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No commits in common. "main" and "feature-node-foreshortening" have entirely different histories.
main
...
feature-no
12
CHANGELOG.md
12
CHANGELOG.md
@ -1,12 +0,0 @@
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CHANGELOG
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=========
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## v1.0 - 16/11/2025
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It's been [two years](https://mikelynch.org/2023/Sep/02/120-cell/)</a> since
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I first made this, and I haven't updated it in a while, but I got tapered links to
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work without too much performance overhead, so that seemed worth a version.
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The results flicker a bit at low opacities but otherwise I'm pretty happy with
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it.
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`
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@ -1,10 +1,7 @@
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import * as THREE from 'three';
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import { TaperedLink } from './taperedLink.js';
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const HYPERPLANE = 2.0;
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const W_FORESHORTENING = 0.04;
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class FourDShape extends THREE.Group {
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@ -18,10 +15,11 @@ class FourDShape extends THREE.Group {
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this.nodes3 = {};
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this.links = structure.links;
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this.faces = ( "faces" in structure ) ? structure.faces : [];
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this.node_size = structure.geometry.node_size;
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this.link_size = structure.geometry.link_size;
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this.node_scale = 1;
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this.link_scale = 1;
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this.hyperplane = HYPERPLANE;
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this.foreshortening = W_FORESHORTENING;
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this.initShapes();
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}
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@ -29,12 +27,12 @@ class FourDShape extends THREE.Group {
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// if a node/link has no label, use the 0th material
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getMaterialLabel(entity) {
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if( "label" in entity ) {
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return entity.label
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} else {
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return 0;
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}
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getMaterial(entity, materials) {
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if( "label" in entity ) {
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return materials[entity.label];
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} else {
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return materials[0];
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}
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}
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makeNode(material, v3, scale) {
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@ -45,23 +43,34 @@ class FourDShape extends THREE.Group {
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return sphere;
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}
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makeLink(materialLabel, link) {
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const n1 = this.nodes3[link.source];
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const n2 = this.nodes3[link.target];
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const s1 = this.link_scale * n1.scale;
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const s2 = this.link_scale * n2.scale;
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const basematerial = this.link_ms[materialLabel];
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const edge = new TaperedLink(basematerial, materialLabel, n1, n2, s1, s2);
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this.add( edge );
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makeLink(material, link) {
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const n1 = this.nodes3[link.source].v3;
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const n2 = this.nodes3[link.target].v3;
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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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const geometry = new THREE.CylinderGeometry(this.link_size, this.link_size, 1);
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const cyl = new THREE.Mesh(geometry, material);
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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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cyl.rotation.x = Math.PI / 2.0;
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this.add(edge);
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return edge;
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}
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updateLink(link, links_show) {
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const n1 = this.nodes3[link.source];
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const n2 = this.nodes3[link.target];
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const s1 = this.link_scale * n1.scale;
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const s2 = this.link_scale * n2.scale;
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link.object.update(n1, n2, s1, s2);
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const n1 = this.nodes3[link.source].v3;
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const n2 = this.nodes3[link.target].v3;
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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(this.link_scale, this.link_scale, length));
