CHANGELOG.md

@@ -0,0 +1,12 @@
+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

@@ -1,9 +1,12 @@
 import * as THREE from 'three';
 
+import { TaperedLink } from './taperedLink.js';
+
 
 const HYPERPLANE = 2.0;
 const W_FORESHORTENING = 0.04;
 
+
 class FourDShape extends THREE.Group {
 
 	constructor(node_ms, link_ms, face_ms, structure) {
@@ -26,11 +29,11 @@ class FourDShape extends THREE.Group {
 
 	// if a node/link has no label, use the 0th material
 
-	getMaterial(entity, materials) {
+	getMaterialLabel(entity) {
     	    if( "label" in entity ) {
-			return materials[entity.label];
+    	        return entity.label
     	    } else {
-			return materials[0];
+     	        return 0;
     	    }
 	}
 
@@ -42,45 +45,23 @@ class FourDShape extends THREE.Group {
 		return sphere;
 	}
 
-	makeLink(material, link) {
+	makeLink(materialLabel, link) {
 		const n1 = this.nodes3[link.source];
 		const n2 = this.nodes3[link.target];
-		const s1 = n1.scale;
+		const s1 = this.link_scale * n1.scale;
-		const s2 = n2.scale;
+		const s2 = this.link_scale * n2.scale;
-		const length = n1.v3.distanceTo(n2.v3);
+		const basematerial = this.link_ms[materialLabel];
-		const centre = new THREE.Vector3();
+		const edge = new TaperedLink(basematerial, materialLabel, n1, n2, s1, s2);
-		centre.lerpVectors(n1.v3, n2.v3, 0.5);
+		this.add( edge );
-		const geometry = new THREE.CylinderGeometry(
-			this.link_scale * s2, this.link_scale * s1, 1,
-			16, 1, true
-		);
-		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);
-		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 s1 = this.link_scale * n1.scale;
-		const s2 = n2.scale;
+		const s2 = this.link_scale * n2.scale;
-		const length = n1.v3.distanceTo(n2.v3);
+		link.object.update(n1, n2, s1, s2);
-		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));
-		link.object.position.copy(centre);
-		link.object.lookAt(n2.v3);
-		link.object.children[0].rotation.x = Math.PI / 2.0;
 		link.object.visible = (!links_show || link.label in links_show); 
 	}
 
@@ -110,15 +91,6 @@ class FourDShape extends THREE.Group {
 	}
 
 
-	fourDtoV3_old(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);
-		return new THREE.Vector3(v4.x * k, v4.y * k, v4.z * k);
-	}
-
 	fourDscale(w) {
 		return this.hyperplane / ( this.hyperplane + w );
 	}
@@ -140,7 +112,7 @@ class FourDShape extends THREE.Group {
 		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.getMaterial(n, this.node_ms);
+			const material = this.node_ms[this.getMaterialLabel(n)];
 			this.nodes3[n.id] = {
 				v3: v3,
 				scale: k,
@@ -149,11 +121,11 @@ class FourDShape extends THREE.Group {
 			};
 		}
 		for( const l of this.links ) {
-			const material = this.getMaterial(l, this.link_ms);
+			const mLabel = this.getMaterialLabel(l);
-			l.object = this.makeLink(material, l);
+			l.object = this.makeLink(mLabel, l);
 		}
 		for( const f of this.faces ) {
-			const material = this.getMaterial(f, this.face_ms);
+			const material = this.face_ms(this.getMaterialLabel(f));
 			f.object = this.makeFace(material, f);
 		}
 	}

gui.js

@@ -2,11 +2,10 @@ import { GUI } from 'lil-gui';
 
