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4 changed files with 94 additions and 257 deletions

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@ -2,7 +2,7 @@ import * as THREE from 'three';
const HYPERPLANE = 2.0;
const W_FORESHORTENING = 0.04;
class FourDShape extends THREE.Group {
@ -15,10 +15,11 @@ class FourDShape extends THREE.Group {
this.nodes3 = {};
this.links = structure.links;
this.faces = ( "faces" in structure ) ? structure.faces : [];
this.node_size = structure.geometry.node_size;
this.link_size = structure.geometry.link_size;
this.node_scale = 1;
this.link_scale = 1;
this.hyperplane = HYPERPLANE;
this.foreshortening = W_FORESHORTENING;
this.initShapes();
}
@ -34,7 +35,7 @@ class FourDShape extends THREE.Group {
}
}
makeNode(material, v3, scale) {
makeNode(material, v3) {
const geometry = new THREE.SphereGeometry(this.node_size);
const sphere = new THREE.Mesh(geometry, material);
sphere.position.copy(v3);
@ -43,43 +44,32 @@ class FourDShape extends THREE.Group {
}
makeLink(material, link) {
const n1 = this.nodes3[link.source];
const n2 = this.nodes3[link.target];
const s1 = n1.scale;
const s2 = n2.scale;
const length = n1.v3.distanceTo(n2.v3);
const n1 = this.nodes3[link.source].v3;
const n2 = this.nodes3[link.target].v3;
const length = n1.distanceTo(n2);
const centre = new THREE.Vector3();
centre.lerpVectors(n1.v3, n2.v3, 0.5);
const geometry = new THREE.CylinderGeometry(
this.link_scale * s2, this.link_scale * s1, 1,
16, 1, true
);
centre.lerpVectors(n1, n2, 0.5);
const geometry = new THREE.CylinderGeometry(this.link_size, this.link_size, 1);
const cyl = new THREE.Mesh(geometry, material);
const edge = new THREE.Group();
edge.add(cyl);
edge.position.copy(centre);
edge.scale.copy(new THREE.Vector3(1, 1, length));
edge.lookAt(n2.v3);
edge.lookAt(n2);
cyl.rotation.x = Math.PI / 2.0;
this.add(edge);
return edge;
}
updateLink(link, links_show) {
const n1 = this.nodes3[link.source];
const n2 = this.nodes3[link.target];
const s1 = n1.scale;
const s2 = n2.scale;
const length = n1.v3.distanceTo(n2.v3);
const n1 = this.nodes3[link.source].v3;
const n2 = this.nodes3[link.target].v3;
const length = n1.distanceTo(n2);
const centre = new THREE.Vector3();
centre.lerpVectors(n1.v3, n2.v3, 0.5);
// take the average of the ends as the thickness - as a workaround,
// because I haven't worked out how to reshape tapered links without
// having to reassign a new geometry to every link
const link_mean = this.link_scale * (s1 + s2) * 0.5;
link.object.scale.copy(new THREE.Vector3(link_mean, link_mean, length));
centre.lerpVectors(n1, n2, 0.5);
link.object.scale.copy(new THREE.Vector3(this.link_scale, this.link_scale, length));
link.object.position.copy(centre);
link.object.lookAt(n2.v3);
link.object.lookAt(n2);
link.object.children[0].rotation.x = Math.PI / 2.0;
link.object.visible = (!links_show || link.label in links_show);
}
@ -110,42 +100,24 @@ class FourDShape extends THREE.Group {
}
fourDtoV3_old(x, y, z, w, rotations) {
fourDtoV3(x, y, z, w, rotations) {
const v4 = new THREE.Vector4(x, y, z, w);
for ( const m4 of rotations ) {
v4.applyMatrix4(m4);
}
const k = this.fourDscale(v4.w);
const k = this.hyperplane / (this.hyperplane + v4.w);
return new THREE.Vector3(v4.x * k, v4.y * k, v4.z * k);
}
fourDscale(w) {
return this.hyperplane / ( this.hyperplane + w );
}
fourDrotate(x, y, z, w, rotations) {
const v4 = new THREE.Vector4(x, y, z, w);
for ( const m4 of rotations ) {
v4.applyMatrix4(m4);
}
return v4;
}
fourDtoV3(v4) {
const k = this.fourDscale(v4.w);
return new THREE.Vector3(v4.x * k, v4.y * k, v4.z * k);
}
initShapes() {
for( const n of this.nodes4 ) {
const k = this.fourDscale(n.w);
const v3 = new THREE.Vector3(n.x * k, n.y * k, n.z * k);
const v3 = this.fourDtoV3(n.x, n.y, n.z, n.w, []);
const material = this.getMaterial(n, this.node_ms);
this.nodes3[n.id] = {
v3: v3,
scale: k,
label: n.label,
object: this.makeNode(material, v3, k)
object: this.makeNode(material, v3)
};
}
for( const l of this.links ) {
@ -162,15 +134,10 @@ class FourDShape extends THREE.Group {
render3(rotations, nodes_show, links_show) {
this.scalev3 = new THREE.Vector3(this.node_scale, this.node_scale, this.node_scale);
for( const n of this.nodes4 ) {
const v4 = this.fourDrotate(n.x, n.y, n.z, n.w, rotations);
const k = this.fourDscale(v4.w);
const v3 = new THREE.Vector3(v4.x * k, v4.y * k, v4.z * k);
const s4 = k * this.node_scale * this.foreshortening;
const s3 = new THREE.Vector3(s4, s4, s4);
const v3 = this.fourDtoV3(n.x, n.y, n.z, n.w, rotations);
this.nodes3[n.id].v3 = v3;
this.nodes3[n.id].scale = k * this.foreshortening;
this.nodes3[n.id].object.position.copy(v3);
this.nodes3[n.id].object.scale.copy(s3);
this.nodes3[n.id].object.scale.copy(this.scalev3);
this.nodes3[n.id].object.visible = ( !nodes_show || n.label in nodes_show );
}
for( const l of this.links ) {

