'use strict'; /** * This file contains source code adapted from Snap.svg (licensed Apache-2.0). * * @see https://github.com/adobe-webplatform/Snap.svg/blob/master/src/path.js */ /* eslint no-fallthrough: "off" */ var p2s = /,?([a-z]),?/gi, toFloat = parseFloat, math = Math, PI = math.PI, mmin = math.min, mmax = math.max, pow = math.pow, abs = math.abs, pathCommand = /([a-z])[\s,]*((-?\d*\.?\d*(?:e[-+]?\d+)?[\s]*,?[\s]*)+)/ig, pathValues = /(-?\d*\.?\d*(?:e[-+]?\d+)?)[\s]*,?[\s]*/ig; var isArray = Array.isArray || function(o) { return o instanceof Array; }; function hasProperty(obj, property) { return Object.prototype.hasOwnProperty.call(obj, property); } function clone(obj) { if (typeof obj == 'function' || Object(obj) !== obj) { return obj; } var res = new obj.constructor; for (var key in obj) { if (hasProperty(obj, key)) { res[key] = clone(obj[key]); } } return res; } function repush(array, item) { for (var i = 0, ii = array.length; i < ii; i++) if (array[i] === item) { return array.push(array.splice(i, 1)[0]); } } function cacher(f) { function newf() { var arg = Array.prototype.slice.call(arguments, 0), args = arg.join('\u2400'), cache = newf.cache = newf.cache || {}, count = newf.count = newf.count || []; if (hasProperty(cache, args)) { repush(count, args); return cache[args]; } count.length >= 1e3 && delete cache[count.shift()]; count.push(args); cache[args] = f.apply(0, arg); return cache[args]; } return newf; } function parsePathString(pathString) { if (!pathString) { return null; } var pth = paths(pathString); if (pth.arr) { return clone(pth.arr); } var paramCounts = { a: 7, c: 6, h: 1, l: 2, m: 2, q: 4, s: 4, t: 2, v: 1, z: 0 }, data = []; if (isArray(pathString) && isArray(pathString[0])) { // rough assumption data = clone(pathString); } if (!data.length) { String(pathString).replace(pathCommand, function(a, b, c) { var params = [], name = b.toLowerCase(); c.replace(pathValues, function(a, b) { b && params.push(+b); }); if (name == 'm' && params.length > 2) { data.push([b].concat(params.splice(0, 2))); name = 'l'; b = b == 'm' ? 'l' : 'L'; } while (params.length >= paramCounts[name]) { data.push([b].concat(params.splice(0, paramCounts[name]))); if (!paramCounts[name]) { break; } } }); } data.toString = paths.toString; pth.arr = clone(data); return data; } function paths(ps) { var p = paths.ps = paths.ps || {}; if (p[ps]) { p[ps].sleep = 100; } else { p[ps] = { sleep: 100 }; } setTimeout(function() { for (var key in p) { if (hasProperty(p, key) && key != ps) { p[key].sleep--; !p[key].sleep && delete p[key]; } } }); return p[ps]; } function rectBBox(x, y, width, height) { if (arguments.length === 1) { y = x.y; width = x.width; height = x.height; x = x.x; } return { x: x, y: y, width: width, height: height, x2: x + width, y2: y + height }; } function pathToString() { return this.join(',').replace(p2s, '$1'); } function pathClone(pathArray) { var res = clone(pathArray); res.toString = pathToString; return res; } function findDotsAtSegment(p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y, t) { var t1 = 1 - t, t13 = pow(t1, 3), t12 = pow(t1, 2), t2 = t * t, t3 = t2 * t, x = t13 * p1x + t12 * 3 * t * c1x + t1 * 3 * t * t * c2x + t3 * p2x, y = t13 * p1y + t12 * 3 * t * c1y + t1 * 3 * t * t * c2y + t3 * p2y; return { x: fixError(x), y: fixError(y) }; } function bezierBBox(points) { var bbox = curveBBox.apply(null, points); return rectBBox( bbox.x0, bbox.y0, bbox.x1 - bbox.x0, bbox.y1 - bbox.y0 ); } function isPointInsideBBox(bbox, x, y) { return x >= bbox.x && x <= bbox.x + bbox.width && y >= bbox.y && y <= bbox.y + bbox.height; } function isBBoxIntersect(bbox1, bbox2) { bbox1 = rectBBox(bbox1); bbox2 = rectBBox(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); } function base3(t, p1, p2, p3, p4) { var t1 = -3 * p1 + 9 * p2 - 9 * p3 + 3 * p4, t2 = t * t1 + 6 * p1 - 12 * p2 + 6 * p3; return t * t2 - 3 * p1 + 3 * p2; } 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, n = 12, Tvalues = [-.1252,.1252,-.3678,.3678,-.5873,.5873,-.7699,.7699,-.9041,.9041,-.9816,.9816], 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], sum = 0; for (var i = 0; i < n; i++) { var ct = z2 * Tvalues[i] + z2, xbase = base3(ct, x1, x2, x3, x4), ybase = base3(ct, y1, y2, y3, y4), comb = xbase * xbase + ybase * ybase; sum += Cvalues[i] * math.sqrt(comb); } return z2 * sum; } function intersectLines(x1, y1, x2, y2, x3, y3, x4, y4) { if ( mmax(x1, x2) < mmin(x3, x4) || mmin(x1, x2) > mmax(x3, x4) || mmax(y1, y2) < mmin(y3, y4) || mmin(y1, y2) > mmax(y3, y4) ) { return; } var nx = (x1 * y2 - y1 * x2) * (x3 - x4) - (x1 - x2) * (x3 * y4 - y3 * x4), ny = (x1 * y2 - y1 * x2) * (y3 - y4) - (y1 - y2) * (x3 * y4 - y3 * x4), denominator = (x1 - x2) * (y3 - y4) - (y1 - y2) * (x3 - x4); if (!denominator) { return; } var px = fixError(nx / denominator), py = fixError(ny / denominator), px2 = +px.toFixed(2), py2 = +py.toFixed(2); if ( px2 < +mmin(x1, x2).toFixed(2) || px2 > +mmax(x1, x2).toFixed(2) || px2 < +mmin(x3, x4).toFixed(2) || px2 > +mmax(x3, x4).toFixed(2) || py2 < +mmin(y1, y2).toFixed(2) || py2 > +mmax(y1, y2).toFixed(2) || py2 < +mmin(y3, y4).toFixed(2) || py2 > +mmax(y3, y4).toFixed(2) ) { return; } return { x: px, y: py }; } function fixError(number) { return Math.round(number * 100000000000) / 100000000000; } function findBezierIntersections(bez1, bez2, justCount) { var bbox1 = bezierBBox(bez1), bbox2 = bezierBBox(bez2); if (!isBBoxIntersect(bbox1, bbox2)) { return justCount ? 0 : []; } // As an optimization, lines will have only 1 segment var l1 = bezlen.apply(0, bez1), l2 = bezlen.apply(0, bez2), n1 = isLine(bez1) ? 1 : ~~(l1 / 5) || 1, n2 = isLine(bez2) ? 1 : ~~(l2 / 5) || 1, dots1 = [], dots2 = [], xy = {}, res = justCount ? 0 : []; for (var i = 0; i < n1 + 1; i++) { var p = findDotsAtSegment.apply(0, bez1.concat(i / n1)); dots1.push({ x: p.x, y: p.y, t: i / n1 }); } for (i = 0; i < n2 + 1; i++) { p = findDotsAtSegment.apply(0, bez2.concat(i / n2)); dots2.push({ x: p.x, y: p.y, t: i / n2 }); } for (i = 0; i < n1; i++) { for (var j = 0; j < n2; j++) { var di = dots1[i], di1 = dots1[i + 1], dj = dots2[j], dj1 = dots2[j + 1], ci = abs(di1.x - di.x) < .01 ? 'y' : 'x', cj = abs(dj1.x - dj.x) < .01 ? 