2d:null 2e:["$","title",null,{"children":"Computational Xmas Tree | randName() | Observable"}] 33:T866,getColor = { const rand = () => Math.random() * 2 - 1 // helper function to get RGB from HSV const tempCol = new THREE.Color() const fromHSV = (h, s, v) => { const { r, g, b } = tempCol.setHSL(h, s, v) return [r, g, b] } // initialization for snow const MAX_Z = Math.max(...LEDs.map(({ z }) => z)) let flakes = [] const stepFlake = () => { while (flakes.length < 50) flakes.push({ x: rand(), y: rand(), z: MAX_Z, v: Math.random() * 0.05 + 0.01 }) for (const flake of flakes) { if (flake.z > 0) { flake.z -= flake.v } } flakes = flakes.filter(({ z }) => z > 0) } // initalization for sweeping planes let pd = 1.5, pdt = 0.01, pdh = 0.5 const norm = new THREE.Vector3() const stepPlane = () => { pd += pdt if (Math.abs(pd) < 2) return // reset normal norm.set(Math.random(), Math.random(), Math.random()) norm.normalize() const dir = (Math.random() > 0.5) ? 1 : -1 pd = dir * -1.5 pdh = Math.random() pdt = dir * (Math.random() * 0.01 + 0.01) } // actual function return (led, state) => { // JS destructuring assignments for convenience const { frame, time } = state const { index, x, y, z, r, θ } = led // split time to get multiple animations const allTime = time % 90 const t = allTime / 10 if (t < 3) { // snow if (!index) stepFlake() if (flakes.some((fl) => Math.hypot(fl.x - x, fl.y - y, fl.z - z) < 0.15)) return [1, 1, 1] } else if (t < 4) { // rotating bisector return (y * Math.cos(t * 20) + (z - 1.5) * Math.sin(t * 20)) > 0 ? [0, 1, 0] : [1, 0, 0] } else if (t < 5) { // radar sweep (view from top) const sweep = Math.abs((t + θ / 6) % 1) return fromHSV(frame / 200, 0.5, sweep < 0.1 ? 0.5 : 0.05 / sweep) } else if (t < 6) { // height sweep return fromHSV(z / 6 - t, 0.5, 0.5) } else { // sweeping planes if (!index) stepPlane() const dist = Math.abs(x * norm.x + y * norm.y + z * norm.z + pd) return fromHSV(pdh, 0.5, dist < 0.1 ? 0.7 : 0.05 / dist) } } }34:T574e,// source: https://github.com/standupmaths/xmastree2021/blob/main/coords_2021.csv ledPositions = [ [ 0.547169811, -0.173584906, 0.698113208], [ 0.547169811, -0.173584906, 0.698113208], [ 0.547169811, -0.173584906, 0.698113208], [ 0.547169811, -0.173584906, 0.698113208], [ 0.547169811, -0.173584906, 0.698113208], [ 0.547169811, -0.173584906, 0.698113208], [ 0.547169811, -0.173584906, 0.698113208], [ 0.547169811, -0.173584906, 0.698113208], [ 0.547169811, -0.173584906, 0.698113208], [ 0.547169811, -0.173584906, 0.698113208], [ 0.547169811, -0.173584906, 0.698113208], [ 0.547169811, -0.173584906, 0.698113208], [ 0.547169811, -0.173584906, 0.698113208], [ 0.547169811, -0.173584906, 0.698113208], [ 0.547169811, -0.173584906, 0.698113208], [ 0.547169811, -0.173584906, 0.698113208], [ 0.547169811, -0.173584906, 0.698113208], [ 0.547169811, -0.173584906, 0.698113208], [ 0.547169811, -0.173584906, 0.698113208], [ 0.362264151, -0.188679245, 0.520754717], [ 0.343396226, -0.464150943, 0.347169811], [ 0.267924528, -0.441509434, 0.58490566], [ 0.305660377, -0.464150943, 0.581132075], [ 0.347169811, -0.490566038, 0.577358491], [ 0.388679245, -0.513207547, 0.573584906], [ 0.430188679, -0.539622642, 0.569811321], [ 0.471698113, -0.566037736, 0.562264151], [ 0.550943396, -0.833962264, 0.479245283], [ 0.509433962, -0.924528302, 0.645283019], [ 0.532075472, -0.905660377, 0.396226415], [ 0.509433962, -0.901886792, 0.4], [ 0.486792453, -0.901886792, 0.403773585], [ 0.464150943, -0.901886792, 0.40754717], [ 0.441509434, -0.901886792, 0.411320755], [ 