Compare commits
No commits in common. "main" and "feature-node-foreshortening" have entirely different histories.
main
...
feature-no
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@ -2,7 +2,7 @@ import * as THREE from 'three';
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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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@ -15,10 +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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@ -43,43 +44,32 @@ class FourDShape extends THREE.Group {
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}
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makeLink(material, 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 = n1.scale;
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const s2 = n2.scale;
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const length = n1.v3.distanceTo(n2.v3);
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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.v3, n2.v3, 0.5);
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const geometry = new THREE.CylinderGeometry(
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this.link_scale * s2, this.link_scale * s1, 1,
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16, 1, true
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);
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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.v3);
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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 = n1.scale;
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const s2 = n2.scale;
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const length = n1.v3.distanceTo(n2.v3);
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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.v3, n2.v3, 0.5);
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// take the average of the ends as the thickness - as a workaround,
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// because I haven't worked out how to reshape tapered links without
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// having to reassign a new geometry to every link
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const link_mean = this.link_scale * (s1 + s2) * 0.5;
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link.object.scale.copy(new THREE.Vector3(link_mean, link_mean, length));
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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.v3);
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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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@ -143,7 +133,6 @@ class FourDShape extends THREE.Group {
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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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@ -165,10 +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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39
gui.js
39
gui.js
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@ -2,11 +2,10 @@ import { GUI } from 'lil-gui';
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const DEFAULTS = {
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nodesize: 0.25,
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nodeopacity: 1,
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linksize: 0.2,
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linkopacity: 0.75,
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link2opacity: 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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@ -14,13 +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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@ -28,7 +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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@ -39,11 +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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@ -52,7 +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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@ -70,22 +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);
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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, 1);
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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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@ -141,11 +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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@ -159,11 +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("link2opacity", this.params.link2opacity.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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10
index.html
10
index.html
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@ -5,15 +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#info {
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position: fixed;
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bottom:0;
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@ -25,7 +16,6 @@
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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="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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49
main.js
49
main.js
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@ -9,7 +9,7 @@ import { FourDShape } from './fourDShape.js';
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import { get_colours } from './colours.js';
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const FACE_OPACITY = 0.3;
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const CAMERA_K = 5;
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const CAMERA_K = 10;
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// scene, lights and camera
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@ -47,19 +47,11 @@ material.opacity = 0.5;
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const node_ms = node_colours.map((c) => new THREE.MeshStandardMaterial({color: c}));
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const link_ms = node_colours.map((c) => new THREE.MeshStandardMaterial({color: c}));
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node_ms.map((m) => {
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m.transparent = true;
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m.opacity = 1.0;
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}
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);
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link_ms.map((m) => {
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m.transparent = true;
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m.opacity = 0.5;
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}
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);
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)
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const face_ms = [
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new THREE.MeshLambertMaterial( { color: 0x44ff44 } )
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@ -93,26 +85,6 @@ function createShape(name, option) {
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setVisibility(option ? option : structure.options[0].name);
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}
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function displayDocs(name) {
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const docdiv = document.getElementById("description");
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const description = STRUCTURES_BY_NAME[name].description;
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if( description ) {
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docdiv.innerHTML =`<p>${name}</p><p>${description}</p>`;
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} else {
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docdiv.innerHTML =`<p>${name}</p>`;
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}
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}
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function showDocs(visible) {
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console.log(`showDocs ${visible}`);
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const docdiv = document.getElementById("description");
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if( visible ) {
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docdiv.style.display = '';
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} else {
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docdiv.style.display = 'none';
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}
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}
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// initialise gui and read params from URL
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// callbacks to do things which are triggered by controls: reset the shape,
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@ -143,17 +115,11 @@ function setLinkOpacity(o, primary) {
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}
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}
