Isometric projections

CHANGELOG.md

@@ -1,12 +0,0 @@
-CHANGELOG
-=========
-
-## v1.0 - 16/11/2025
-
-It's been [two years](https://mikelynch.org/2023/Sep/02/120-cell/)</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.
-
-The results flicker a bit at low opacities but otherwise I'm pretty happy with
-it.
-`

fourDShape.js

@@ -1,11 +1,8 @@
 import * as THREE from 'three';
 
-import { TaperedLink } from './taperedLink.js';
-
 
 const HYPERPLANE = 2.0;
-const W_FORESHORTENING = 0.04;
+const NODE_FORESHORTENING = 0.4;
-
 
 class FourDShape extends THREE.Group {
 
@@ -18,10 +15,12 @@ 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.projection = 1;
 		this.initShapes();
 	}
 
@@ -29,12 +28,12 @@ class FourDShape extends THREE.Group {
 
 	// if a node/link has no label, use the 0th material
 
-	getMaterialLabel(entity) {
+	getMaterial(entity, materials) {
-    	    if( "label" in entity ) {
+		if( "label" in entity ) {
-    	        return entity.label
+			return materials[entity.label];
-    	    } else {
+		} else {
-     	        return 0;
+			return materials[0];
-    	    }
+		}
 	}
 
 	makeNode(material, v3, scale) {
@@ -45,23 +44,34 @@ class FourDShape extends THREE.Group {
 		return sphere;
 	}
 
-	makeLink(materialLabel, link) {
+	makeLink(material, link) {
-		const n1 = this.nodes3[link.source];
+		const n1 = this.nodes3[link.source].v3;
-		const n2 = this.nodes3[link.target];
+		const n2 = this.nodes3[link.target].v3;
-		const s1 = this.link_scale * n1.scale;
+		const length = n1.distanceTo(n2);
-		const s2 = this.link_scale * n2.scale;
+		const centre = new THREE.Vector3();
-		const basematerial = this.link_ms[materialLabel];
+		centre.lerpVectors(n1, n2, 0.5);
-		const edge = new TaperedLink(basematerial, materialLabel, n1, n2, s1, s2);
+		const geometry = new THREE.CylinderGeometry(this.link_size, this.link_size, 1);
-		this.add( edge );
+		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);
+		cyl.rotation.x = Math.PI / 2.0;
+		this.add(edge);
 		return edge;
 	}
 
 	updateLink(link, links_show) {
-		const n1 = this.nodes3[link.source];
+		const n1 = this.nodes3[link.source].v3;
-		const n2 = this.nodes3[link.target];
+		const n2 = this.nodes3[link.target].v3;
-		const s1 = this.link_scale * n1.scale;
+		const length = n1.distanceTo(n2);
-		const s2 = this.link_scale * n2.scale;
+		const centre = new THREE.Vector3();
-		link.object.update(n1, n2, s1, s2);
+		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);
+		link.object.children[0].rotation.x = Math.PI / 2.0;
 		link.object.visible = (!links_show || link.label in links_show); 
 	}
 
@@ -103,29 +113,41 @@ class FourDShape extends THREE.Group {
 		return v4;
 	}
 
-	fourDtoV3(v4) {
+	renderNodePerspective(n, rotations) {
+		const v4 = this.fourDrotate(n.x, n.y, n.z, n.w, rotations);
 		const k = this.fourDscale(v4.w);
-		return new THREE.Vector3(v4.x * k, v4.y * k, v4.z * k);		
+		const position = new THREE.Vector3(v4.x * k, v4.y * k, v4.z * k);
+		const s4 = k * this.node_scale * NODE_FORESHORTENING;
+		const scale = new THREE.Vector3(s4, s4, s4);
+		return { position: position, scale: scale }
 	}
 