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link.object.position.copy(centre);
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link.object.lookAt(n2);
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link.object.children[0].rotation.x = Math.PI / 2.0;
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link.object.visible = (!links_show || link.label in links_show);
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}
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@ -91,6 +100,15 @@ class FourDShape extends THREE.Group {
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}
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fourDtoV3_old(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 = this.fourDscale(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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fourDscale(w) {
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return this.hyperplane / ( this.hyperplane + w );
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}
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@ -112,20 +130,19 @@ class FourDShape extends THREE.Group {
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for( const n of this.nodes4 ) {
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const k = this.fourDscale(n.w);
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const v3 = new THREE.Vector3(n.x * k, n.y * k, n.z * k);
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const material = this.node_ms[this.getMaterialLabel(n)];
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const material = this.getMaterial(n, this.node_ms);
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this.nodes3[n.id] = {
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v3: v3,
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scale: k,
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label: n.label,
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object: this.makeNode(material, v3, k)
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};
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}
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for( const l of this.links ) {
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const mLabel = this.getMaterialLabel(l);
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l.object = this.makeLink(mLabel, l);
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const material = this.getMaterial(l, this.link_ms);
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l.object = this.makeLink(material, l);
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}
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for( const f of this.faces ) {
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const material = this.face_ms(this.getMaterialLabel(f));
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const material = this.getMaterial(f, this.face_ms);
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f.object = this.makeFace(material, f);
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}
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}
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@ -137,10 +154,9 @@ class FourDShape extends THREE.Group {
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const v4 = this.fourDrotate(n.x, n.y, n.z, n.w, rotations);
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const k = this.fourDscale(v4.w);
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const v3 = new THREE.Vector3(v4.x * k, v4.y * k, v4.z * k);
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const s4 = k * this.node_scale * this.foreshortening;
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const s4 = k * this.node_scale;
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const s3 = new THREE.Vector3(s4, s4, s4);
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this.nodes3[n.id].v3 = v3;
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this.nodes3[n.id].scale = k * this.foreshortening;
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this.nodes3[n.id].object.position.copy(v3);
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this.nodes3[n.id].object.scale.copy(s3);
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this.nodes3[n.id].object.visible = ( !nodes_show || n.label in nodes_show );
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46
gui.js
46
gui.js
@ -2,10 +2,10 @@ import { GUI } from 'lil-gui';
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const DEFAULTS = {
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nodesize: 0.6,
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nodeopacity: 1,
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linksize: 1.0,
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linkopacity: 0.75,
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thickness: 1.0,
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nodesize: 2.0,
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linkopacity: 0.5,
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link2opacity: 0.5,
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shape: '120-cell',
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option: 'none',
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visibility: 5,
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@ -13,13 +13,11 @@ const DEFAULTS = {
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inscribe_all: false,
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color: 0x3293a9,
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background: 0xd4d4d4,
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hyperplane: 0.93,
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hyperplane: 1.5,
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zoom: 1,
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xRotate: 'YW',
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yRotate: 'XW',
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yRotate: 'XZ',
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dtheta: 0,
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damping: false,
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captions: true,
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dpsi: 0,
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}
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@ -27,7 +25,7 @@ const DEFAULTS = {
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class FourDGUI {
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constructor(shapes, changeShape, setColor, setBackground, setNodeOpacity,setLinkOpacity, setVisibility, showDocs) {