'y' : 'x', is = intersectLines(di.x, di.y, di1.x, di1.y, dj.x, dj.y, dj1.x, dj1.y), key; if (is) { key = is.x.toFixed(9) + '#' + is.y.toFixed(9); if (xy[key]) { continue; } xy[key] = true; var t1 = di.t + abs((is[ci] - di[ci]) / (di1[ci] - di[ci])) * (di1.t - di.t), t2 = dj.t + 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; } /** * Find or counts the intersections between two SVG paths. * * Returns a number in counting mode and a list of intersections otherwise. * * A single intersection entry contains the intersection coordinates (x, y) * as well as additional information regarding the intersecting segments * on each path (segment1, segment2) and the relative location of the * intersection on these segments (t1, t2). * * The path may be an SVG path string or a list of path components * such as `[ [ 'M', 0, 10 ], [ 'L', 20, 0 ] ]`. * * @example * * var intersections = findPathIntersections( * 'M0,0L100,100', * [ [ 'M', 0, 100 ], [ 'L', 100, 0 ] ] * ); * * // intersections = [ * // { x: 50, y: 50, segment1: 1, segment2: 1, t1: 0.5, t2: 0.5 } * // ] * * @param {String|Array} path1 * @param {String|Array} path2 * @param {Boolean} [justCount=false] * * @return {Array|Number} */ function findPathIntersections(path1, path2, justCount) { path1 = pathToCurve(path1); path2 = pathToCurve(path2); var x1, y1, x2, y2, x1m, y1m, x2m, y2m, bez1, bez2, 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 = findBezierIntersections(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; } function pathToAbsolute(pathArray) { var pth = paths(pathArray); if (pth.abs) { return pathClone(pth.abs); } if (!isArray(pathArray) || !isArray(pathArray && pathArray[0])) { // rough assumption pathArray = parsePathString(pathArray); } if (!pathArray || !pathArray.length) { return [['M', 0, 0]]; } var res = [], x = 0, y = 0, mx = 0, my = 0, start = 0, pa0; if (pathArray[0][0] == 'M') { x = +pathArray[0][1]; y = +pathArray[0][2]; mx = x; my = y; start++; res[0] = ['M', x, y]; } for (var r, pa, i = start, ii = pathArray.length; i < ii; i++) { res.push(r = []); pa = pathArray[i]; pa0 = pa[0]; if (pa0 != pa0.toUpperCase()) { r[0] = pa0.toUpperCase(); switch (r[0]) { case 'A': r[1] = pa[1]; r[2] = pa[2]; r[3] = pa[3]; r[4] = pa[4]; r[5] = pa[5]; r[6] = +pa[6] + x; r[7] = +pa[7] + y; break; case 'V': r[1] = +pa[1] + y; break; case 'H': r[1] = +pa[1] + x; break; case 'M': mx = +pa[1] + x; my = +pa[2] + y; default: for (var j = 1, jj = pa.length; j < jj; j++) { r[j] = +pa[j] + ((j % 2) ? x : y); } } } else { for (var k = 0, kk = pa.length; k < kk; k++) { r[k] = pa[k]; } } pa0 = pa0.toUpperCase(); switch (r[0]) { case 'Z': x = +mx; y = +my; break; case 'H': x = r[1]; break; case 'V': y = r[1]; break; case 'M': mx = r[r.length - 2]; my = r[r.length - 1]; default: x = r[r.length - 2]; y = r[r.length - 1]; } } res.toString = pathToString; pth.abs = pathClone(res); return res; } function isLine(bez) { return ( bez[0] === bez[2] && bez[1] === bez[3] && bez[4] === bez[6] && bez[5] === bez[7] ); } function lineToCurve(x1, y1, x2, y2) { return [ x1, y1, x2, y2, x2, y2 ]; } function qubicToCurve(x1, y1, ax, ay, x2, y2) { var _13 = 1 / 3, _23 = 2 / 3; return [ _13 * x1 + _23 * ax, _13 * y1 + _23 * ay, _13 * x2 + _23 * ax, _13 * y2 + _23 * ay, x2, y2 ]; } function arcToCurve(x1, y1, rx, ry, angle, large_arc_flag, sweep_flag, x2, y2, recursive) { // for more