 
 const DEFAULTS = {
-	nodesize: 0.25,
+	nodesize: 0.6,
 	nodeopacity: 1,
-	linksize: 0.2,
+	linksize: 1.0,
 	linkopacity: 0.75,
-	link2opacity: 0.75,
 	shape: '120-cell',
 	option: 'none',
 	visibility: 5,
@@ -41,7 +40,6 @@ class FourDGUI {
 			inscribe_all: this.link['inscribe_all'],
 			linksize: this.link['linksize'],
 			linkopacity: this.link['linkopacity'],
-			link2opacity: this.link['linkopacity'],
 			nodesize: this.link['nodesize'],
 			nodeopacity: this.link['nodeopacity'],
 			depth: this.link['depth'],
@@ -72,15 +70,10 @@ class FourDGUI {
 		});
 		this.gui.add(this.params, 'hyperplane', 0.5, 1 / 0.8);
 		this.gui.add(this.params, 'zoom', 0.1, 2.0);
-		this.gui.add(this.params, 'nodesize', 0, 1);
+		this.gui.add(this.params, 'nodesize', 0, 1.5);
 		this.gui.add(this.params, 'nodeopacity', 0, 1).onChange(setNodeOpacity);
-		this.gui.add(this.params, 'linksize', 0, 1);
+		this.gui.add(this.params, 'linksize', 0, 2);
-		this.gui.add(this.params, 'linkopacity', 0, 1).onChange(
+		this.gui.add(this.params, 'linkopacity', 0, 1).onChange(setLinkOpacity);
-			(v) => setLinkOpacity(v, true)
-		);
-		this.gui.add(this.params, 'link2opacity', 0, 1).onChange(
-			(v) => setLinkOpacity(v, false)
-		);
 		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' ]);
@@ -143,7 +136,6 @@ class FourDGUI {
 		this.link['zoom'] = this.numParam('zoom', parseFloat);
 		this.link['linksize'] = this.numParam('linksize', 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));
@@ -163,7 +155,6 @@ class FourDGUI {
 		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("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

@@ -14,6 +14,17 @@
 				font-family: sans-serif;
 				padding: 1em;
 			}
+			div#release_notes {
+				position: fixed;
+				top: 0;
+				left: 0;
+				width: 50%;
+				z-index: 2;
+				font-family: sans-serif;
+				padding: 1em;
+				visibility: none;
+				background: #ffffff;
+			}
 			div#info {
 				position: fixed;
 				bottom:0;
@@ -26,7 +37,10 @@
 	<body>
 		<script type="module" src="/main.js"></script>
 		<div id="description"></div>
-		<div id="info">by <a target="_blank" href="https://mikelynch.org/">Mike Lynch</a> -
+		<div id="release_notes"></div>
+		<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

@@ -0,0 +1,119 @@
+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

@@ -1,5 +1,16 @@
 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';
@@ -31,19 +42,17 @@ 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}));
 
@@ -62,7 +71,7 @@ link_ms.map((m) => {
 
 
 const face_ms = [
-	new THREE.MeshLambertMaterial( { color: 0x44ff44 } )
+	new THREE.MeshStandardMaterial( { color: 0x44ff44 } )
 	];
 
 for( const face_m of face_ms ) {
@@ -104,7 +113,6 @@ function displayDocs(name) {
 }
 
 function showDocs(visible) {
-	console.log(`showDocs ${visible}`);
 	const docdiv = document.getElementById("description");
 	if( visible ) {
 		docdiv.style.display = '';
@@ -113,6 +121,25 @@ function showDocs(visible) {
 	}
 }
 
+function releaseNotes() {
+    showDocs(false);
+    const docdiv = document.getElementById("release_notes");
+    docdiv.style.display = '';
+    docdiv.innerHTML = RELEASE_NOTES + '<p><a id="no_notes" href="#">[hide]</a>';
+    const goaway = document.getElementById("no_notes");
+    goaway.addEventListener('click', noNotes);
+    }
+
+function noNotes() {
+    	const docdiv = document.getElementById("release_notes");
+ 	docdiv.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,
@@ -124,22 +151,24 @@ function setColors(c) {
     	node_ms[i].color = new THREE.Color(nc[i]);
     	link_ms[i].color = new THREE.Color(nc[i]);
     }
-	material.color = new THREE.Color(c);
+    if( shape ) {
+        // 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) {
-	if( structure.nolink2opacity ) {
     link_ms.map((lm) => lm.opacity = o);
-	} else {
+    if( shape ) {
-		if( primary ) {
+        shape.links.map((l) => l.object.material.opacity = o);
-			link_ms[0].opacity = o;
-		} else {
-			link_ms.slice(1).map((lm) => lm.opacity = o);
-		}
     }
 }
 

polytopes.js

@@ -55,8 +55,28 @@ 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;
 	return {
@@ -844,6 +864,7 @@ export const icosahedron = () => {
 
 export const build_all = () => {
 	return [
+	        linkTest(),
 		tetrahedron(),
 		octahedron(),
 		cube(),

taperedLink.js

@@ -0,0 +1,66 @@
+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 };