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constructor(shapes, changeShape, setColor, setBackground, setLinkOpacity, setVisibility) {
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this.gui = new GUI();
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const SHAPE_NAMES = shapes.map((s) => s.name);
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@ -38,10 +36,10 @@ class FourDGUI {
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option: this.link['option'],
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inscribed: this.link['inscribed'],
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inscribe_all: this.link['inscribe_all'],
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linksize: this.link['linksize'],
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thickness: this.link['thickness'],
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linkopacity: this.link['linkopacity'],
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link2opacity: this.link['linkopacity'],
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nodesize: this.link['nodesize'],
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nodeopacity: this.link['nodeopacity'],
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depth: this.link['depth'],
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color: this.link['color'],
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background: this.link['background'],
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@ -50,7 +48,6 @@ class FourDGUI {
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xRotate: this.link['xRotate'],
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yRotate: this.link['yRotate'],
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damping: false,
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captions: true,
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dtheta: this.link['dtheta'],
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dpsi: this.link['dpsi'],
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"copy link": function () { guiObj.copyUrl() }
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@ -68,17 +65,20 @@ class FourDGUI {
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options_ctrl = this.gui.add(this.params, 'option').options(options).onChange((option) => {
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setVisibility(option)
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});
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this.gui.add(this.params, 'hyperplane', 0.5, 1 / 0.8);
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this.gui.add(this.params, 'hyperplane', 1.4, 2.0);
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this.gui.add(this.params, 'zoom', 0.1, 2.0);
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this.gui.add(this.params, 'nodesize', 0, 1.5);
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this.gui.add(this.params, 'nodeopacity', 0, 1).onChange(setNodeOpacity);
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this.gui.add(this.params, 'linksize', 0, 2);
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this.gui.add(this.params, 'linkopacity', 0, 1).onChange(setLinkOpacity);
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this.gui.add(this.params, 'thickness', 0, 2);
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this.gui.add(this.params, 'linkopacity', 0, 1).onChange(
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(v) => setLinkOpacity(v, true)
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);
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this.gui.add(this.params, 'link2opacity', 0, 1).onChange(
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(v) => setLinkOpacity(v, false)
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);
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this.gui.add(this.params, 'nodesize', 0.1, 4);
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this.gui.addColor(this.params, 'color').onChange(setColor);
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this.gui.addColor(this.params, 'background').onChange(setBackground);
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this.gui.add(this.params, 'xRotate', [ 'YW', 'YZ', 'ZW' ]);
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this.gui.add(this.params, 'yRotate', [ 'XZ', 'XY', 'XW' ]);
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this.gui.add(this.params, 'captions').onChange(showDocs);
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this.gui.add(this.params, 'damping');
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this.gui.add(this.params, 'copy link');
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@ -134,10 +134,10 @@ class FourDGUI {
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}
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this.link['hyperplane'] = this.numParam('hyperplane', parseFloat);
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this.link['zoom'] = this.numParam('zoom', parseFloat);
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this.link['linksize'] = this.numParam('linksize', parseFloat);
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this.link['thickness'] = this.numParam('thickness', parseFloat);
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this.link['linkopacity'] = this.numParam('linkopacity', parseFloat);
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this.link['link2opacity'] = this.numParam('link2opacity', parseFloat);
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this.link['nodesize'] = this.numParam('nodesize', parseFloat);
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this.link['nodeopacity'] = this.numParam('nodeopacity', parseFloat);
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this.link['color'] = this.numParam('color', (s) => guiObj.stringToHex(s));
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this.link['background'] = this.numParam('background', (s) => guiObj.stringToHex(s));
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this.link['dpsi'] = this.numParam('dpsi', parseFloat);
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@ -151,10 +151,10 @@ class FourDGUI {
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url.searchParams.append("option", this.params.option);
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url.searchParams.append("inscribed", this.params.inscribed ? 'y': 'n');
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url.searchParams.append("inscribe_all", this.params.inscribe_all ? 'y': 'n');
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url.searchParams.append("linksize", this.params.linksize.toString());
