var isArray = require('../type/is-array'); var rectPath = require('./rect-path'); var pathTocurve = require('./path2curve'); var base3 = function base3(t, p1, p2, p3, p4) { var t1 = -3 * p1 + 9 * p2 - 9 * p3 + 3 * p4; var t2 = t * t1 + 6 * p1 - 12 * p2 + 6 * p3; return t * t2 - 3 * p1 + 3 * p2; }; var bezlen = function bezlen(x1, y1, x2, y2, x3, y3, x4, y4, z) { if (z === null) { z = 1; } z = z > 1 ? 1 : z < 0 ? 0 : z; var z2 = z / 2; var n = 12; var Tvalues = [-0.1252, 0.1252, -0.3678, 0.3678, -0.5873, 0.5873, -0.7699, 0.7699, -0.9041, 0.9041, -0.9816, 0.9816]; var Cvalues = [0.2491, 0.2491, 0.2335, 0.2335, 0.2032, 0.2032, 0.1601, 0.1601, 0.1069, 0.1069, 0.0472, 0.0472]; var sum = 0; for (var i = 0; i < n; i++) { var ct = z2 * Tvalues[i] + z2; var xbase = base3(ct, x1, x2, x3, x4); var ybase = base3(ct, y1, y2, y3, y4); var comb = xbase * xbase + ybase * ybase; sum += Cvalues[i] * Math.sqrt(comb); } return z2 * sum; }; var curveDim = function curveDim(x0, y0, x1, y1, x2, y2, x3, y3) { var tvalues = []; var bounds = [[], []]; var a = void 0; var b = void 0; var c = void 0; var t = void 0; for (var i = 0; i < 2; ++i) { if (i === 0) { b = 6 * x0 - 12 * x1 + 6 * x2; a = -3 * x0 + 9 * x1 - 9 * x2 + 3 * x3; c = 3 * x1 - 3 * x0; } else { b = 6 * y0 - 12 * y1 + 6 * y2; a = -3 * y0 + 9 * y1 - 9 * y2 + 3 * y3; c = 3 * y1 - 3 * y0; } if (Math.abs(a) < 1e-12) { if (Math.abs(b) < 1e-12) { continue; } t = -c / b; if (t > 0 && t < 1) { tvalues.push(t); } continue; } var b2ac = b * b - 4 * c * a; var sqrtb2ac = Math.sqrt(b2ac); if (b2ac < 0) { continue; } var t1 = (-b + sqrtb2ac) / (2 * a); if (t1 > 0 && t1 < 1) { tvalues.push(t1); } var t2 = (-b - sqrtb2ac) / (2 * a); if (t2 > 0 && t2 < 1) { tvalues.push(t2); } } var j = tvalues.length; var jlen = j; var mt = void 0; while (j--) { t = tvalues[j]; mt = 1 - t; bounds[0][j] = mt * mt * mt * x0 + 3 * mt * mt * t * x1 + 3 * mt * t * t * x2 + t * t * t * x3; bounds[1][j] = mt * mt * mt * y0 + 3 * mt * mt * t * y1 + 3 * mt * t * t * y2 + t * t * t * y3; } bounds[0][jlen] = x0; bounds[1][jlen] = y0; bounds[0][jlen + 1] = x3; bounds[1][jlen + 1] = y3; bounds[0].length = bounds[1].length = jlen + 2; return { min: { x: Math.min.apply(0, bounds[0]), y: Math.min.apply(0, bounds[1]) }, max: { x: Math.max.apply(0, bounds[0]), y: Math.max.apply(0, bounds[1]) } }; }; var intersect = function intersect(x1, y1, x2, y2, x3, y3, x4, y4) { if (Math.max(x1, x2) < Math.min(x3, x4) || Math.min(x1, x2) > Math.max(x3, x4) || Math.max(y1, y2) < Math.min(y3, y4) || Math.min(y1, y2) > Math.max(y3, y4)) { return; } var nx = (x1 * y2 - y1 * x2) * (x3 - x4) - (x1 - x2) * (x3 * y4 - y3 * x4); var ny = (x1 * y2 - y1 * x2) * (y3 - y4) - (y1 - y2) * (x3 * y4 - y3 * x4); var denominator = (x1 - x2) * (y3 - y4) - (y1 - y2) * (x3 - x4); if (!denominator) { return; } var px = nx / denominator; var py = ny / denominator; var