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function setNodeOpacity(o) {
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node_ms.map((nm) => nm.opacity = o);
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}
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let gui;
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function changeShape() {
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createShape(gui.params.shape);
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displayDocs(gui.params.shape);
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}
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function setVisibility(option_name) {
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@ -172,10 +138,8 @@ gui = new FourDGUI(
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changeShape,
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setColors,
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setBackground,
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setNodeOpacity,
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setLinkOpacity,
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setVisibility,
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showDocs
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setVisibility
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);
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// these are here to pick up colour settings from the URL params
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@ -220,7 +184,6 @@ renderer.domElement.addEventListener("pointerup", (event) => {
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})
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createShape(gui.params.shape, gui.params.option);
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displayDocs(gui.params.shape);
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function animate() {
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requestAnimationFrame( animate );
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@ -238,11 +201,11 @@ function animate() {
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rotfn[gui.params.xRotate](theta),
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rotfn[gui.params.yRotate](psi)
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];
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shape.hyperplane = 1 / gui.params.hyperplane;
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camera.position.set(0, 0, gui.params.zoom * CAMERA_K * gui.params.hyperplane);
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shape.hyperplane = gui.params.hyperplane;
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camera.position.set(0, 0, gui.params.zoom * CAMERA_K / gui.params.hyperplane);
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shape.link_scale = gui.params.thickness;
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shape.node_scale = gui.params.nodesize;
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shape.link_scale = gui.params.linksize * gui.params.nodesize * 0.5;
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shape.render3(rotations, node_show, link_show);
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|
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262
polytopes.js
262
polytopes.js
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@ -58,15 +58,16 @@ export function auto_detect_edges(nodes, neighbours, debug=false) {
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// too small and simple to calculate
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export const cell5 = () => {
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const c1 = Math.sqrt(5) / 4;
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const r5 = Math.sqrt(5);
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const r2 = Math.sqrt(2) / 2;
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return {
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name: '5-cell',
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nodes: [
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{id:1, label: 1, x: c1, y: c1, z: c1, w: -0.25 },
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{id:2, label: 2, x: c1, y: -c1, z: -c1, w: -0.25 },
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{id:3, label: 3, x: -c1, y: c1, z: -c1, w: -0.25 },
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{id:4, label: 4, x: -c1, y: -c1, z: c1, w: -0.25 },
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{id:5, label: 5, x: 0, y: 0, z: 0, w: 1 },
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{id:1, label: 1, x: r2, y: r2, z: r2, w: -r2 / r5 },
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{id:2, label: 2, x: r2, y: -r2, z: -r2, w: -r2 / r5 },
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{id:3, label: 3, x: -r2, y: r2, z: -r2, w: -r2 / r5 },
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{id:4, label: 4, x: -r2, y: -r2, z: r2, w: -r2 / r5 },
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{id:5, label: 5, x: 0, y: 0, z: 0, w: 4 * r2 / r5 },
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],
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links: [
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{ id:1, source:1, target: 2},
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@ -80,12 +81,11 @@ export const cell5 = () => {
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{ id:9, source:3, target: 5},
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{ id:10, source:4, target: 5},
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],
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options: [ { name: '--' }],
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description: `Five tetrahedra joined at ten faces with three
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tetrahedra around each edge. The 5-cell is the simplest regular
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four-D polytope and the four-dimensional analogue of the tetrahedron.
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A corresponding polytope, or simplex, exists for every n-dimensional
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space.`,
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geometry: {
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node_size: 0.02,
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link_size: 0.02
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},
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options: [ { name: '--' }]
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||||
};
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||||
};
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@ -104,18 +104,18 @@ export const cell16 = () => {
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nodes[1].label = 4;
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index_nodes(nodes);
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scale_nodes(nodes, 0.5);
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scale_nodes(nodes, 0.75);
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const links = auto_detect_edges(nodes, 6);
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return {
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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: '--' }]
|
||||
};
|
||||
};
|
||||
|
||||
|
|
@ -133,7 +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 });
|
||||
|
||||
|
|
@ -146,20 +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.`,
|
||||
};
|
||||
}
|
||||
|
||||
|
|
@ -185,7 +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);
|
||||
|
|
@ -209,16 +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.`,
|
||||
]
|
||||
};
|
||||
}
|
||||
|
||||
|
|
@ -322,7 +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;
|
||||
}
|
||||
|
||||
|
|
@ -396,10 +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
|
||||
}
|
||||
}
|
||||
|
||||
|
|
@ -427,15 +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.`,
|
||||
]
|
||||
}
|
||||
}
|
||||
|
||||
|
|
@ -516,7 +515,7 @@ export function make_600cell_vertices() {
|
|||
|
||||
|
||||
index_nodes(nodes);
|
||||
scale_nodes(nodes, 0.5);
|
||||
scale_nodes(nodes, 0.75);
|
||||
return nodes;
|
||||
}
|
||||
|
||||
|
|
@ -558,16 +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.`,
|
||||
]
|
||||
}
|
||||
}
|
||||
|
||||
|
|
@ -607,10 +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
|
||||
}
|
||||
|
||||
|
||||
|
|
@ -631,15 +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.`
|
||||
|
||||
}
|
||||
|
||||
|
||||
|
|
@ -679,7 +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;
|
||||
}
|
||||
|
|
@ -697,146 +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.`
|
||||
]
|
||||
|
||||
}
|
||||
}
|
||||
|
|
@ -844,10 +714,6 @@ export const icosahedron = () => {
|
|||
|
||||
export const build_all = () => {
|
||||
return [
|
||||
tetrahedron(),
|
||||
octahedron(),
|
||||
cube(),
|
||||
icosahedron(),
|
||||
dodecahedron(),
|
||||
cell5(),
|
||||
cell16(),
|
||||
|
|
@ -860,7 +726,3 @@ export const build_all = () => {
|
|||
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))
|
||||
}
|
||||
Loading…
Reference in New Issue