information of where this math came from visit: // http://www.w3.org/TR/SVG11/implnote.html#ArcImplementationNotes var _120 = PI * 120 / 180, rad = PI / 180 * (+angle || 0), res = [], xy, rotate = cacher(function(x, y, rad) { var X = x * math.cos(rad) - y * math.sin(rad), Y = x * math.sin(rad) + y * math.cos(rad); return { x: X, y: Y }; }); if (!recursive) { xy = rotate(x1, y1, -rad); x1 = xy.x; y1 = xy.y; xy = rotate(x2, y2, -rad); x2 = xy.x; y2 = xy.y; var x = (x1 - x2) / 2, y = (y1 - y2) / 2; var h = (x * x) / (rx * rx) + (y * y) / (ry * ry); if (h > 1) { h = math.sqrt(h); rx = h * rx; ry = h * ry; } var rx2 = rx * rx, ry2 = ry * ry, k = (large_arc_flag == sweep_flag ? -1 : 1) * math.sqrt(abs((rx2 * ry2 - rx2 * y * y - ry2 * x * x) / (rx2 * y * y + ry2 * x * x))), cx = k * rx * y / ry + (x1 + x2) / 2, cy = k * -ry * x / rx + (y1 + y2) / 2, f1 = math.asin(((y1 - cy) / ry).toFixed(9)), f2 = math.asin(((y2 - cy) / ry).toFixed(9)); f1 = x1 < cx ? PI - f1 : f1; f2 = x2 < cx ? PI - f2 : f2; f1 < 0 && (f1 = PI * 2 + f1); f2 < 0 && (f2 = PI * 2 + f2); if (sweep_flag && f1 > f2) { f1 = f1 - PI * 2; } if (!sweep_flag && f2 > f1) { f2 = f2 - PI * 2; } } else { f1 = recursive[0]; f2 = recursive[1]; cx = recursive[2]; cy = recursive[3]; } var df = f2 - f1; if (abs(df) > _120) { var f2old = f2, x2old = x2, y2old = y2; f2 = f1 + _120 * (sweep_flag && f2 > f1 ? 1 : -1); x2 = cx + rx * math.cos(f2); y2 = cy + ry * math.sin(f2); res = arcToCurve(x2, y2, rx, ry, angle, 0, sweep_flag, x2old, y2old, [f2, f2old, cx, cy]); } df = f2 - f1; var c1 = math.cos(f1), s1 = math.sin(f1), c2 = math.cos(f2), s2 = math.sin(f2), t = math.tan(df / 4), hx = 4 / 3 * rx * t, hy = 4 / 3 * ry * t, m1 = [x1, y1], m2 = [x1 + hx * s1, y1 - hy * c1], m3 = [x2 + hx * s2, y2 - hy * c2], m4 = [x2, y2]; m2[0] = 2 * m1[0] - m2[0]; m2[1] = 2 * m1[1] - m2[1]; if (recursive) { return [m2, m3, m4].concat(res); } else { res = [m2, m3, m4].concat(res).join().split(','); var newres = []; for (var i = 0, ii = res.length; i < ii; i++) { newres[i] = i % 2 ? rotate(res[i - 1], res[i], rad).y : rotate(res[i], res[i + 1], rad).x; } return newres; } } // Returns bounding box of cubic bezier curve. // Source: http://blog.hackers-cafe.net/2009/06/how-to-calculate-bezier-curves-bounding.html // Original version: NISHIO Hirokazu // Modifications: https://github.com/timo22345 function curveBBox(x0, y0, x1, y1, x2, y2, x3, y3) { var tvalues = [], bounds = [[], []], a, b, c, t, t1, t2, b2ac, sqrtb2ac; 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 (abs(a) < 1e-12) { if (abs(b) < 1e-12) { continue; } t = -c / b; if (0 < t && t < 1) { tvalues.push(t); } continue; } b2ac = b * b - 4 * c * a; sqrtb2ac = math.sqrt(b2ac); if (b2ac < 0) { continue; } t1 = (-b + sqrtb2ac) / (2 * a); if (0 < t1 && t1 < 1) { tvalues.push(t1); } t2 = (-b - sqrtb2ac) / (2 * a); if (0 < t2 && t2 < 1) { tvalues.push(t2); } } var j = tvalues.length, jlen = j, mt; 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 { x0: mmin.apply(0, bounds[0]), y0: mmin.apply(0, bounds[1]), x1: mmax.apply(0, bounds[0]), y1: mmax.apply(0, bounds[1]) }; } function pathToCurve(path) { var pth = paths(path); // return cached curve, if existing if (pth.curve) { return pathClone(pth.curve); } var curvedPath = pathToAbsolute(path), attrs = { x: 0, y: 0, bx: 0, by: 0, X: 0, Y: 0, qx: null, qy: null }, processPath = function(path, d, pathCommand) { var nx, ny; if (!path) { return ['C', d.x, d.y, d.x, d.y, d.x, d.y]; } !