Testing my polygon-clipping algorithm of Polygon hatching more.
#polygons
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// Polygon weaving. Created by Reinder Nijhoff 2018 // @reindernijhoff // // https://turtletoy.net/turtle/6b7bb60f9d // Canvas.setpenopacity(.75); const turtle = new Turtle(); const num_polygons = 20; const polygons = []; const sort_matrix = []; function walk(i) { if (i == 0) { for (let x=0; x<=num_polygons; x++) { polygons.push(createPolygon(x/num_polygons*200-100, 0, Math.PI/2)); } for (let y=0; y<=num_polygons; y++) { polygons.push(createPolygon(0, y/num_polygons*200-100, 0)); } // create sort matrix for (let j=0; j<polygons.length; j++) { sort_matrix[j] = []; for (let k=0; k<polygons.length; k++) { if (k < j) { sort_matrix[j][k] = !sort_matrix[k][j]; } else { sort_matrix[j][k] = Math.random() > .5 ? true : false; } } } } // clip polygon to polygons const c = polygons[i]; let vis = true; for (let j=0; j<polygons.length; j++) { if(i != j && sort_matrix[i][j] && !c.boolean(polygons[j])) { vis = false; break; } } if (vis) { c.draw(turtle, 0); } return i < polygons.length - 1; } function createPolygon(x, y, a) { x += (Math.random()-.5)*2; y += (Math.random()-.5)*2; a += (Math.random()-.5)*.05; const w = Math.random()*2+1; const cp = []; cp.push( [Math.cos(a)*500 - Math.sin(a)*w + x, Math.sin(a)*500 + Math.cos(a)*w + y] ); cp.push( [Math.cos(a)*500 + Math.sin(a)*w + x, Math.sin(a)*500 - Math.cos(a)*w + y] ); cp.push( [-Math.cos(a)*500 + Math.sin(a)*w + x, -Math.sin(a)*500 - Math.cos(a)*w + y] ); cp.push( [-Math.cos(a)*500 - Math.sin(a)*w + x, -Math.sin(a)*500 + Math.cos(a)*w + y] ); const p = new Polygon(); p.cp = cp; p.addOutline(); p.addHatching(Math.random()*2*Math.PI, .4+Math.random()*1.5); return p; } // polygon functions function LineSegment(p1, p2) { this.p1 = p1; this.p2 = p2; } function Polygon() { this.cp = []; // clip path: array of [x,y] pairs this.dp = []; // 2d line to draw: array of linesegments } Polygon.prototype.addOutline = function() { for (let i=0, l=this.cp.length; i<l; i++) { this.dp.push(new LineSegment(this.cp[i], this.cp[(i+1)%l])); } } Polygon.prototype.createPoly = function(x,y,c,r,a) { this.cp = []; for (let i=0; i<c; i++) { this.cp.push( [x + Math.sin(i*Math.PI*2/c+a) * r, y + Math.cos(i*Math.PI*2/c+a) * r] ); } } Polygon.prototype.addHatching = function(a,d) { // todo, create a tight bounding polygon, for now fill screen const tp = new Polygon(); tp.createPoly(0,0,4,200,Math.PI*.5); const dx = Math.sin(a)*d, dy = Math.cos(a)*d; const cx = Math.sin(a)*300, cy = Math.cos(a)*300; for (let i = .5; i<300/d; i++) { tp.dp.push(new LineSegment([dx*i+cy,dy*i-cx], [dx*i-cy,dy*i+cx])); tp.dp.push(new LineSegment([-dx*i+cy,-dy*i-cx], [-dx*i-cy,-dy*i+cx])); } tp.boolean(this, false); this.dp = this.dp.concat(tp.dp); } Polygon.prototype.draw = function(t, inp=0) { if (this.dp.length ==0) { return; } for (let i=0, l=this.dp.length; i<l; i++) { const d = this.dp[i]; if (!vec2_equal(d.p1, t.pos())) { t.penup(); t.goto([d.p1[0]+inp*(Math.random()-.5), d.p1[1]+inp*(Math.random()-.5)]); t.pendown(); } t.goto([d.p2[0]+inp*(Math.random()-.5), d.p2[1]+inp*(Math.random()-.5)]); } } Polygon.prototype.inside = function(p) { // find number of intersections from p to far away - if even you're outside const p1 = [0, -1000]; let int = 0; for (let i=0, l=this.cp.length; i<l; i++) { if (vec2_find_segment_intersect(p, p1, this.cp[i], this.cp[(i+1)%l])) { int ++; } } return int & 1; } Polygon.prototype.boolean = function(p, diff = true) { // very naive polygon diff algorithm - made this up myself const ndp = []; for (let i=0, l=this.dp.length; i<l; i++) { const ls = this.dp[i]; // find all intersections with clip path const int = []; for (let j=0, cl=p.cp.length; j<cl; j++) { const pint = vec2_find_segment_intersect(ls.p1,ls.p2,p.cp[j],p.cp[(j+1)%cl]); if (pint) { int.push(pint); } } if (int.length == 0) { // 0 intersections, inside or outside? if (diff == !p.inside(ls.p1)) { ndp.push(ls); } } else { int.push(ls.p1); int.push(ls.p2); // order intersection points on line ls.p1 to ls.p2 const cmp = [ls.p2[0]-ls.p1[0], ls.p2[1]-ls.p1[1]]; int.sort( (a,b) => { const db = vec2_dot([b[0]-ls.p1[0], b[1]-ls.p1[1]], cmp); const da = vec2_dot([a[0]-ls.p1[0], a[1]-ls.p1[1]], cmp); return da - db; }); for (let j=0; j<int.length-1; j++) { if (!vec2_equal(int[j], int[j+1])) { if (diff == !p.inside([(int[j][0]+int[j+1][0])/2,(int[j][1]+int[j+1][1])/2])) { ndp.push(new LineSegment(int[j], int[j+1])); } } } } } this.dp = ndp; return this.dp.length > 0; } // vec2 functions function vec2_equal(a,b) { return vec2_dist_sqr(a,b) < 0.001; } function vec2_dot(a, b) { return a[0]*b[0]+a[1]*b[1]; } function vec2_dist_sqr(a, b) { return (a[0]-b[0])*(a[0]-b[0]) + (a[1]-b[1])*(a[1]-b[1]); } //port of http://paulbourke.net/geometry/pointlineplane/Helpers.cs function vec2_find_segment_intersect(l1p1, l1p2, l2p1, l2p2){ const d = (l2p2[1] - l2p1[1]) * (l1p2[0] - l1p1[0]) - (l2p2[0] - l2p1[0]) * (l1p2[1] - l1p1[1]); const n_a = (l2p2[0] - l2p1[0]) * (l1p1[1] - l2p1[1]) - (l2p2[1] - l2p1[1]) * (l1p1[0] - l2p1[0]); const n_b = (l1p2[0] - l1p1[0]) * (l1p1[1] - l2p1[1]) - (l1p2[1] - l1p1[1]) * (l1p1[0] - l2p1[0]); if (d == 0) { return false; } const ua = n_a / d; const ub = n_b / d; if (ua > 0 && ua <= 1 && ub >= 0 && ub < 1) { return [l1p1[0] + (ua * (l1p2[0] - l1p1[0])), l1p1[1] + (ua * (l1p2[1] - l1p1[1])) ]; } return false; }