.Group {
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this.initShapes();
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}
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makeNode(v3) {
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const geometry = new THREE.SphereGeometry(NODE_SIZE);
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const sphere = new THREE.Mesh(geometry, this.node_m);
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@ -187,8 +249,8 @@ class FourDShape extends THREE.Group {
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const edge = new THREE.Group();
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edge.add(cyl);
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edge.position.copy(centre);
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edge.scale.copy(new THREE.Vector3(1, 1, length));
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edge.lookAt(n2);
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edge.scale.copy(new THREE.Vector3(1, length, 1));
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cyl.rotation.x = Math.PI / 2.0;
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this.add(edge);
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return edge;
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@ -200,14 +262,15 @@ class FourDShape extends THREE.Group {
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const length = n1.distanceTo(n2);
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const centre = new THREE.Vector3();
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centre.lerpVectors(n1, n2, 0.5);
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link.object.scale.copy(new THREE.Vector3(1, 1, length));
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link.object.position.copy(centre);
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link.object.lookAt(n2);
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link.object.scale.copy(new THREE.Vector3(1, 1, length));
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link.object.children[0].rotation.x = Math.PI / 2.0;
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}
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initShapes() {
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for( const n of this.nodes4 ) {
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const v3 = fourDtoV3(n.x, n.y, n.z, n.w, new THREE.Matrix4());
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const v3 = fourDtoV3(n.x, n.y, n.z, n.w, []);
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this.nodes3[n.id] = {
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v3: v3,
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object: this.makeNode(v3)
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@ -218,18 +281,20 @@ class FourDShape extends THREE.Group {
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}
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}
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update(m4) {
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render3(rotations) {
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for( const n of this.nodes4 ) {
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const v3 = fourDtoV3(n.x, n.y, n.z, n.w, m4);
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const v3 = fourDtoV3(n.x, n.y, n.z, n.w, rotations);
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this.nodes3[n.id].v3 = v3;
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this.nodes3[n.id].object.position.copy(v3);
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// could do scaling here
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}
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for( const l of this.links ) {
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this.updateLink(l);
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}
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}
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}
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@ -250,7 +315,8 @@ scene.add(amblight);
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scene.background = new THREE.Color(0xdddddd);
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const renderer = new THREE.WebGLRenderer();
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const renderer = new THREE.WebGLRenderer({antialias: true});
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//renderer.physicallyCorrectLights = true;
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renderer.setSize( window.innerWidth, window.innerHeight );
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document.body.appendChild( renderer.domElement );
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@ -260,17 +326,17 @@ const node_m = new THREE.MeshStandardMaterial(
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node_m.roughness = 0.2;
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const link_m = new THREE.MeshStandardMaterial(
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{ color: 0xf0f0f0 } );
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{ color: 0xb0b0b0 } );
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link_m.metalness = 0.4;
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link_m.roughness = 0.0;
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link_m.transparent = true;
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link_m.opacity = 0.3;
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link_m.opacity = 0.5;
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const shape = new FourDShape(node_m, link_m, CELL5);
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const shape = new FourDShape(node_m, link_m, TESSERACT);
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scene.add(shape);
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@ -285,9 +351,12 @@ const rotation = new THREE.Matrix4();
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function animate() {
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requestAnimationFrame( animate );
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theta += 0.02;
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theta += 0.01;
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const rotations = [rotXY(theta * 0.5), rotXW(theta)];
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shape.render3(rotations);
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shape.update(rotXY(theta));
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renderer.render( scene, camera );
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}
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animate();
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