px2 = +px.toFixed(2); var py2 = +py.toFixed(2); if (px2 < +Math.min(x1, x2).toFixed(2) || px2 > +Math.max(x1, x2).toFixed(2) || px2 < +Math.min(x3, x4).toFixed(2) || px2 > +Math.max(x3, x4).toFixed(2) || py2 < +Math.min(y1, y2).toFixed(2) || py2 > +Math.max(y1, y2).toFixed(2) || py2 < +Math.min(y3, y4).toFixed(2) || py2 > +Math.max(y3, y4).toFixed(2)) { return; } return { x: px, y: py }; }; var isPointInsideBBox = function isPointInsideBBox(bbox, x, y) { return x >= bbox.x && x <= bbox.x + bbox.width && y >= bbox.y && y <= bbox.y + bbox.height; }; var box = function box(x, y, width, height) { if (x === null) { x = y = width = height = 0; } if (y === null) { y = x.y; width = x.width; height = x.height; x = x.x; } return { x: x, y: y, width: width, w: width, height: height, h: height, x2: x + width, y2: y + height, cx: x + width / 2, cy: y + height / 2, r1: Math.min(width, height) / 2, r2: Math.max(width, height) / 2, r0: Math.sqrt(width * width + height * height) / 2, path: rectPath(x, y, width, height), vb: [x, y, width, height].join(' ') }; }; var isBBoxIntersect = function isBBoxIntersect(bbox1, bbox2) { bbox1 = box(bbox1); bbox2 = box(bbox2); return isPointInsideBBox(bbox2, bbox1.x, bbox1.y) || isPointInsideBBox(bbox2, bbox1.x2, bbox1.y) || isPointInsideBBox(bbox2, bbox1.x, bbox1.y2) || isPointInsideBBox(bbox2, bbox1.x2, bbox1.y2) || isPointInsideBBox(bbox1, bbox2.x, bbox2.y) || isPointInsideBBox(bbox1, bbox2.x2, bbox2.y) || isPointInsideBBox(bbox1, bbox2.x, bbox2.y2) || isPointInsideBBox(bbox1, bbox2.x2, bbox2.y2) || (bbox1.x < bbox2.x2 && bbox1.x > bbox2.x || bbox2.x < bbox1.x2 && bbox2.x > bbox1.x) && (bbox1.y < bbox2.y2 && bbox1.y > bbox2.y || bbox2.y < bbox1.y2 && bbox2.y > bbox1.y); }; var bezierBBox = function bezierBBox(p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y) { if (!isArray(p1x)) { p1x = [p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y]; } var bbox = curveDim.apply(null, p1x); return box(bbox.min.x, bbox.min.y, bbox.max.x - bbox.min.x, bbox.max.y - bbox.min.y); }; var findDotsAtSegment = function findDotsAtSegment(p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y, t) { var t1 = 1 - t; var t13 = Math.pow(t1, 3); var t12 = Math.pow(t1, 2); var t2 = t * t; var t3 = t2 * t; var x = t13 * p1x + t12 * 3 * t * c1x + t1 * 3 * t * t * c2x + t3 * p2x; var y = t13 * p1y + t12 * 3 * t * c1y + t1 * 3 * t * t * c2y + t3 * p2y; var mx = p1x + 2 * t * (c1x - p1x) + t2 * (c2x - 2 * c1x + p1x); var my = p1y + 2 * t * (c1y - p1y) + t2 * (c2y - 2 * c1y + p1y); var nx = c1x + 2 * t * (c2x - c1x) + t2 * (p2x - 2 * c2x + c1x); var ny = c1y + 2 * t * (c2y - c1y) + t2 * (p2y - 2 * c2y + c1y); var ax = t1 * p1x + t * c1x; var ay = t1 * p1y + t * c1y; var cx = t1 * c2x + t * p2x; var cy = t1 * c2y + t * p2y; var alpha = 90 - Math.atan2(mx - nx, my - ny) * 180 / Math.PI; // (mx > nx || my < ny) && (alpha += 180); return { x: x, y: y, m: { x: mx, y: my }, n: { x: nx, y: ny }, start: { x: ax, y: ay }, end: { x: cx, y: cy }, alpha: alpha }; }; var interHelper = function interHelper(bez1, bez2, justCount) { var bbox1 = bezierBBox(bez1); var bbox2 = bezierBBox(bez2); if (!isBBoxIntersect(bbox1, bbox2)) { return justCount ? 