0.418867925, -0.901886792, 0.41509434], [ 0.396226415, -0.901886792, 0.418867925], [ 0.373584906, -0.901886792, 0.422641509], [ 0.350943396, -0.901886792, 0.426415094], [ 0.332075472, -0.901886792, 0.430188679], [ 0.309433962, -0.901886792, 0.433962264], [ 0.286792453, -0.901886792, 0.437735849], [ 0.264150943, -0.901886792, 0.441509434], [ 0.241509434, -0.901886792, 0.445283019], [ 0.218867925, -0.901886792, 0.449056604], [ 0.196226415, -0.901886792, 0.452830189], [ 0.173584906, -0.901886792, 0.456603774], [ 0.154716981, -0.901886792, 0.460377358], [ 0.132075472, -0.901886792, 0.464150943], [ 0.109433962, -0.901886792, 0.467924528], [ 0.086792453, -0.901886792, 0.471698113], [ 0.067924528, -0.901886792, 0.475471698], [ 0.045283019, -0.901886792, 0.479245283], [ 0.022641509, -0.901886792, 0.483018868], [ 0.000000000, -0.901886792, 0.486792453], [-0.022641509, -0.901886792, 0.486792453], [-0.030188679, -0.920754717, 0.245283019], [ 0.083018868, -0.811320755, 0.396226415], [ 0.056603774, -0.784905660, 0.4], [ 0.030188679, -0.762264151, 0.4], [ 0.003773585, -0.739622642, 0.4], [-0.022641509, -0.716981132, 0.4], [-0.049056604, -0.694339623, 0.4], [-0.075471698, -0.671698113, 0.4], [-0.101886792, -0.649056604, 0.4], [-0.128301887, -0.626415094, 0.4], [-0.154716981, -0.603773585, 0.4], [-0.181132075, -0.581132075, 0.4], [-0.207547170, -0.558490566, 0.4], [-0.233962264, -0.535849057, 0.403773585], [-0.260377358, -0.513207547, 0.403773585], [-0.286792453, -0.490566038, 0.403773585], [-0.313207547, -0.467924528, 0.403773585], [-0.339622642, -0.445283019, 0.403773585], [-0.366037736, -0.422641509, 0.403773585], [-0.392452830, -0.400000000, 0.403773585], [-0.418867925, -0.377358491, 0.403773585], [-0.445283019, -0.354716981, 0.403773585], [-0.471698113, -0.332075472, 0.403773585], [-0.498113208, -0.309433962, 0.403773585], [-0.415094340, -0.196226415, 0.562264151], [-0.343396226, -0.222641509, 0.241509434], [-0.343396226, -0.275471698, 0.509433962], [-0.347169811, -0.120754717, 0.41509434], [-0.403773585, -0.120754717, 0.4], [-0.464150943, -0.120754717, 0.38490566], [-0.524528302, -0.120754717, 0.366037736], [-0.584905660, -0.124528302, 0.350943396], [-0.645283019, -0.124528302, 0.332075472], [-0.701886792, -0.124528302, 0.316981132], [-0.762264151, -0.128301887, 0.301886792], [-0.822641509, -0.128301887, 0.283018868], [-0.883018868, -0.128301887, 0.267924528], [-0.943396226, -0.132075472, 0.249056604], [-0.826415094, -0.060377358, 0.011320755], [-0.875471698, -0.120754717, 0.275471698], [-0.864150943, -0.083018868, 0.294339623], [-0.852830189, -0.045283019, 0.313207547], [-0.841509434, -0.015094340, 0.328301887], [-0.830188679, 0.022641509, 0.347169811], [-0.818867925, 0.056603774, 0.366037736], [-0.807547170, 0.094339623, 0.381132075], [-0.796226415, 0.128301887, 0.4], [-0.784905660, 0.166037736, 0.41509434], [-0.773584906, 0.200000000, 0.433962264], [-0.762264151, 0.237735849, 0.452830189], [-0.750943396, 0.271698113, 0.467924528], [-0.739622642, 0.309433962, 0.486792453], [-0.728301887, 0.347169811, 0.501886792], [-0.773584906, 0.154716981, 0.267924528], [-0.886792453, 0.316981132, 0.2], [-1.000000000, 0.581132075, 0.343396226], [-0.916981132, 0.603773585, 0.105660377], [-0.788679245, 0.316981132, 0.109433962], [-0.569811321, 0.445283019, 0.283018868], [-0.618867925, 0.475471698, 0.162264151], [-0.600000000, 0.486792453, 0.177358491], [-0.584905660, 0.501886792, 0.19245283], [-0.569811321, 0.516981132, 0.20754717], [-0.550943396, 0.528301887, 0.222641509], [-0.535849057, 