39
gui.js
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@ -2,11 +2,10 @@ import { GUI } from 'lil-gui';
const DEFAULTS = {
nodesize: 0.25,
nodeopacity: 1,
linksize: 0.2,
linkopacity: 0.75,
link2opacity: 0.75,
thickness: 1.0,
nodesize: 2.0,
linkopacity: 0.5,
link2opacity: 0.5,
shape: '120-cell',
option: 'none',
visibility: 5,
@ -14,13 +13,11 @@ const DEFAULTS = {
inscribe_all: false,
color: 0x3293a9,
background: 0xd4d4d4,
hyperplane: 0.93,
hyperplane: 1.5,
zoom: 1,
xRotate: 'YW',
yRotate: 'XW',
yRotate: 'XZ',
dtheta: 0,
damping: false,
captions: true,
dpsi: 0,
}
@ -28,7 +25,7 @@ const DEFAULTS = {
class FourDGUI {
constructor(shapes, changeShape, setColor, setBackground, setNodeOpacity,setLinkOpacity, setVisibility, showDocs) {
constructor(shapes, changeShape, setColor, setBackground, setLinkOpacity, setVisibility) {
this.gui = new GUI();
const SHAPE_NAMES = shapes.map((s) => s.name);
@ -39,11 +36,10 @@ class FourDGUI {
option: this.link['option'],
inscribed: this.link['inscribed'],
inscribe_all: this.link['inscribe_all'],
linksize: this.link['linksize'],
thickness: this.link['thickness'],
linkopacity: this.link['linkopacity'],
link2opacity: this.link['linkopacity'],
nodesize: this.link['nodesize'],
nodeopacity: this.link['nodeopacity'],
depth: this.link['depth'],
color: this.link['color'],
background: this.link['background'],
@ -52,7 +48,6 @@ class FourDGUI {
xRotate: this.link['xRotate'],
yRotate: this.link['yRotate'],
damping: false,
captions: true,
dtheta: this.link['dtheta'],
dpsi: this.link['dpsi'],
"copy link": function () { guiObj.copyUrl() }
@ -70,22 +65,20 @@ class FourDGUI {
options_ctrl = this.gui.add(this.params, 'option').options(options).onChange((option) => {
setVisibility(option)
});
this.gui.add(this.params, 'hyperplane', 0.5, 1 / 0.8);
this.gui.add(this.params, 'hyperplane', 1.4, 2.0);
this.gui.add(this.params, 'zoom', 0.1, 2.0);
this.gui.add(this.params, 'nodesize', 0, 1);
this.gui.add(this.params, 'nodeopacity', 0, 1).onChange(setNodeOpacity);
this.gui.add(this.params, 'linksize', 0, 1);
this.gui.add(this.params, 'thickness', 0, 2);
this.gui.add(this.params, 'linkopacity', 0, 1).onChange(
(v) => setLinkOpacity(v, true)
);
this.gui.add(this.params, 'link2opacity', 0, 1).onChange(
(v) => setLinkOpacity(v, false)
);
this.gui.add(this.params, 'nodesize', 0.1, 4);
this.gui.addColor(this.params, 'color').onChange(setColor);
this.gui.addColor(this.params, 'background').onChange(setBackground);
this.gui.add(this.params, 'xRotate', [ 'YW', 'YZ', 'ZW' ]);
this.gui.add(this.params, 'yRotate', [ 'XZ', 'XY', 'XW' ]);
this.gui.add(this.params, 'captions').onChange(showDocs);
this.gui.add(this.params, 'damping');
this.gui.add(this.params, 'copy link');
@ -141,11 +134,10 @@ class FourDGUI {
}
this.link['hyperplane'] = this.numParam('hyperplane', parseFloat);
this.link['zoom'] = this.numParam('zoom', parseFloat);
this.link['linksize'] = this.numParam('linksize', parseFloat);
this.link['thickness'] = this.numParam('thickness', parseFloat);
this.link['linkopacity'] = this.numParam('linkopacity', parseFloat);
this.link['link2opacity'] = this.numParam('link2opacity', parseFloat);
this.link['nodesize'] = this.numParam('nodesize', parseFloat);
this.link['nodeopacity'] = this.numParam('nodeopacity', parseFloat);
this.link['color'] = this.numParam('color', (s) => guiObj.stringToHex(s));
this.link['background'] = this.numParam('background', (s) => guiObj.stringToHex(s));
this.link['dpsi'] = this.numParam('dpsi', parseFloat);
@ -159,11 +151,10 @@ class FourDGUI {
url.searchParams.append("option", this.params.option);
url.searchParams.append("inscribed", this.params.inscribed ? 'y': 'n');
url.searchParams.append("inscribe_all", this.params.inscribe_all ? 'y': 'n');
url.searchParams.append("linksize", this.params.linksize.toString());
url.searchParams.append("thickness", this.params.thickness.toString());
url.searchParams.append("nodesize", this.params.nodesize.toString());
url.searchParams.append("nodeopacity", this.params.nodesize.toString());
url.searchParams.append("linkopacity", this.params.nodeopacity.toString());
url.searchParams.append("link2opacity", this.params.link2opacity.toString());
url.searchParams.append("linkopacity", this.params.thickness.toString());
url.searchParams.append("link2opacity", this.params.nodesize.toString());
url.searchParams.append("color", this.hexToString(this.params.color));
url.searchParams.append("background", this.hexToString(this.params.background));
url.searchParams.append("hyperplane", this.params.hyperplane.toString());

