2a:null 2b:["$","title",null,{"children":"Smooth Curve | Dmitry Baranovskiy | Observable"}] 30:T523,smooth = (points = [], close = false, strength = 1) => { const data = {segments: []}; if (close) { const last1 = points[points.length - 1]; const last2 = points[points.length - 2]; points.push(points[0]); points.push(points[1]); points.push(points[2]); points.push(points[3]); points.unshift(last1); points.unshift(last2); } const size = points.length; const last = size - 4; const start = close * 2; const startX = points[start]; const startY = points[start + 1]; data.start = [startX, startY]; let path = `M${data.start}`; const max = size - 2 - start; for (let i = start; i < max; i += 2) { const x0 = i ? points[i - 2] : points[0]; const y0 = i ? points[i - 1] : points[1]; const x1 = points[i]; const y1 = points[i + 1]; const x2 = points[i + 2]; const y2 = points[i + 3]; const x3 = i != last ? points[i + 4] : x2; const y3 = i != last ? points[i + 5] : y2; const cp1x = x1 + ((x2 - x0) / 6) * strength; const cp1y = y1 + ((y2 - y0) / 6) * strength; const cp2x = x2 - ((x3 - x1) / 6) * strength; const cp2y = y2 - ((y3 - y1) / 6) * strength; const segment = [cp1x, cp1y, cp2x, cp2y, x2, y2]; data.segments.push(segment); path += `C${segment}`; } data.path = path; return data; }31:T407,catmullRom = function catmullRom2bezier(crp, z) { // http://schepers.cc/getting-to-the-point var d = []; for (var i = 0, iLen = crp.length; iLen - 2 * !z > i; i += 2) { var p = [ { x: +crp[i - 2], y: +crp[i - 1] }, { x: +crp[i], y: +crp[i + 1] }, { x: +crp[i + 2], y: +crp[i + 3] }, { x: +crp[i + 4], y: +crp[i + 5] } ]; if (z) { if (!i) { p[0] = { x: +crp[iLen - 2], y: +crp[iLen - 1] }; } else if (iLen - 4 == i) { p[3] = { x: +crp[0], y: +crp[1] }; } else if (iLen - 2 == i) { p[2] = { x: +crp[0], y: +crp[1] }; p[3] = { x: +crp[2], y: +crp[3] }; } } else { if (iLen - 4 == i) { p[3] = p[2]; } else if (!i) { p[0] = { x: +crp[i], y: +crp[i + 1] }; } } d.push([ (-p[0].x + 6 * p[1].x + p[2].x) / 6, (-p[0].y + 6 * p[1].y + p[2].y) / 6, (p[1].x + 6 * p[2].x - p[3].x) / 6, (p[1].y + 6 * p[2].y - p[3].y) / 6, p[2].x, p[2].y ]); } return d; }32:[] 2e:{"id":"d5e1c6cfb721474e","slug":"smooth-curve","title":"Smooth Curve","thumbnail":"c4b16425aa8f8b4f1f52c7b455ebdcae61284aa9134cbfc6ceba8e5f5c4f02d5","access_level":"public","create_time":"$D2021-06-11T08:01:36.733Z","update_time":"$D2023-01-20T02:13:59.222Z","view_time":null,"first_public_time":"$D2021-06-14T00:27:53.747Z","has_unpublished_edits":null,"fork":false,"stars":2,"starred":false,"owner":{"type":"team","id":"e3672025b6b6f436","login":"dmitrybaranovskiy","name":"Dmitry Baranovskiy","avatar_url":"https://avatars-next.observableusercontent.com/c31e7f084a49a6e09f7724ab70028e1f8a03923326f084b8f9e86a014705daf0","tier":"starter_2024"},"version":304,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"230ca2847200ccc9","login":"dmitrybaranovskiy","name":"Dmitry Baranovskiy","avatar_url":"https://avatars-next.observableusercontent.com/c31e7f084a49a6e09f7724ab70028e1f8a03923326f084b8f9e86a014705daf0","tier":null}],"members":[{"type":"individual","id":"230ca2847200ccc9","login":"dmitrybaranovskiy","name":"Dmitry Baranovskiy","avatar_url":"https://avatars-next.observableusercontent.com/c31e7f084a49a6e09f7724ab70028e1f8a03923326f084b8f9e86a014705daf0","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":1,"collection":null,"type":"notebook","body":{"titling":"auto","title":"Smooth