import * as THREE from 'three'; import * as POLYTOPES from './polytopes.js'; import { FourDShape } from './fourDShape.js'; import { GUI } from 'lil-gui'; const DEFAULT_SHAPE = '120-cell'; // hacky stuff for 4d rotations // see https://math.stackexchange.com/questions/1402362/can-rotations-in-4d-be-given-an-explicit-matrix-form#1402376 function rotZW(theta) { const ctheta = Math.cos(theta); const stheta = Math.sin(theta); return new THREE.Matrix4( ctheta, -stheta, 0, 0, stheta, ctheta, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1 ); } function rotYW(theta) { const ctheta = Math.cos(theta); const stheta = Math.sin(theta); return new THREE.Matrix4( ctheta, 0, -stheta, 0, 0, 1, 0, 0, stheta, 0, ctheta, 0, 0, 0, 0, 1, ); } function rotYZ(theta) { const ctheta = Math.cos(theta); const stheta = Math.sin(theta); return new THREE.Matrix4( ctheta, 0, 0, -stheta, 0, 1, 0, 0, 0, 0, 1, 0, stheta, 0, 0, ctheta, ); } function rotXW(theta) { const ctheta = Math.cos(theta); const stheta = Math.sin(theta); return new THREE.Matrix4( 1, 0, 0, 0, 0, ctheta, -stheta, 0, 0, stheta, ctheta, 0, 0, 0, 0, 1 ); } function rotXZ(theta) { const ctheta = Math.cos(theta); const stheta = Math.sin(theta); return new THREE.Matrix4( 1, 0, 0, 0, 0, ctheta, 0, -stheta, 0, 0, 1, 0, 0, stheta, 0, ctheta, ); } function rotXY(theta) { const ctheta = Math.cos(theta); const stheta = Math.sin(theta); return new THREE.Matrix4( 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, ctheta, -stheta, 0, 0, stheta, ctheta, ); } 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 amblight = new THREE.AmbientLight(0xffffff, 0.5); scene.add(amblight); scene.background = new THREE.Color(0xdddddd); const renderer = new THREE.WebGLRenderer({antialias: true}); renderer.setSize( window.innerWidth, window.innerHeight ); document.body.appendChild( renderer.domElement ); const NODE_OPACITY = 1.0; const LINK_OPACITY = 0.7; // nodes. links // 0 R 0 (0-1) Y // 1 G 1 (1-2) C // 2 B 2 (0-2) M // duals // 0 C 0 (0-1) G // 1 Y 1 (1-2) R // 2 M 2 (0-2) B const node_ms = [ new THREE.MeshStandardMaterial( { color: 0xc0c0ff } ), new THREE.MeshStandardMaterial( { color: 0x20dddd } ), new THREE.MeshStandardMaterial( { color: 0xdddd20 } ), new THREE.MeshStandardMaterial( { color: 0xdd20dd } ), ]; for( const node_m of node_ms ) { node_m.roughness = 0.9; if( NODE_OPACITY < 1.0 ) { node_m.transparent = true; node_m.opacity = NODE_OPACITY; } } const link_ms = [ new THREE.MeshStandardMaterial( { color: 0xc0c0ff } ), new THREE.MeshStandardMaterial( { color: 0x20dd20 } ), new THREE.MeshStandardMaterial( { color: 0xdd2020 } ), new THREE.MeshStandardMaterial( { color: 0x2020dd } ), ]; for( const link_m of link_ms ) { link_m.metalness = 0.8; link_m.roughness = 0.1; if( LINK_OPACITY < 1.0 ) { link_m.transparent = true; link_m.opacity = LINK_OPACITY; } } const STRUCTURES = { '5-cell': POLYTOPES.cell5(), '16-cell': POLYTOPES.cell16(), 'tesseract': POLYTOPES.tesseract(), '24-cell': POLYTOPES.cell24(), '120-cell': POLYTOPES.cell120() }; console.log(STRUCTURES); let shape = false; function createShape(name) { if( shape ) { scene.remove(shape); } console.log(STRUCTURES[name]); shape = new FourDShape(node_ms, link_ms, STRUCTURES[name]); scene.add(shape); } createShape(DEFAULT_SHAPE); camera.position.z = 4; const dragK = 0.005; let theta = 0; let psi = 0; let startX = 0; let startY = 0; let startX0 = 0; let startY0 = 0; renderer.domElement.addEventListener("mousedown", (event) => { if( event.buttons === 1 ) { startX = event.clientX; startY = event.clientY; startX0 = theta / dragK; startY0 = theta / dragK; } }) renderer.domElement.addEventListener("mousemove", (event) => { if( event.buttons === 1 ) { theta = (event.clientX - startX + startX0) * dragK; psi = (event.clientY - startY + startY0) * dragK; } }) // set up GUI const gui = new GUI(); const gui_params = { shape: DEFAULT_SHAPE, hyperplane: 2, xRotate: 'YW', yRotate: 'XZ', }; gui.add(gui_params, 'shape', [ '5-cell', '16-cell', 'tesseract', '24-cell', '120-cell' ] ).onChange(createShape) gui.add(gui_params, 'hyperplane', 1.5, 4); gui.add(gui_params, 'xRotate', [ 'YW', 'YZ', 'ZW' ]); gui.add(gui_params, 'yRotate', [ 'XZ', 'XY', 'XW' ]); const ROTFN = { XY: rotXY, XZ: rotXZ, XW: rotXW, YZ: rotYZ, YW: rotYW, ZW: rotZW, }; const rotation = new THREE.Matrix4(); function animate() { requestAnimationFrame( animate ); const rotations = [ ROTFN[gui_params.xRotate](theta), ROTFN[gui_params.yRotate](psi) ]; shape.hyperplane = gui_params.hyperplane; shape.render3(rotations); renderer.render( scene, camera ); } animate();