(path[0] in { T: 1, Q: 1 }) && (d.qx = d.qy = null); switch (path[0]) { case 'M': d.X = path[1]; d.Y = path[2]; break; case 'A': path = ['C'].concat(arcToCurve.apply(0, [d.x, d.y].concat(path.slice(1)))); break; case 'S': if (pathCommand == 'C' || pathCommand == 'S') { // In 'S' case we have to take into account, if the previous command is C/S. nx = d.x * 2 - d.bx; // And reflect the previous ny = d.y * 2 - d.by; // command's control point relative to the current point. } else { // or some else or nothing nx = d.x; ny = d.y; } path = ['C', nx, ny].concat(path.slice(1)); break; case 'T': if (pathCommand == 'Q' || pathCommand == 'T') { // In 'T' case we have to take into account, if the previous command is Q/T. d.qx = d.x * 2 - d.qx; // And make a reflection similar d.qy = d.y * 2 - d.qy; // to case 'S'. } else { // or something else or nothing d.qx = d.x; d.qy = d.y; } path = ['C'].concat(qubicToCurve(d.x, d.y, d.qx, d.qy, path[1], path[2])); break; case 'Q': d.qx = path[1]; d.qy = path[2]; path = ['C'].concat(qubicToCurve(d.x, d.y, path[1], path[2], path[3], path[4])); break; case 'L': path = ['C'].concat(lineToCurve(d.x, d.y, path[1], path[2])); break; case 'H': path = ['C'].concat(lineToCurve(d.x, d.y, path[1], d.y)); break; case 'V': path = ['C'].concat(lineToCurve(d.x, d.y, d.x, path[1])); break; case 'Z': path = ['C'].concat(lineToCurve(d.x, d.y, d.X, d.Y)); break; } return path; }, fixArc = function(pp, i) { if (pp[i].length > 7) { pp[i].shift(); var pi = pp[i]; while (pi.length) { pathCommands[i] = 'A'; // if created multiple C:s, their original seg is saved pp.splice(i++, 0, ['C'].concat(pi.splice(0, 6))); } pp.splice(i, 1); ii = curvedPath.length; } }, pathCommands = [], // path commands of original path p pfirst = '', // temporary holder for original path command pathCommand = ''; // holder for previous path command of original path for (var i = 0, ii = curvedPath.length; i < ii; i++) { curvedPath[i] && (pfirst = curvedPath[i][0]); // save current path command if (pfirst != 'C') // C is not saved yet, because it may be result of conversion { pathCommands[i] = pfirst; // Save current path command i && (pathCommand = pathCommands[i - 1]); // Get previous path command pathCommand } curvedPath[i] = processPath(curvedPath[i], attrs, pathCommand); // Previous path command is inputted to processPath if (pathCommands[i] != 'A' && pfirst == 'C') pathCommands[i] = 'C'; // A is the only command // which may produce multiple C:s // so we have to make sure that C is also C in original path fixArc(curvedPath, i); // fixArc adds also the right amount of A:s to pathCommands var seg = curvedPath[i], seglen = seg.length; attrs.x = seg[seglen - 2]; attrs.y = seg[seglen - 1]; attrs.bx = toFloat(seg[seglen - 4]) || attrs.x; attrs.by = toFloat(seg[seglen - 3]) || attrs.y; } // cache curve pth.curve = pathClone(curvedPath); return curvedPath; } module.exports = findPathIntersections;