2e:null 2f:["$","title",null,{"children":"Lou Reed, The Bells - Fourier Series | Paul Buffa | Observable"}] 34:T406,m = { const scale = 1.75 const context = DOM.context2d(data.width * scale, data.height * scale); context.lineCap = "round"; context.lineJoin = "round"; for (let m = 0; true; m = (m + 1) % M) { context.save(); context.fillStyle = "rgba(255, 255, 255, .1)"; context.fillRect(0, 0, data.width, data.height); context.scale(scale, scale) for(let x = 0; x < dftArray.length; x++) { const thisPath = dftArray[x]; context.beginPath(); for (let t = 0; t < q; ++t) { const a = t * 2 / q * Math.PI; let p = [0, 0]; for (let i = 0; i < m; ++i) { p = add(p, mul(thisPath.DFT[i], expim(a * thisPath.K[i]))); } if (t === 0) context.moveTo(...p); else context.lineTo(...p); } context.closePath(); context.fillStyle = colorScale(x) context.strokeStyle = colorScale(2) context.fill(); context.stroke(); } context.restore(); context.canvas.value = m; yield context.canvas; } }35:T480,{ const scale = 1.25; const div = html`

` d3.select(div).style("text-align", 'left') const mArray = [2, 10, 20, 30, 40, 50, M] mArray.forEach(m => { const canvas = d3.select(div).append("canvas").attr("width", data.width * scale).attr("height", data.height * scale); const context = canvas.node().getContext('2d'); context.scale(scale, scale); context.lineCap = "round"; context.lineJoin = "round"; context.fillStyle = "rgba(255, 255, 255, .1)"; context.fillRect(0, 0, data.width, data.height); for(let x = 0; x < dftArray.length; x++) { const thisPath = dftArray[x]; context.beginPath(); for (let t = 0; t < q; ++t) { const a = t * 2 / q * Math.PI; let p = [0, 0]; for (let i = 0; i < m; ++i) { p = add(p, mul(thisPath.DFT[i], expim(a * thisPath.K[i]))); } if (t === 0) context.moveTo(...p); else context.lineTo(...p); } context.closePath(); context.fillStyle = colorScale(x) context.strokeStyle = colorScale(2) context.fill(); context.stroke(); } }) return div }36:T2ce3,palette = 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32:{"id":"602aaebbb49c6d14","slug":"lou-reed-the-bells-fourier-series","title":"Lou Reed, The Bells - Fourier Series","thumbnail":"d0a0c6313b3d3fd59b45b284e64c4802548a5da3196f4901e63107fabdf8ae51","access_level":"public","create_time":"$D2020-06-25T01:37:03.770Z","update_time":"$D2020-07-10T01:53:07.970Z","view_time":null,"first_public_time":"$D2020-06-29T01:19:31.839Z","has_unpublished_edits":null,"fork":{"id":"4a6edd8daad7d841","slug":"roy-lichtenstein-fourier-series","title":"Roy Lichtenstein Fourier Series","owner":{"id":"d9d161ec29750ad6","login":"pstuffa","name":"Paul Buffa"}},"stars":3,"starred":false,"owner":{"type":"team","id":"d9d161ec29750ad6","login":"pstuffa","name":"Paul Buffa","avatar_url":"https://avatars-next.observableusercontent.com/32c09bb97a2bb742225b949dcc4cf81a03dcd2b0caae97325970223a48a14b94","tier":"starter_2024"},"version":250,"publish_version":250,"role":null,"authored":false,"authors":[{"type":"individual","id":"42520cea6c99d3c8","login":"pstuffa","name":"Paul Buffa","avatar_url":"https://avatars-next.observableusercontent.com/32c09bb97a2bb742225b949dcc4cf81a03dcd2b0caae97325970223a48a14b94","tier":null}],"members":[{"type":"individual","id":"42520cea6c99d3c8","login":"pstuffa","name":"Paul Buffa","avatar_url":"https://avatars-next.observableusercontent.com/32c09bb97a2bb742225b949dcc4cf81a03dcd2b0caae97325970223a48a14b94","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":1,"collection":{"id":"49b647449d81ca11","slug":"art","title":"Art","owner":{"id":"d9d161ec29750ad6","login":"pstuffa","name":"Paul Buffa"}},"type":"notebook","body":{"title":"Lou Reed, The Bells - Fourier Series","cells":[{"id":0,"value":"md`# Lou Reed, The Bells - Fourier Series`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2,"value":"$34","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":125,"value":"$35","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":17,"value":"colorScale = d3.scaleOrdinal()\n // .range([\"#000\", \"#C40017\", \"#E6DB31\",\"#fff\"])\n // .domain([0, 1, 2, 3])\n .range(palette)\n .domain(d3.range(palette).map(d => d))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":58,"value":"md`## Data Processing`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":7,"value":"dftArray = generateDFTArray(svgData)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":11,"value":"N = 1000","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":13,"value":"M = 100","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":15,"value":"q = 1000","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":19,"value":"svgData = potrace.traceCanvas(data.canvas.canvas)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":21,"value":"data = {\n let img = await FileAttachment(\"lou.jpg\").image();\n let ctx = DOM.canvas(img.width, img.height).getContext('2d');\n ctx.drawImage(img, 0, 0);\n return {\n image: ctx.getImageData(0, 0, img.width, img.height).data,\n width: img.width,\n height: img.height,\n canvas: ctx\n };\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":227,"value":"$36","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":52,"value":"md`#### Original`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":5,"value":" FileAttachment(\"lou.jpg\").image()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":67,"value":"md`## Imported Modules`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":23,"value":"potrace = require(\"potrace-js-dev@0.0.3/lib/dist/index.js\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":9,"value":"import { PathSampler, abs, expim, add, mul, L, C } from '@pstuffa/image-to-progressive-fourier-series'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":224,"value":"import { extractPalette } from '@makio135/give-me-colors'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":25,"value":"d3 = require(\"d3\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":27,"value":"function* generateDFTArray(input) {\n \n const filter = input.filter(d => d.area > 20 && d.m > 15);\n const data = filter.map(d => `M ${d.points.map(e => `${e.x} ${e.y}`).join(\"L \")} Z`)\n console.log(data)\n const output = []\n for(let i = 0; i < data.length; i++) {\n const array = data[i]\n const sampler = new PathSampler(array);\n const P = Array.from({length: N}, (_, i) => sampler.pointAt(i / N));\n const K = Int16Array.from({length: M}, (_, i) => (1 + i >> 1) * (i & 1 ? -1 : 1));\n const DFT = Array.from(K, k => {\n let x = [0, 0];\n for (let i = 0; i < N; ++i) {\n x = add(x, mul(P[i], expim(k * i * 2 / N * -Math.PI)));\n }\n return [x[0] / N, x[1] / N];\n })\n output.push({\n P: P,\n K: K,\n DFT: DFT,\n sampler: sampler,\n array: array\n })\n }\n \n yield output\n\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W37","stdlib":"1","titling":"auto"}} 33:"$32:body"