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url.searchParams.append("thickness", this.params.thickness.toString());
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url.searchParams.append("nodesize", this.params.nodesize.toString());
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url.searchParams.append("nodeopacity", this.params.nodesize.toString());
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url.searchParams.append("linkopacity", this.params.nodeopacity.toString());
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url.searchParams.append("linkopacity", this.params.thickness.toString());
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url.searchParams.append("link2opacity", this.params.nodesize.toString());
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url.searchParams.append("color", this.hexToString(this.params.color));
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url.searchParams.append("background", this.hexToString(this.params.background));
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url.searchParams.append("hyperplane", this.params.hyperplane.toString());
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26
index.html
26
index.html
@ -5,24 +5,6 @@
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<title>FourD</title>
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<style>
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body { margin: 0; }
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div#description {
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position: fixed;
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top: 0;
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left: 0;
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width: 20%;
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z-index: 2;
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font-family: sans-serif;
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padding: 1em;
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}
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div#release_notes {
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position: fixed;
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top: 0;
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left: 0;
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width: 20%;
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z-index: 2;
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padding: 1em;
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font-family: sans-serif;
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}
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div#info {
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position: fixed;
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bottom:0;
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@ -34,11 +16,7 @@
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</head>
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<body>
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<script type="module" src="/main.js"></script>
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<div id="description"></div>
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<div id="release_notes"></div>
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<div id="info"><a href="#" id="show_notes">release 1.0</a> |
|
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by <a target="_blank" href="https://mikelynch.org/">Mike Lynch</a> |
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<div id="info">by <a target="_blank" href="https://mikelynch.org/">Mike Lynch</a> -
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<a target="_blank" href="https://git.tilde.town/bombinans/fourdjs">source</a></div>
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</body>
|
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</html>
|
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</html>
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119
linktest.js
119
linktest.js
@ -1,119 +0,0 @@
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import * as THREE from 'three';
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import { OrbitControls } from 'three/addons/controls/OrbitControls.js';
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import { GUI } from 'lil-gui';
|
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|
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import { TaperedLink } from './taperedLink.js';
|
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|
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const FACE_OPACITY = 0.3;
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const CAMERA_K = 5;
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// scene, lights and camera
|
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|
||||
|
||||
|
||||
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const scene = new THREE.Scene();
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const camera = new THREE.PerspectiveCamera( 75, window.innerWidth / window.innerHeight, 0.1, 1000 );
|
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const light = new THREE.PointLight(0xffffff, 2);
|
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light.position.set(10, 10, 10);
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scene.add(light);
|
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const light2 = new THREE.PointLight(0xffffff, 2);
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light2.position.set(-10, 5, 10);
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scene.add(light);
|
||||
const amblight = new THREE.AmbientLight(0xffffff, 0.5);
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scene.add(amblight);
|
||||
|
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camera.position.set(0, 0, CAMERA_K / 2);
|
||||
|
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camera.lookAt(0, 0, 0);
|
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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();
|
||||
124
main.js
124
main.js
@ -1,16 +1,5 @@
|
||||
import * as THREE from 'three';
|
||||
|
||||
const RELEASE_NOTES = `
|
||||
<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';
|
||||
@ -20,7 +9,7 @@ import { FourDShape } from './fourDShape.js';
|
||||
import { get_colours } from './colours.js';
|
||||
|
||||
const FACE_OPACITY = 0.3;
|
||||
const CAMERA_K = 5;
|
||||
const CAMERA_K = 10;
|
||||
|
||||
// scene, lights and camera
|
||||
|
||||
@ -42,36 +31,30 @@ camera.lookAt(0, 0, 0);
|
||||
|
||||
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;