Curve","cells":[{"id":0,"value":"# Smooth Curve","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":7,"value":"","pinned":false,"hidden":false,"mode":"html","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2,"value":"$30","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":247,"value":"$31","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":128,"value":"almostRandom = (seed = 42) => () => {\n seed = (seed * 9301 + 49297) % 233280;\n return seed / 233280;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":184,"value":"dotAtSegment = (p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y, t) => {\n const t1 = 1 - t,\n t12 = t1 * t1,\n t13 = t12 * t1,\n t2 = t * t,\n t3 = t2 * t,\n x = t13 * p1x + t12 * 3 * t * c1x + t1 * 3 * t * t * c2x + t3 * p2x,\n y = t13 * p1y + t12 * 3 * t * c1y + t1 * 3 * t * t * c2y + t3 * p2y;\n return { x, y };\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":206,"value":"bezlen = (x1, y1, x2, y2, x3, y3, x4, y4, z) => {\n if (z == null) {\n z = 1;\n }\n z = z > 1 ? 1 : z < 0 ? 0 : z;\n var z2 = z / 2,\n n = 12,\n sum = 0;\n for (var i = 0; i < n; i++) {\n var ct = z2 * Tvalues[i] + z2,\n xbase = base3(ct, x1, x2, x3, x4),\n ybase = base3(ct, y1, y2, y3, y4),\n comb = xbase ** 2 + ybase ** 2;\n sum += Cvalues[i] * Math.sqrt(comb);\n }\n return z2 * sum;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":222,"value":"---","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":204,"value":"base3 = (t, p1, p2, p3, p4) => {\n const t1 = -3 * p1 + 9 * p2 - 9 * p3 + 3 * p4,\n t2 = t * t1 + 6 * p1 - 12 * p2 + 6 * p3;\n return t * t2 - 3 * p1 + 3 * p2;\n};","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":210,"value":"Tvalues = [\n -0.1252,\n 0.1252,\n -0.3678,\n 0.3678,\n -0.5873,\n 0.5873,\n -0.7699,\n 0.7699,\n -0.9041,\n 0.9041,\n -0.9816,\n 0.9816\n]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":213,"value":"Cvalues = [\n 0.2491,\n 0.2491,\n 0.2335,\n 0.2335,\n 0.2032,\n 0.2032,\n 0.1601,\n 0.1601,\n 0.1069,\n 0.1069,\n 0.0472,\n 0.0472\n]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":133,"value":"spreadAround = (cx, cy, r, num) => {\n const π = Math.PI;\n const out = [];\n if (!Array.isArray(r)) {\n r = new Array(num).fill(r);\n }\n for (let i = 0; i < num; ++i) {\n const α = ((2 * π) / num) * i;\n out.push(cx + r[i] * Math.cos(α), cy + r[i] * Math.sin(α));\n }\n return out;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":9,"value":"dots = [\n [100, 100],\n [120, 80],\n [140, 130],\n [160, 140],\n [180, 50]\n]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":60,"value":"path1 = smooth(dots.flat(), false, 1).path","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":68,"value":"path2 = smooth(dots.map((dot) => [dot[0] + 200, dot[1]]).flat(), true, 1.5).path","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":146,"value":"num = 20","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":145,"value":"shift = {\n const rnd = almostRandom(num);\n return new Array(num)\n .fill(0)\n .map((x, i) => (i % 2 ? 150 + rnd() * 40 - 20 : 100));\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":135,"value":"path3 = smooth(spreadAround(600, 200, shift, num).flat(), true, 1.5).path","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W32","stdlib":"1"}} 2f:"$2e:body"