0 : []; } var l1 = bezlen.apply(0, bez1); var l2 = bezlen.apply(0, bez2); var n1 = ~~(l1 / 8); var n2 = ~~(l2 / 8); var dots1 = []; var dots2 = []; var xy = {}; var res = justCount ? 0 : []; for (var i = 0; i < n1 + 1; i++) { var d = findDotsAtSegment.apply(0, bez1.concat(i / n1)); dots1.push({ x: d.x, y: d.y, t: i / n1 }); } for (var _i = 0; _i < n2 + 1; _i++) { var _d = findDotsAtSegment.apply(0, bez2.concat(_i / n2)); dots2.push({ x: _d.x, y: _d.y, t: _i / n2 }); } for (var _i2 = 0; _i2 < n1; _i2++) { for (var j = 0; j < n2; j++) { var di = dots1[_i2]; var di1 = dots1[_i2 + 1]; var dj = dots2[j]; var dj1 = dots2[j + 1]; var ci = Math.abs(di1.x - di.x) < 0.001 ? 'y' : 'x'; var cj = Math.abs(dj1.x - dj.x) < 0.001 ? 'y' : 'x'; var is = intersect(di.x, di.y, di1.x, di1.y, dj.x, dj.y, dj1.x, dj1.y); if (is) { if (xy[is.x.toFixed(4)] === is.y.toFixed(4)) { continue; } xy[is.x.toFixed(4)] = is.y.toFixed(4); var t1 = di.t + Math.abs((is[ci] - di[ci]) / (di1[ci] - di[ci])) * (di1.t - di.t); var t2 = dj.t + Math.abs((is[cj] - dj[cj]) / (dj1[cj] - dj[cj])) * (dj1.t - dj.t); if (t1 >= 0 && t1 <= 1 && t2 >= 0 && t2 <= 1) { if (justCount) { res++; } else { res.push({ x: is.x, y: is.y, t1: t1, t2: t2 }); } } } } } return res; }; var interPathHelper = function interPathHelper(path1, path2, justCount) { path1 = pathTocurve(path1); path2 = pathTocurve(path2); var x1 = void 0; var y1 = void 0; var x2 = void 0; var y2 = void 0; var x1m = void 0; var y1m = void 0; var x2m = void 0; var y2m = void 0; var bez1 = void 0; var bez2 = void 0; var res = justCount ? 0 : []; for (var i = 0, ii = path1.length; i < ii; i++) { var pi = path1[i]; if (pi[0] === 'M') { x1 = x1m = pi[1]; y1 = y1m = pi[2]; } else { if (pi[0] === 'C') { bez1 = [x1, y1].concat(pi.slice(1)); x1 = bez1[6]; y1 = bez1[7]; } else { bez1 = [x1, y1, x1, y1, x1m, y1m, x1m, y1m]; x1 = x1m; y1 = y1m; } for (var j = 0, jj = path2.length; j < jj; j++) { var pj = path2[j]; if (pj[0] === 'M') { x2 = x2m = pj[1]; y2 = y2m = pj[2]; } else { if (pj[0] === 'C') { bez2 = [x2, y2].concat(pj.slice(1)); x2 = bez2[6]; y2 = bez2[7]; } else { bez2 = [x2, y2, x2, y2, x2m, y2m, x2m, y2m]; x2 = x2m; y2 = y2m; } var intr = interHelper(bez1, bez2, justCount); if (justCount) { res += intr; } else { for (var k = 0, kk = intr.length; k < kk; k++) { intr[k].segment1 = i; intr[k].segment2 = j; intr[k].bez1 = bez1; intr[k].bez2 = bez2; } res = res.concat(intr); } } } } } return res; }; module.exports = function pathIntersection(path1, path2) { return interPathHelper(path1, path2); };