+	renderNodeIsometric(n, rotations) {
+		const v4 = this.fourDrotate(n.x, n.y, n.z, n.w, rotations);
+		const position = new THREE.Vector3(v4.x, v4.y + v4.w, v4.z);
+		const s4 = this.node_scale;
+		const scale = new THREE.Vector3(s4, s4, s4);
+		return { position: position, scale: scale }
+	}
+
+
 	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 material = this.node_ms[this.getMaterialLabel(n)];
+			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)
 			};
 		}
 		for( const l of this.links ) {
-			const mLabel = this.getMaterialLabel(l);
+			const material = this.getMaterial(l, this.link_ms);
-			l.object = this.makeLink(mLabel, l);
+			l.object = this.makeLink(material, l);
 		}
 		for( const f of this.faces ) {
-			const material = this.face_ms(this.getMaterialLabel(f));
+			const material = this.getMaterial(f, this.face_ms);
 			f.object = this.makeFace(material, f);
 		}
 	}
@@ -134,15 +156,10 @@ 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 node3d = this.renderNodeIsometric(n, rotations);
-			const k = this.fourDscale(v4.w);
+			this.nodes3[n.id].v3 = node3d.position;
-			const v3 = new THREE.Vector3(v4.x * k, v4.y * k, v4.z * k);
+			this.nodes3[n.id].object.position.copy(node3d.position);
-			const s4 = k * this.node_scale * this.foreshortening;
+			this.nodes3[n.id].object.scale.copy(node3d.scale);
-			const s3 = new THREE.Vector3(s4, s4, s4);
-			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.visible = ( !nodes_show || n.label in nodes_show );
 		}
 		for( const l of this.links ) {

gui.js

@@ -2,10 +2,10 @@ import { GUI } from 'lil-gui';
 
 
 const DEFAULTS = {
-	nodesize: 0.6,
+	thickness: 1.0,
-	nodeopacity: 1,
+	nodesize: 2.0,
-	linksize: 1.0,
+	linkopacity: 0.5,
-	linkopacity: 0.75,
+	link2opacity: 0.5,
 	shape: '120-cell',
 	option: 'none',
 	visibility: 5,
@@ -13,13 +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,
 }
 
@@ -27,7 +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);
 
@@ -38,10 +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'],
@@ -50,7 +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() }
@@ -68,17 +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, 1.5);
+		this.gui.add(this.params, 'thickness', 0, 2);
-		this.gui.add(this.params, 'nodeopacity', 0, 1).onChange(setNodeOpacity);
+		this.gui.add(this.params, 'linkopacity', 0, 1).onChange(
-		this.gui.add(this.params, 'linksize', 0, 2);
+			(v) => setLinkOpacity(v, true)
-		this.gui.add(this.params, 'linkopacity', 0, 1).onChange(setLinkOpacity);
+		);
+		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');
 
@@ -134,10 +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);
@@ -151,10 +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.thickness.toString());
-		url.searchParams.append("linkopacity", this.params.nodeopacity.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());

index.html

@@ -14,15 +14,6 @@
 				font-family: sans-serif;
 				padding: 1em;
 			}
-			div#release_notes {
-				position: fixed;
-				top: 0;
-				left: 0;
-				width: 20%;
-				z-index: 2;
-				padding: 1em;
-				font-family: sans-serif;
-			}
 			div#info {
 				position: fixed;
 				bottom:0;
@@ -35,10 +26,7 @@
 	<body>
 		<script type="module" src="/main.js"></script>
 		<div id="description"></div>
-		<div id="release_notes"></div>
+		<div id="info">by <a target="_blank" href="https://mikelynch.org/">Mike Lynch</a> -
-		<div id="info"><a href="#" id="show_notes">release 1.0</a> |
-
-    		by <a target="_blank" href="https://mikelynch.org/">Mike Lynch</a> |
 			<a target="_blank" href="https://git.tilde.town/bombinans/fourdjs">source</a></div>
 	</body>
 </html>

linktest.js

@@ -1,119 +0,0 @@
-import * as THREE from 'three';
-
-import { OrbitControls } from 'three/addons/controls/OrbitControls.js';
-import { GUI } from 'lil-gui';
-
-import { TaperedLink } from './taperedLink.js';
-
-const FACE_OPACITY = 0.3;
-const CAMERA_K = 5;
-
-// scene, lights and camera
-
-
-
-
-const scene = new THREE.Scene();
-const camera = new THREE.PerspectiveCamera( 75, window.innerWidth / window.innerHeight, 0.1, 1000 );
-const light = new THREE.PointLight(0xffffff, 2);
-light.position.set(10, 10, 10);
-scene.add(light);
-const light2 = new THREE.PointLight(0xffffff, 2);
-light2.position.set(-10, 5, 10);
-scene.add(light);
-const amblight = new THREE.AmbientLight(0xffffff, 0.5);
-scene.add(amblight);
-
-camera.position.set(0, 0, CAMERA_K / 2);
-
-camera.lookAt(0, 0, 0);
-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();

