25:["$","title",null,{"children":"mesh surface sampler | stwindlb | Observable"}] 49:T722,b64encode = { // https://gist.github.com/jonleighton/958841 const encodings = 'ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/'; return buffer => { let base64 = ''; const bytes = new Uint8Array(buffer); const byteLength = bytes.byteLength; const byteRemainder = byteLength % 3; const mainLength = byteLength - byteRemainder; let a, b, c, d, chunk; // Main loop deals with bytes in chunks of 3 for (var i = 0; i < mainLength; i = i + 3) { // Combine the three bytes into a single integer chunk = (bytes[i] << 16) | (bytes[i + 1] << 8) | bytes[i + 2] // Use bitmasks to extract 6-bit segments from the triplet a = (chunk & 16515072) >> 18 // 16515072 = (2^6 - 1) << 18 b = (chunk & 258048) >> 12 // 258048 = (2^6 - 1) << 12 c = (chunk & 4032) >> 6 // 4032 = (2^6 - 1) << 6 d = chunk & 63 // 63 = 2^6 - 1 // Convert the raw binary segments to the appropriate ASCII encoding base64 += encodings[a] + encodings[b] + encodings[c] + encodings[d] } // Deal with the remaining bytes and padding if (byteRemainder == 1) { chunk = bytes[mainLength] a = (chunk & 252) >> 2 // 252 = (2^6 - 1) << 2 // Set the 4 least significant bits to zero b = (chunk & 3) << 4 // 3 = 2^2 - 1 base64 += encodings[a] + encodings[b] + '==' } else if (byteRemainder == 2) { chunk = (bytes[mainLength] << 8) | bytes[mainLength + 1] a = (chunk & 64512) >> 10 // 64512 = (2^6 - 1) << 10 b = (chunk & 1008) >> 4 // 1008 = (2^6 - 1) << 4 // Set the 2 least significant bits to zero c = (chunk & 15) << 2 // 15 = 2^4 - 1 base64 += encodings[a] + encodings[b] + encodings[c] + '=' } return base64 }; }4a:[{"id":"11220145c9b2fb053ce077df3c4db3039218c8e0a86a1c0dc362402812e69ead09943de400d36b187897577958e57dfee88bc10d2199a35a8ae2ec808e13094f","href":"https://static.observableusercontent.com/files/11220145c9b2fb053ce077df3c4db3039218c8e0a86a1c0dc362402812e69ead09943de400d36b187897577958e57dfee88bc10d2199a35a8ae2ec808e13094f","name":"Heart.glb","type":"model/gltf-binary","lastModified":1670052386407.114,"size":6248}] 29:{"id":"9e1af12fe274a3b3","slug":null,"title":"mesh surface 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surface sampler","cells":[{"id":0,"value":"# mesh surface sampler","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":42,"value":"{\n const geom = tetrahedron;\n const n = geom.vertices.length / 3;\n const m = geom.indices.length / 3;\n const data= [\n {\n opacity: 0.8,\n type: 'mesh3d',\n x: d3.range(n).map(i => getS(geom.vertices, i, 0, 3)),\n y: d3.range(n).map(i => getS(geom.vertices, i, 1, 3)),\n z: d3.range(n).map(i => getS(geom.vertices, i, 2, 3)),\n i: d3.range(m).map(i => getS(geom.indices, i, 0, 3)),\n j: d3.range(m).map(i => getS(geom.indices, i, 1, 3)),\n k: d3.range(m).map(i => getS(geom.indices, i, 2, 3))\n }\n ];\n return Plotly.plot(DOM.element('div'), data, {\n width: 512, height: 512,\n margin: { l: 0, r: 0, b: 0, t: 0 },\n hovermode: false,\n font: { size: 10 },\n });\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":80,"value":"tetrahedron = {\n const vertices = new Float32Array([ 0.94280905, 0. , -0.33333334, -0.47140452, 0.8164966 ,\n -0.33333334, -0.47140452, -0.8164966 , -0.33333334, 0. ,\n 0. , 1. ]);\n const indices = new Int8Array([0, 1, 2, 0, 1, 3, 0, 2, 3, 1, 2, 3]);\n return { vertices, indices };\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":355,"value":"cube = ({\n vertices: new