0.543396226, 0.237735849], [-0.520754717, 0.558490566, 0.252830189], [-0.505660377, 0.573584906, 0.264150943], [-0.713207547, 0.664150943, 0.433962264], [-0.562264151, 0.437735849, 0.652830189], [-0.630188679, 0.626415094, 0.905660377], [-0.516981132, 0.384905660, 1.049056604], [-0.698113208, 0.490566038, 1.150943396], [-0.418867925, 0.415094340, 1.260377358], [-0.596226415, 0.400000000, 1.301886792], [-0.566037736, 0.309433962, 1.196226415], [-0.539622642, 0.222641509, 1.090566038], [-0.471698113, 0.279245283, 1.188679245], [-0.267924528, 0.026415094, 1.154716981], [-0.267924528, 0.030188679, 1.162264151], [-0.267924528, 0.033962264, 1.166037736], [-0.271698113, 0.037735849, 1.169811321], [-0.271698113, 0.041509434, 1.173584906], [-0.275471698, 0.045283019, 1.181132075], [-0.275471698, 0.049056604, 1.18490566], [-0.279245283, 0.052830189, 1.188679245], [-0.279245283, 0.056603774, 1.19245283], [-0.283018868, 0.060377358, 1.196226415], [-0.056603774, 0.030188679, 1.377358491], [-0.188679245, -0.124528302, 1.249056604], [-0.226415094, -0.003773585, 1.2], [-0.230188679, 0.079245283, 1.116981132], [-0.233962264, 0.166037736, 1.033962264], [-0.241509434, 0.252830189, 0.947169811], [-0.245283019, 0.339622642, 0.864150943], [-0.249056604, 0.422641509, 0.781132075], [-0.256603774, 0.509433962, 0.694339623], [-0.260377358, 0.596226415, 0.611320755], [-0.267924528, 0.683018868, 0.524528302], [-0.426415094, 0.909433962, 0.516981132], [-0.305660377, 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0.339622642, 0.132075472, 0.113207547], [ 0.490566038, 0.192452830, 0], [ 0.592452830, 0.249056604, 0.150943396], [ 0.660377358, 0.324528302, 0.2], [ 0.660377358, 0.335849057, 0.290566038], [ 0.675471698, 0.169811321, 0.456603774], [ 0.743396226, 0.184905660, 0.449056604], [ 0.815094340, 0.203773585, 0.437735849], [ 0.886792453, 0.218867925, 0.430188679], [ 0.958490566, 0.237735849, 0.418867925], [ 0.811320755, 0.196226415, 0.60754717], [ 0.750943396, 0.158490566, 0.573584906], [ 0.622641509, 0.000000000, 0.637735849], [ 0.535849057, 0.052830189, 0.728301887], [ 0.441509434, -0.079245283, 0.977358491], [ 0.411320755, 0.116981132, 1.011320755], [ 0.305660377, 0.113207547, 1.188679245], [ 0.392452830, 0.207547170, 1.203773585], [ 0.483018868, 0.301886792, 1.218867925], [ 0.637735849, 0.328301887, 0.928301887], [ 0.532075472, 0.332075472, 1.105660377], [ 0.558490566, 0.067924528, 1.245283019], [ 0.524528302, 0.098113208, 1.143396226], [ 0.494339623, 0.128301887, 1.041509434], [ 0.464150943, 0.158490566, 0.935849057], [ 0.550943396, 0.056603774, 0.811320755], [ 0.501886792, 0.256603774, 0.99245283], [ 0.641509434, 0.535849057, 0.826415094], [ 0.649056604, 0.362264151, 0.905660377], [ 0.656603774, 0.188679245, 0.98490566], [ 0.747169811, 0.184905660, 0.656603774], [ 0.581132075, 0.362264151, 0.558490566], [ 0.766037736, 0.449056604, 0.61509434], [ 0.954716981, 0.535849057, 0.667924528], [ 0.716981132, 0.550943396, 0.750943396], [ 0.920754717, 0.581132075, 0.958490566], [ 0.762264151, 0.532075472, 1.022641509], [ 0.954716981, 0.350943396, 0.849056604], [ 0.947169811, 0.324528302, 0.943396226], [ 0.939622642, 0.298113208, 1.037735849], [ 0.932075472, 0.271698113, 1.132075472], [ 0.924528302, 0.245283019, 1.226415094], [ 0.935849057, -0.071698113, 1.222641509], [ 1.000000000, -0.007547170, 1.430188679], [ 0.867924528, -0.230188679, 1.494339623], [ 0.758490566, -0.362264151, 1.467924528], [ 0.762264151, -0.290566038, 1.520754717], [ 0.766037736, -0.218867925, 