37
main.js
View File

@ -9,7 +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
@ -47,19 +47,11 @@ 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.MeshLambertMaterial( { color: 0x44ff44 } )
@ -103,16 +95,6 @@ function displayDocs(name) {
}
}
function showDocs(visible) {
console.log(`showDocs ${visible}`);
const docdiv = document.getElementById("description");
if( visible ) {
docdiv.style.display = '';
} else {
docdiv.style.display = 'none';
}
}
// initialise gui and read params from URL
// callbacks to do things which are triggered by controls: reset the shape,
@ -143,11 +125,6 @@ function setLinkOpacity(o, primary) {
}
}
function setNodeOpacity(o) {
node_ms.map((nm) => nm.opacity = o);
}
let gui;
@ -172,10 +149,8 @@ gui = new FourDGUI(
changeShape,
setColors,
setBackground,
setNodeOpacity,
setLinkOpacity,
setVisibility,
showDocs
setVisibility
);
// these are here to pick up colour settings from the URL params
@ -238,11 +213,11 @@ 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);

View File

@ -58,15 +58,16 @@ export function auto_detect_edges(nodes, neighbours, debug=false) {
// 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},
@ -80,6 +81,10 @@ export const cell5 = () => {
{ id:9, source:3, target: 5},
{ id:10, source:4, target: 5},
],
geometry: {
node_size: 0.02,
link_size: 0.02
},
options: [ { name: '--' }],
description: `Five tetrahedra joined at ten faces with three
tetrahedra around each edge. The 5-cell is the simplest regular
@ -104,13 +109,17 @@ 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,
geometry: {
node_size: 0.02,
link_size: 0.02
},
options: [ { name: '--' }],
description: `Sixteen tetrahedra joined at 32 faces with four
tetrahedra around each edge. The 16-cell is the four-dimensional
@ -133,7 +142,7 @@ 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 });
@ -149,6 +158,10 @@ export const 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 ] },
@ -185,7 +198,6 @@ 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);
@ -209,6 +221,10 @@ 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 ] },
@ -322,7 +338,7 @@ 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;
}
@ -396,6 +412,10 @@ 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
@ -427,6 +447,10 @@ 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 ] },
@ -516,7 +540,7 @@ export function make_600cell_vertices() {
index_nodes(nodes);
scale_nodes(nodes, 0.5);
scale_nodes(nodes, 0.75);
return nodes;
}
@ -558,6 +582,10 @@ 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 ] },
@ -607,6 +635,10 @@ 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
@ -634,6 +666,10 @@ export const snub24cell = () => {
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
@ -679,7 +715,6 @@ 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;
}
@ -700,6 +735,10 @@ export const 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 ] },
@ -715,139 +754,8 @@ export const dodecahedron = () => {
}
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.`
}
}
export const build_all = () => {
return [
tetrahedron(),
octahedron(),
cube(),
icosahedron(),
dodecahedron(),
cell5(),
cell16(),
@ -859,8 +767,4 @@ 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))
}