Float32Array([ 1., 1., 1., -1., 1., 1., -1., -1., 1., 1., -1., 1., 1.,\n 1., -1., 1., 1., 1., 1., -1., 1., 1., -1., -1., 1., 1.,\n -1., -1., 1., -1., -1., 1., 1., 1., 1., 1., -1., 1., 1.,\n -1., 1., -1., -1., -1., -1., -1., -1., 1., 1., -1., 1., -1.,\n -1., 1., -1., -1., -1., 1., -1., -1., -1., 1., -1., 1., 1.,\n -1., 1., -1., -1., -1., -1., -1.]),\n indices: new Uint16Array([ 0, 1, 2, 0, 2, 3, 4, 5, 6, 4, 6, 7, 8, 9, 10, 8, 10,\n 11, 12, 13, 14, 12, 14, 15, 16, 17, 18, 16, 18, 19, 20, 21, 22, 20,\n 22, 23])\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":286,"value":"{\n const n = points.length / 3;\n const data= [\n {\n type: 'scatter3d',\n mode: 'markers',\n marker: { size: 3 },\n opacity: .2,\n x: d3.range(n).map(i => getS(points, i, 0, 3)),\n y: d3.range(n).map(i => getS(points, i, 1, 3)),\n z: d3.range(n).map(i => getS(points, i, 2, 3)),\n }\n ];\n return Plotly.plot(DOM.element('div'), data, {\n width: 512, height: 512,\n margin: { l: 0, r: 0, b: 0, t: 0 },\n hovermode: false,\n font: { size: 10 },\n });\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":502,"value":"points = {\n const n = 5000;\n const out = new Float32Array(n * 3);\n const sampler = surfaceSampler(tetrahedron.vertices, tetrahedron.indices);\n for (let i = 0; i < n; i++)\n sampler(out, i);\n return out;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":632,"value":"surfaceSampler = (vertices, indices) => {\n const areas = getAreas(vertices, indices);\n const tot = d3.sum(areas);\n const rand = randWeighted(areas.map(x => x / tot));\n\n return (out, i, o = 0, s = 3) => {\n const idx = rand() * 3;\n sampleTriangle(\n out, vertices, vertices, vertices,\n o + i * s, indices[idx] * 3, indices[idx + 1] * 3, indices[idx + 2] * 3,\n 1, 1, 1, 1\n );\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":391,"value":"sampleTriangle = {\n const a = [], b = [], c = [];\n return (out, A, B, C, oo, oa, ob, oc, so, sa, sb, sc) => {\n let p = Math.random(), q = Math.random();\n if (p + q > 1) p = 1 - p, q = 1 - q;\n\n v.mulNS3(a, A, 1 - p - q, 0, oa, 1, sa);\n v.mulNS3(b, B, p, 0, ob, 1, sb);\n v.mulNS3(c, C, q, 0, oc, 1, sc);\n v.add3(null, v.add3(null, a, b), c);\n return v.setS3(out, a, oo, 0, so);\n };\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":162,"value":"getAreas = {\n const ba = [], ca = []\n return (V, I) => {\n const n = I.length / 3;\n const areas = new Float32Array(n);\n for (let i = 0; i < n; i++) {\n v.subS3(ba, V, V, 0, I[i * 3 + 1] * 3, I[i * 3] * 3);\n v.subS3(ca, V, V, 0, I[i * 3 + 2] * 3, I[i * 3] * 3);\n areas[i] = v.mag(v.cross3(null, ba, ca));\n }\n return areas;\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":427,"value":"randWeighted = vals => {\n const cum = cumsum(vals);\n return () => bisect(cum, Math.random());\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":685,"value":"cumsum = vals => {\n const out = [];\n let sum = 0;\n vals.forEach(x => out.push(sum += x));\n return out;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":100,"value":"bisect = (arr, val) => {\n let l = -1, r = arr.length - 1, mid;\n while (r - l > 1) {\n mid = (l + r) >> 1;\n if (arr[mid] <= val) l = mid;\n else r = mid;\n }\n return r;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":774,"value":"{\n const n = pointsHeart.length / 3;\n const data= [\n {\n type: 'scatter3d',\n mode: 'markers',\n marker: { size: 3 },\n opacity: .2,\n x: d3.range(n).map(i => getS(pointsHeart, i, 