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Tree","thumbnail":"21da9d161424892e081c72b0a28574b06da6ad418460fe891392438b3f610472","access_level":"public","create_time":"$D2021-12-26T01:54:50.799Z","update_time":"$D2021-12-28T14:30:35.954Z","view_time":null,"first_public_time":"$D2021-12-26T04:49:52.297Z","has_unpublished_edits":null,"fork":{"id":"4d9b7665f00a916c","slug":"three-js","title":"Three.js","owner":{"id":"f35c755083683fe5","login":"observablehq","name":"Observable"}},"stars":1,"starred":false,"owner":{"type":"team","id":"af680361d1ea8ba5","login":"randname","name":"randName()","avatar_url":"https://avatars-next.observableusercontent.com/f16c819c73deae04aebd89cd214320d2b848d288cea0ed4487f835cc1b3e9c04","tier":"starter_2024"},"version":890,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"6af62fd51a9b60df","login":"randname","name":"randName()","avatar_url":"https://avatars-next.observableusercontent.com/f16c819c73deae04aebd89cd214320d2b848d288cea0ed4487f835cc1b3e9c04","tier":null}],"members":[{"type":"individual","id":"6af62fd51a9b60df","login":"randname","name":"randName()","avatar_url":"https://avatars-next.observableusercontent.com/f16c819c73deae04aebd89cd214320d2b848d288cea0ed4487f835cc1b3e9c04","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":true,"trashed":false,"lapsed":null,"subscribed":null,"forks":1,"collection":null,"type":"notebook","body":{"title":"Computational Xmas Tree","cells":[{"id":242,"value":"# Computational Xmas Tree\n\nFor more details, watch [Matt Parker's video on the tree](https://youtu.be/WuMRJf6B5Q4). You might want to watch the first video too.\n\n## Pixel Shader\nThe `getColor` function is run for each LED, and it should return the colour as an array of RGB values (from 0 to 1)\n\nIf nothing is returned, it defaults to turning the pixel off.\n\nParameters provided to the function are:\n- LED\n - index: position of the LED in the strip (0 - 499)\n - x, y, z: cartesian coordinates of the LED (GIFT coordinates)\n - r, θ: polar coordinates of the LED in the xy plane\n- state\n - time: duration since animation start (seconds)\n - frame: current frame of the animation","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":849,"value":"viewof currentAnimation = {\n const values = new Map([\n ['sno', 'snow'],\n ['rbi', 'rotating bisector'],\n ['rdr', 'radar sweep'],\n ['pln', 'sweeping planes'],\n ['hei', 'height sweep'],\n ])\n const sel = html``\n const el = html`animation: ${sel}`\n sel.addEventListener('input', () => { el.value = sel.options[sel.selectedIndex].value })\n const choose = (val) => {\n const options = sel.options\n for (let i = 0; i < options.length; ++i) {\n if (options[i].value === val) {\n sel.selectedIndex = i\n sel.dispatchEvent(new CustomEvent('input'))\n break\n }\n }\n el.value = val\n el.dispatchEvent(new CustomEvent('input'))\n }\n choose('sno')\n return Object.assign(el, { values, choose })\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":266,"value":"renderer.domElement","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":484,"value":"$33","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":563,"value":"## Export animation","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":543,"value":"viewof duration = html``","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":524,"value":"{\n const RGB = [...'RGB']\n const header = `FRAME_ID,${LEDs.flatMap((_, i) => RGB.map((c) => `${c}_${i}`)).join(',')}`\n const scale = (c) => Math.floor(c * 256)\n const dt = 1 / 60\n const total = Math.floor(duration * 60)\n\n const el = DOM.download(() => {\n const rows = [header]\n for (let frame = 0; frame < total; ++frame) {\n rows.push(`${frame},${LEDs.flatMap((led) => (getColor(led, { frame, dt }) || OFF).map(scale)).join(',')}`)\n }\n return new Blob([rows.join('\\n')], { type: 'text/csv' })\n }, 'animation.csv', 'Download CSV')\n return html`

