30:T59c,function thomas(points) { let xs = points.map(pt => pt[0]) let ys = points.map(pt => pt[1]) let pxs = computeControlPoints(xs) let pys = computeControlPoints(ys) let result = [] for(var i = 0; i < points.length - 1; i++) { result.push([ [pxs.p1[i], pys.p1[i]], [pxs.p2[i], pys.p2[i]] ]) } return result /*computes control points given knots K, this is the brain of the operation*/ function computeControlPoints(K) { let p1=new Array(); let p2=new Array(); let n = K.length-1; /*rhs vector*/ let a=new Array(); let b=new Array(); let c=new Array(); let r=new Array(); /*left most segment*/ a[0]=0; b[0]=2; c[0]=1; r[0] = K[0]+2*K[1]; /*internal segments*/ for (i = 1; i < n - 1; i++) { a[i]=1; b[i]=4; c[i]=1; r[i] = 4 * K[i] + 2 * K[i+1]; } /*right segment*/ a[n-1]=2; b[n-1]=7; c[n-1]=0; r[n-1] = 8*K[n-1]+K[n]; /*solves Ax=b with the Thomas algorithm (from Wikipedia)*/ for (i = 1; i < n; i++) { let m = a[i]/b[i-1]; b[i] = b[i] - m * c[i - 1]; r[i] = r[i] - m*r[i-1]; } p1[n-1] = r[n-1]/b[n-1]; for (i = n - 2; i >= 0; --i) p1[i] = (r[i] - c[i] * p1[i+1]) / b[i]; /*we have p1, now compute p2*/ for (i=0;i pt[0]) let ys = points.map(pt => pt[1]) let weights = [] for (var i=0;i= 0; --i) { p[i] = (r[i] - c[i] * p[i+1]-d[i]*p[i+2]) / b[i]; } /* p[n] = 0 // c[n-1] and d[n-2] are outside the matrix p[n+1]=0 // d[n-1] is outside the matrix for (i = n - 1; i >= 0; --i) { p[i] = (r[i] - c[i] * p[i+1]-d[i]*p[i+2]) / b[i]; } */ return p } function computeControlPointsBigWThomas(K,W) { var p, p1, p2, a, b, c, d, r, n p = new Array(); p1=new Array(); p2=new Array(); n = K.length-1; /*rhs vector*/ a=new Array(); b=new Array(); c=new Array(); d=new Array(); r=new Array(); /*left most segment*/ a[0]=0; // outside the matrix b[0]=2; c[0]=-1; d[0]=0 r[0] = K[0]+0;// add curvature at K0 /*internal segments*/ for (i = 1; i < n ; i++) { a[2*i-1]=1*W[i]*W[i]; b[2*i-1]=-2*W[i]*W[i]; c[2*i-1]=2*W[i-1]*W[i-1]; d[2*i-1]=-1*W[i-1]*W[i-1] r[2*i-1] = K[i]*((-W[i]*W[i]+W[i-1]*W[i-1]))// a[2*i]=W[i]; b[2*i]=W[i-1]; c[2*i]=0; d[2*i]=0; // note: d[2n-2] is already outside the matrix r[2*i] = (W[i-1]+W[i])*K[i]; } /*right segment*/ a[2*n-1]=-1; b[2*n-1]=2; r[2*n-1]=K[n];// curvature at last point // the following array elements are not in the original matrix, so they should not be used: c[2*n-1]=0; // outside the matrix d[2*n-2]=0; // outside the matrix d[2*n-1]=0; // outside the matrix /*solves Ax=b with the Thomas algorithm (from Wikipedia)*/ p = Thomas4(r,a,b,c,d) /*re-arrange the array*/ for (i=0;i pt[0]) let ys = points.map(pt => pt[1]) if(xs[0] == xs[points.length-1] && ys[0] == ys[points.length - 1]){ closed = true xs.pop() ys.pop() } let weights = [] let weighting = function(x1,x2,y1,y2) { /* calculate Euclidean distance */ var d = Math.sqrt(Math.pow((x1-x2),2) +Math.pow((y1-y2),2)) // if the weight is too small, the calculation becomes instable return d<1?1:d } for (var i=0;i [pt[1], pt[0]]))","pinned":true,"hidden":false,"mode":"ojs"},{"id":153,"value":"draw(loopyThomas, Points)","pinned":true,"hidden":false,"mode":"ojs"},{"id":2,"value":"function draw(fn, pts) {\n let xs = pts.map(p => p[0])\n let minX = Math.min(...xs)\n let maxX = Math.max(...xs)\n let ys = pts.map(p => p[1])\n let minY = Math.min(...ys)\n let maxY = Math.max(...ys)\n let points = pts.map(p => [(p[0] - minX) / (maxX - minX) * 500 + 50, (p[1] - minY) / (maxY - minY) * 500 + 50])\n let controls = fn(points)\n let start = \"M \" + points[0][0] + \" \" + points[0][1]\n let straight = []\n let curved = []\n for(var i = 1; i < points.length; i++) {\n straight.push(\"L \" + points[i][0] + \" \" + points[i][1])\n curved.push(\"C \" + controls[i-1][0][0] + \" \" + controls[i-1][0][1] + \", \" +\n controls[i-1][1][0] + \" \" + controls[i-1][1][1] + \", \" +\n points[i][0] + \" \" + points[i][1])\n }\n return html`\n `\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":171,"value":"draw(catmullRom, Points)","pinned":true,"hidden":false,"mode":"ojs"},{"id":188,"value":"loopyThomas(Points)","pinned":true,"hidden":false,"mode":"ojs"}],"files":"$W34","stdlib":"1","titling":"auto"}