|
||||
}
|
||||
);
|
||||
|
||||
|
||||
)
|
||||
|
||||
const face_ms = [
|
||||
new THREE.MeshStandardMaterial( { color: 0x44ff44 } )
|
||||
new THREE.MeshLambertMaterial( { color: 0x44ff44 } )
|
||||
];
|
||||
|
||||
for( const face_m of face_ms ) {
|
||||
@ -102,87 +85,41 @@ function createShape(name, option) {
|
||||
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) => l.object.material.opacity = o);
|
||||
}
|
||||
if( structure.nolink2opacity ) {
|
||||
link_ms.map((lm) => lm.opacity = o);
|
||||
} else {
|
||||
if( primary ) {
|
||||
link_ms[0].opacity = o;
|
||||
} else {
|
||||
link_ms.slice(1).map((lm) => lm.opacity = o);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
function setNodeOpacity(o) {
|
||||
node_ms.map((nm) => nm.opacity = o);
|
||||
}
|
||||
|
||||
|
||||
let gui;
|
||||
|
||||
|
||||
function changeShape() {
|
||||
createShape(gui.params.shape);
|
||||
displayDocs(gui.params.shape);
|
||||
createShape(gui.params.shape);
|
||||
}
|
||||
|
||||
function setVisibility(option_name) {
|
||||
@ -201,10 +138,8 @@ gui = new FourDGUI(
|
||||
changeShape,
|
||||
setColors,
|
||||
setBackground,
|
||||
setNodeOpacity,
|
||||
setLinkOpacity,
|
||||
setVisibility,
|
||||
showDocs
|
||||
setVisibility
|
||||
);
|
||||
|
||||
// these are here to pick up colour settings from the URL params
|
||||
@ -249,7 +184,6 @@ renderer.domElement.addEventListener("pointerup", (event) => {
|
||||
})
|
||||
|
||||
createShape(gui.params.shape, gui.params.option);
|
||||
displayDocs(gui.params.shape);
|
||||
|
||||
function animate() {
|
||||
requestAnimationFrame( animate );
|
||||
@ -267,11 +201,11 @@ function animate() {
|
||||
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);
|
||||
shape.hyperplane = gui.params.hyperplane;
|
||||
camera.position.set(0, 0, gui.params.zoom * CAMERA_K / 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);
|
||||
|
||||
|
||||
|
||||
285
polytopes.js
285
polytopes.js
@ -55,38 +55,19 @@ 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 +81,11 @@ 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
|
||||
},
|
||||
options: [ { name: '--' }]
|
||||
};
|
||||
};
|
||||
|
||||
@ -124,18 +104,18 @@ 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
|
||||
},
|
||||
options: [ { name: '--' }]
|
||||
};
|
||||
};
|
||||
|
||||
@ -153,7 +133,7 @@ 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 });
|
||||
|
||||
@ -166,20 +146,18 @@ export const tesseract = () => {
|
||||
|
||||
|
||||
return {
|
||||
name: 'Tesseract',
|
||||
name: 'tesseract',
|
||||
nodes: nodes,
|
||||
links: links,
|
||||
geometry: {
|
||||
node_size: 0.02,
|
||||
link_size: 0.02
|
||||
},
|
||||
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.`,
|
||||
};
|
||||
}
|
||||
|
||||
@ -205,7 +183,6 @@ 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);
|
||||
@ -229,16 +206,16 @@ export const cell24 = () => {
|
||||
name: '24-cell',
|
||||
nodes: nodes,
|
||||
links: links,
|
||||
geometry: {
|
||||
node_size: 0.02,
|
||||
link_size: 0.02
|
||||
},
|
||||
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.`,
|
||||
]
|
||||
};
|
||||
}
|
||||
|
||||
@ -342,7 +319,7 @@ 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);
|
||||
return nodes;
|
||||
}
|
||||
|
||||
@ -416,10 +393,12 @@ export const cell120_layered = (max) => {
|
||||
name: '120-cell layered',
|
||||
nodes: nodes,
|
||||
links: links,
|
||||
geometry: {
|
||||
node_size: 0.02,
|
||||
link_size: 0.02
|
||||
},
|
||||
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.`,
|
||||
options: options
|
||||
}
|
||||
}
|
||||
|
||||
@ -447,15 +426,15 @@ export const cell120_inscribed = () => {
|
||||
name: '120-cell',
|
||||
nodes: nodes,
|
||||
links: links,
|
||||
geometry: {
|
||||
node_size: 0.02,
|
||||
link_size: 0.02
|
||||
},
|
||||
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 ] }
|
||||
],
|
||||
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.`,
|
||||
]
|
||||
}
|
||||
}
|
||||
|
||||
@ -536,7 +515,7 @@ export function make_600cell_vertices() {
|
||||
|
||||
|
||||
index_nodes(nodes);
|
||||
scale_nodes(nodes, 0.5);
|
||||
scale_nodes(nodes, 0.75);
|
||||
return nodes;
|
||||
}
|
||||
|
||||
@ -578,16 +557,15 @@ export const cell600 = () => {
|
||||
name: '600-cell',
|
||||
nodes: nodes,
|
||||
links: links,
|
||||
geometry: {
|
||||
node_size: 0.02,
|
||||
link_size: 0.02
|
||||
},
|
||||
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.`,
|
||||
]
|
||||
}
|
||||
}
|
||||
|
||||
@ -627,10 +605,12 @@ export const cell600_layered = () => {
|
||||
name: '600-cell layered',
|
||||
nodes: nodes,
|
||||
links: links,
|
||||
geometry: {
|
||||
node_size: 0.02,
|
||||
link_size: 0.02
|
||||
},
|
||||
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.`,
|
||||
options: options
|
||||
}
|
||||
|
||||
|
||||
@ -651,15 +631,14 @@ export const snub24cell = () => {
|
||||
links.map((l) => l.label = 0);
|
||||
|
||||
return {
|
||||
name: 'Snub 24-cell',
|
||||
name: 'snub 24-cell',
|
||||
nodes: nodes,
|
||||
links: links,
|
||||
geometry: {
|
||||
node_size: 0.02,
|
||||
link_size: 0.02
|
||||
},
|
||||
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.`
|
||||
|
||||
}
|
||||
|
||||
|
||||
@ -699,7 +678,6 @@ 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;
|
||||
}
|
||||
@ -717,146 +695,18 @@ export const dodecahedron = () => {
|
||||
}
|
||||
|
||||
return {
|
||||
name: 'Dodecahedron',
|
||||
name: 'dodecahedron',
|
||||
nodes: nodes,
|
||||
links: links,
|
||||
geometry: {
|
||||
node_size: 0.02,
|
||||
link_size: 0.02
|
||||
},
|
||||
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.`
|
||||
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
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.`,
|
||||
};
|
||||
|
||||
}
|
||||
|
||||
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));
|
||||
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.`,
|
||||
};
|
||||
|
||||
}
|
||||
|
||||
|
||||
|
||||
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);
|
||||
|
||||
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.`
|
||||
]
|
||||
|
||||
}
|
||||
}
|
||||
@ -864,11 +714,6 @@ export const icosahedron = () => {
|
||||
|
||||
export const build_all = () => {
|
||||
return [
|
||||
linkTest(),
|
||||
tetrahedron(),
|
||||
octahedron(),
|
||||
cube(),
|
||||
icosahedron(),
|
||||
dodecahedron(),
|
||||
cell5(),
|
||||
cell16(),
|
||||
@ -880,8 +725,4 @@ export const build_all = () => {
|
||||
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))
|
||||
}
|
||||
}
|
||||
@ -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 };
|
||||
Loading…
x
Reference in New Issue
Block a user