0, 3)),\n y: d3.range(n).map(i => getS(pointsHeart, i, 1, 3)),\n z: d3.range(n).map(i => getS(pointsHeart, i, 2, 3)),\n }\n ];\n return Plotly.plot(DOM.element('div'), data, {\n width: 512, height: 512,\n margin: { l: 0, r: 0, b: 0, t: 0 },\n hovermode: false,\n font: { size: 10 },\n });\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":764,"value":"pointsHeart = {\n const geom = (await heart.getPrimitives(0).next()).value.geometry;\n const n = 5000;\n const out = new Float32Array(n * 3);\n const sampler = surfaceSampler(geom.attribs.position.data, geom.indices.data);\n for (let i = 0; i < n; i++)\n sampler(out, i);\n return out;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":817,"value":"(await heart.getPrimitives(0).next()).value.geometry;","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":721,"value":"heart = gltf.GLTF.fromGLB(buffer)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":788,"value":"buffer = b64decode(b64encode(await FileAttachment(\"Heart.glb\").arrayBuffer()))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":785,"value":"$49","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":796,"value":"b64decode = (base64) => {\n const string = atob(base64);\n const n = string.length;\n const bytes = new Uint8Array(n);\n for (let i = 0; i < n; i++)\n bytes[i] = string.charCodeAt(i);\n return bytes.buffer;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":63,"value":"### Utils","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":70,"value":"setS = (a, i, v, o = 0, s = 1) => a[o + i * s] = v","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":77,"value":"getS = (a, i, o = 0, s = 1) => a[o + i * s]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":746,"value":"fetchURL = {\n function concat(arrays) {\n let i = 0, n = 0;\n for (const a of arrays) n += a.length;\n const concat = new Uint8Array(n);\n for (let a of arrays) concat.set(a, i), i += a.length;\n return concat.buffer;\n }\n \n return (url, init, { progress } = {}) => {\n assert(typeof init !== \"string\", \"fetchURL deprecated\");\n let cur = 0;\n return fetch(url, init).then(async response => {\n const cl = response.headers.get(\"content-length\");\n const tot = cl ? parseInt(cl) : -1;\n const reader = response.body.getReader();\n const values = [];\n while (true) {\n const { done, value } = await reader.read();\n if (done) break;\n cur += value.length;\n progress && progress(cur, tot);\n values.push(value);\n }\n return concat(values);\n });\n };\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":737,"value":"assert = (condition, msg) => { if (!condition) throw new Error(msg); }","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":61,"value":"### Appendix","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":39,"value":"Plotly = require(\"https://cdn.plot.ly/plotly-latest.min.js\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":113,"value":"m = import(\"https://cdn.skypack.dev/@thi.ng/matrices@v2.1.35\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":110,"value":"v = import(\"https://cdn.skypack.dev/@thi.ng/vectors@v7.5.26\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":698,"value":"wgl2 = import(\"https://cdn.skypack.dev/@wgl2/core@0.0.56\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":700,"value":"gltf = import(\"https://cdn.skypack.dev/@wgl2/gltf@0.0.2\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W4a","stdlib":"1"}} 24:null