duration: ${duration}s (frames: ${total})

${el}`\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":579,"value":"## Appendix","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":304,"value":"{\n // init\n scene.background = new THREE.Color(0x010101)\n camera.position.set(0, 1.5, -3)\n camera.lookAt(new THREE.Vector3(0, 0, 0))\n\n let frame = 0\n const start = Date.now()\n const colors = tree.geometry.getAttribute('color')\n\n while (true) { // animation loop\n ++frame\n const time = (Date.now() - start) / 1000\n colors.array.set(LEDs.flatMap((led) => getColor(led, { frame, time }) || OFF))\n colors.needsUpdate = true\n renderer.render(scene, camera)\n yield time\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":788,"value":"OFF = [0, 0, 0]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":375,"value":"$34","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":426,"value":"LEDs = ledPositions.map(([x, y, z], index) => ({\n x, y, z, index,\n // polar coordinates\n r: Math.hypot(x, y),\n θ: Math.atan2(y, x),\n}))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":444,"value":"tree = {\n const bufSize = LEDs.length * 3\n const geometry = new THREE.BufferGeometry()\n \n const positions = new Float32Array(bufSize)\n for (const { index, x, y, z } of LEDs) positions.set([x, y, z], index * 3)\n \n geometry.setAttribute('color', new THREE.BufferAttribute(new Float32Array(bufSize), 3))\n geometry.setAttribute('position', new THREE.BufferAttribute(positions, 3))\n geometry.computeBoundingBox()\n \n const material = new THREE.PointsMaterial({ size: 0.03, vertexColors: true })\n const mesh = new THREE.Points(geometry, material)\n\n // rotate to correct orientation\n mesh.rotation.x = -Math.PI / 2\n mesh.rotation.z = Math.PI / 2\n mesh.position.y = -1.5\n\n scene.add(mesh)\n invalidation.then(() => scene.remove(mesh))\n return mesh\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":7,"value":"renderer = {\n const ren = new THREE.WebGLRenderer({ antialias: true })\n ren.setSize(width, height)\n ren.setPixelRatio(devicePixelRatio)\n\n const controls = new THREE.OrbitControls(camera, ren.domElement)\n controls.addEventListener(\"change\", () => ren.render(scene, camera))\n invalidation.then(() => (controls.dispose(), ren.dispose()))\n return ren\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":52,"value":"viewof height = html``","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":875,"value":"{\n while (true) {\n for (const anim of viewof currentAnimation.values.keys()) {\n viewof currentAnimation.choose(anim)\n await Promises.delay(5000)\n }\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":18,"value":"camera = new THREE.PerspectiveCamera(60, width / height, 1, 1000)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":249,"value":"scene = new THREE.Scene()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":3,"value":"THREE = {\n const t = window.THREE = await require(\"three@0.136.0/build/three.min.js\")\n await require(\"three@0.136.0/examples/js/controls/OrbitControls.js\").catch(() => {})\n return t\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W35","stdlib":"1","titling":"auto"}} 32:"$31:body"