| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 | 1× 1× | // Delaunay Triangulation // Modified from https://github.com/ironwallaby/delaunay var EPSILON = 1.0 / 1048576.0; function supertriangle(vertices) { var xmin = Number.POSITIVE_INFINITY; var ymin = Number.POSITIVE_INFINITY; var xmax = Number.NEGATIVE_INFINITY; var ymax = Number.NEGATIVE_INFINITY; var i, dx, dy, dmax, xmid, ymid; for (i = vertices.length; i--; ) { if (vertices[i][0] < xmin) { xmin = vertices[i][0]; } if (vertices[i][0] > xmax) { xmax = vertices[i][0]; } if (vertices[i][1] < ymin) { ymin = vertices[i][1]; } if (vertices[i][1] > ymax) { ymax = vertices[i][1]; } } dx = xmax - xmin; dy = ymax - ymin; dmax = Math.max(dx, dy); xmid = xmin + dx * 0.5; ymid = ymin + dy * 0.5; return [ [xmid - 20 * dmax, ymid - dmax], [xmid , ymid + 20 * dmax], [xmid + 20 * dmax, ymid - dmax] ]; } function circumcircle(vertices, i, j, k) { var x1 = vertices[i][0], y1 = vertices[i][1], x2 = vertices[j][0], y2 = vertices[j][1], x3 = vertices[k][0], y3 = vertices[k][1], fabsy1y2 = Math.abs(y1 - y2), fabsy2y3 = Math.abs(y2 - y3), xc, yc, m1, m2, mx1, mx2, my1, my2, dx, dy; /* Check for coincident points */ if (fabsy1y2 < EPSILON && fabsy2y3 < EPSILON) { throw new Error('Eek! Coincident points!'); } if (fabsy1y2 < EPSILON) { m2 = -((x3 - x2) / (y3 - y2)); mx2 = (x2 + x3) / 2.0; my2 = (y2 + y3) / 2.0; xc = (x2 + x1) / 2.0; yc = m2 * (xc - mx2) + my2; } else if (fabsy2y3 < EPSILON) { m1 = -((x2 - x1) / (y2 - y1)); mx1 = (x1 + x2) / 2.0; my1 = (y1 + y2) / 2.0; xc = (x3 + x2) / 2.0; yc = m1 * (xc - mx1) + my1; } else { m1 = -((x2 - x1) / (y2 - y1)); m2 = -((x3 - x2) / (y3 - y2)); mx1 = (x1 + x2) / 2.0; mx2 = (x2 + x3) / 2.0; my1 = (y1 + y2) / 2.0; my2 = (y2 + y3) / 2.0; xc = (m1 * mx1 - m2 * mx2 + my2 - my1) / (m1 - m2); yc = (fabsy1y2 > fabsy2y3) ? m1 * (xc - mx1) + my1 : m2 * (xc - mx2) + my2; } dx = x2 - xc; dy = y2 - yc; return {i: i, j: j, k: k, x: xc, y: yc, r: dx * dx + dy * dy}; } function dedup(edges) { var i, j, a, b, m, n; for (j = edges.length; j; ) { b = edges[--j]; a = edges[--j]; for (i = j; i; ) { n = edges[--i]; m = edges[--i]; if ((a === m && b === n) || (a === n && b === m)) { edges.splice(j, 2); edges.splice(i, 2); break; } } } } var delaunay = { triangulate: function(vertices, key) { var n = vertices.length; var i, j, indices, st, open, closed, edges, dx, dy, a, b, c; /* Bail if there aren't enough vertices to form any triangles. */ if (n < 3) { return []; } /* Slice out the actual vertices from the passed objects. (Duplicate the * array even if we don't, though, since we need to make a supertriangle * later on!) */ vertices = vertices.slice(0); if (key) { for (i = n; i--; ) { vertices[i] = vertices[i][key]; } } /* Make an array of indices into the vertex array, sorted by the * vertices' x-position. Force stable sorting by comparing indices if * the x-positions are equal. */ indices = new Array(n); for (i = n; i--; ) { indices[i] = i; } indices.sort(function(i, j) { var diff = vertices[j][0] - vertices[i][0]; return diff !== 0 ? diff : i - j; }); /* Next, find the vertices of the supertriangle (which contains all other * triangles), and append them onto the end of a (copy of) the vertex * array. */ st = supertriangle(vertices); vertices.push(st[0], st[1], st[2]); /* Initialize the open list (containing the supertriangle and nothing * else) and the closed list (which is empty since we havn't processed * any triangles yet). */ open = [circumcircle(vertices, n + 0, n + 1, n + 2)]; closed = []; edges = []; /* Incrementally add each vertex to the mesh. */ for (i = indices.length; i--; edges.length = 0) { c = indices[i]; /* For each open triangle, check to see if the current point is * inside it's circumcircle. If it is, remove the triangle and add * it's edges to an edge list. */ for (j = open.length; j--; ) { /* If this point is to the right of this triangle's circumcircle, * then this triangle should never get checked again. Remove it * from the open list, add it to the closed list, and skip. */ dx = vertices[c][0] - open[j].x; if (dx > 0.0 && dx * dx > open[j].r) { closed.push(open[j]); open.splice(j, 1); continue; } /* If we're outside the circumcircle, skip this triangle. */ dy = vertices[c][1] - open[j].y; if (dx * dx + dy * dy - open[j].r > EPSILON) { continue; } /* Remove the triangle and add it's edges to the edge list. */ edges.push( open[j].i, open[j].j, open[j].j, open[j].k, open[j].k, open[j].i ); open.splice(j, 1); } /* Remove any doubled edges. */ dedup(edges); /* Add a new triangle for each edge. */ for (j = edges.length; j; ) { b = edges[--j]; a = edges[--j]; open.push(circumcircle(vertices, a, b, c)); } } /* Copy any remaining open triangles to the closed list, and then * remove any triangles that share a vertex with the supertriangle, * building a list of triplets that represent triangles. */ for (i = open.length; i--; ) { closed.push(open[i]); } open.length = 0; for (i = closed.length; i--; ) { if (closed[i].i < n && closed[i].j < n && closed[i].k < n) { open.push(closed[i].i, closed[i].j, closed[i].k); } } /* Yay, we're done! */ return open; }, contains: function(tri, p) { /* Bounding box test first, for quick rejections. */ if ((p[0] < tri[0][0] && p[0] < tri[1][0] && p[0] < tri[2][0]) || (p[0] > tri[0][0] && p[0] > tri[1][0] && p[0] > tri[2][0]) || (p[1] < tri[0][1] && p[1] < tri[1][1] && p[1] < tri[2][1]) || (p[1] > tri[0][1] && p[1] > tri[1][1] && p[1] > tri[2][1])) { return null; } var a = tri[1][0] - tri[0][0]; var b = tri[2][0] - tri[0][0]; var c = tri[1][1] - tri[0][1]; var d = tri[2][1] - tri[0][1]; var i = a * d - b * c; /* Degenerate tri. */ if (i === 0.0) { return null; } var u = (d * (p[0] - tri[0][0]) - b * (p[1] - tri[0][1])) / i, v = (a * (p[1] - tri[0][1]) - c * (p[0] - tri[0][0])) / i; /* If we're outside the tri, fail. */ if (u < 0.0 || v < 0.0 || (u + v) > 1.0) { return null; } return [u, v]; } }; export default delaunay; |