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 ) {
@@ -112,71 +95,36 @@ function displayDocs(name) {
 	}
 }
 
-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);
+	const nc = get_colours(c);
-    for( let i = 0; i < node_ms.length; i++ ) {
+	for( let i = 0; i < node_ms.length; i++ ) {
-    	node_ms[i].color = new THREE.Color(nc[i]);
+		node_ms[i].color = new THREE.Color(nc[i]);
-    	link_ms[i].color = new THREE.Color(nc[i]);
+		link_ms[i].color = new THREE.Color(nc[i]);
-    }
+	}
-    if( shape ) {
+	material.color = new THREE.Color(c);
-        // taperedLink.set_color updates according to the link index
-       shape.links.map((l) => l.object.set_color(nc));
-    }
 }
 
 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( structure.nolink2opacity ) {
-    if( shape ) {
+		link_ms.map((lm) => lm.opacity = o);
-        shape.links.map((l) => l.object.material.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; 
 
 
@@ -201,10 +149,8 @@ gui = new FourDGUI(
 	changeShape,
 	setColors,
 	setBackground,
-	setNodeOpacity,
 	setLinkOpacity,
-	setVisibility,
+	setVisibility
-	showDocs
 );
 
 // these are here to pick up colour settings from the URL params
@@ -267,11 +213,11 @@ function animate() {
 		rotfn[gui.params.xRotate](theta), 
 		rotfn[gui.params.yRotate](psi)
 	];
-	shape.hyperplane = 1 / gui.params.hyperplane;
+	shape.hyperplane = gui.params.hyperplane;
-	camera.position.set(0, 0, gui.params.zoom * CAMERA_K * 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);
 
 

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:1, label: 1, x: r2, y: r2, z: r2, w: -r2 / r5 },
-	      {id:2, label: 2, x: c1, y: -c1, z: -c1, w: -0.25 },
+	      {id:2, label: 2, x: r2, y: -r2, z: -r2, w: -r2 / r5 },
-	      {id:3, label: 3, x: -c1, y: c1, z: -c1, w: -0.25 },
+	      {id:3, label: 3, x: -r2, y: r2, z: -r2, w: -r2 / r5 },
-	      {id:4, label: 4, x: -c1, y: -c1, z: c1, w: -0.25 },
+	      {id:4, label: 4, x: -r2, y: -r2, z: r2, w: -r2 / r5 },
-	      {id:5, label: 5, x: 0, y: 0, z: 0, w: 1 },
+	      {id:5, label: 5, x: 0, y: 0, z: 0, w: 4 * r2 / r5 },
 		],
 		links: [
 			{ id:1, source:1, target: 2},
@@ -100,6 +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
@@ -124,13 +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
@@ -153,7 +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 });
 
@@ -169,6 +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 ] },
@@ -205,7 +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);
@@ -229,6 +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 ] },
@@ -342,7 +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;
 }
 
@@ -416,6 +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
@@ -447,6 +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 ] },
@@ -536,7 +540,7 @@ export function make_600cell_vertices() {
 
 
 	index_nodes(nodes);
-	scale_nodes(nodes, 0.5);
+	scale_nodes(nodes, 0.75);
 	return nodes;
 }
 
@@ -578,6 +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 ] },
@@ -627,6 +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
@@ -654,6 +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
@@ -699,7 +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;
 }
@@ -720,6 +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 ] },
@@ -735,140 +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 [
-	        linkTest(),
-		tetrahedron(),
-		octahedron(),
-		cube(),
-		icosahedron(),
 	 	dodecahedron(),
 	 	cell5(),
 		cell16(),
@@ -881,7 +768,3 @@ 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))
-}

taperedLink.js

@@ -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 };