28:null 29:["$","title",null,{"children":"Archimedean tilings | Claudio Esperança | Observable"}] 2e:T46d,// // Given a tiling which is to be rendered scaled by edgeSize within a canvas of size w by h, returns // a list of polygons that intersect the canvas rectangle. // function coverRect(tiling, edgeSize, w, h) { let imin = 0, imax = 0, jmin = 0, jmax = 0; let tileCoords = planeToTileCoords(tiling); let corners = [Vec(0, 0), Vec(w, 0), Vec(0, h), Vec(w, h)]; for (let { x, y } of corners) { let [i, j] = tileCoords(x / edgeSize, y / edgeSize); if (i < imin) imin = i; if (j < jmin) jmin = j; if (i > imax) imax = i; if (j > jmax) jmax = j; } imin = Math.floor(imin - 1); imax = Math.ceil(imax + 1); jmin = Math.floor(jmin - 1); jmax = Math.ceil(jmax + 1); let faces = tilingFaces(tiling); let cover = []; let rect = new MBR(...corners); for (let i = imin; i <= imax; i++) { for (let j = jmin; j <= jmax; j++) { for (let f of translateFaces(tiling, faces, i, j)) { let poly = f.map((L) => planeCoords(L).scale(edgeSize)); let polyMbr = new MBR(...poly); if (rect.intersects(polyMbr)) cover.push(poly); } } } return cover; }2f:T446,// // Returns an array with the fundamental faces of the given tiling. // A face is an array of lattice points // function tilingFaces (tiling) { let {T1,T2,Seed} = tiling; // Points in neighboring cells let V = {} for (let s of Seed) { for (let [i,j] of [[-1,0],[0,0],[1,0],[-1,-1],[0,-1], [1,-1],[-1,1],[0,1],[1,1]]) { let p = sum(s,sum(scale(T1,i),scale(T2,j))) V[p] = 1 } } // Computes one face with m points starting at anchor point v // starting at edge with direction w^k let face = (v,k,m) => { let f = [v, sum(v,wpow[k])]; for (let i = 2; i a.map((x,i) => x + b[i])","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":111,"value":"// dot product of two lattice vectors\ndot = (a,b) => (a.map((x,i) => x*b[i]).reduce((x,y) => x+y))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":125,"value":"// Lattice vector scale\nscale = (a, s) => a.map(x=>x*s)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":25,"value":"md`### Conversion from lattice coordinates to plane coordinates`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":32,"value":"planeCoords = L => L.map((x,i) => W[i].scale(x)).reduce((a,b) => a.add(b))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":371,"value":"function planeToTileCoords(tiling) {\n let { T1, T2 } = tiling;\n let { x: a, y: b } = planeCoords(T1);\n let { x: c, y: d } = planeCoords(T2);\n let m = [\n [a, b],\n [c, d]\n ];\n let det = a * d - b * c;\n let [[ai, bi], [ci, di]] = [\n [d / det, -c / det],\n [-b / det, a / det]\n ];\n\n // Maps canvas coordinates back to tile coordinates\n return (x, y) => [ai * x + bi * y, ci * x + di * y];\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":444,"value":"md`### Tiling to faces within a rectangle`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":378,"value":"$2e","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":68,"value":"md`### Generic plot function
\n(used in the algorithm demos below)\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":168,"value":"plot = function (ctx, primitives) {\n \n let {points=[], edges =[], faces=[]} = primitives;\n let canvasCoords = L => modelview.apply(planeCoords(L))\n \n // Draw points\n for (let v of points) {\n let p = canvasCoords(v);\n ctx.beginPath ();\n ctx.arc (p.x,p.y,4,0,2*Math.PI)\n ctx.stroke()\n ctx.fill()\n }\n \n // Draw edges\n for (let [v1,v2] of edges) {\n ctx.beginPath ();\n let p1 = canvasCoords(v1); ctx.moveTo(p1.x,p1.y)\n let p2 = canvasCoords(v2); ctx.lineTo(p2.x,p2.y)\n ctx.stroke()\n }\n \n // Draw faces\n for (let f of faces) {\n ctx.beginPath ();\n let p = canvasCoords(f[0]); ctx.moveTo(p.x,p.y)\n for (let i = 1; i f.map(v => sum(v,TIJ)));\n}\n ","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":251,"value":"md`## Libraries`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":227,"value":"colorScales = require(\"d3-scale-chromatic\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":29,"value":"import { Vec, Vector, Matrix, MBR } from \"@esperanc/2d-geometry-utils\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":256,"value":"import {button} from \"@jashkenas/inputs\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W30","stdlib":"1","titling":"auto"}} 2d:"$2c:body"