/
path.js
1457 lines (1439 loc) · 51.8 KB
/
path.js
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// Copyright (c) 2013 Adobe Systems Incorporated. All rights reserved.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
Snap.plugin(function (Snap, Element, Paper, glob) {
var elproto = Element.prototype,
is = Snap.is,
clone = Snap._.clone,
has = "hasOwnProperty",
p2s = /,?([a-z]),?/gi,
toFloat = parseFloat,
math = Math,
PI = math.PI,
mmin = math.min,
mmax = math.max,
pow = math.pow,
abs = math.abs;
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 (p[has](key) && key != ps) {
p[key].sleep--;
!p[key].sleep && delete p[key];
}
});
return p[ps];
}
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(" ")
};
}
function toString() {
return this.join(",").replace(p2s, "$1");
}
function pathClone(pathArray) {
var res = clone(pathArray);
res.toString = toString;
return res;
}
function getPointAtSegmentLength(p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y, length) {
if (length == null) {
return bezlen(p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y);
} else {
return findDotsAtSegment(p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y,
getTotLen(p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y, length));
}
}
function getLengthFactory(istotal, subpath) {
function O(val) {
return +(+val).toFixed(3);
}
return Snap._.cacher(function (path, length, onlystart) {
if (path instanceof Element) {
path = path.attr("d");
}
path = path2curve(path);
var x, y, p, l, sp = "", subpaths = {}, point,
len = 0;
for (var i = 0, ii = path.length; i < ii; i++) {
p = path[i];
if (p[0] == "M") {
x = +p[1];
y = +p[2];
} else {
l = getPointAtSegmentLength(x, y, p[1], p[2], p[3], p[4], p[5], p[6]);
if (len + l > length) {
if (subpath && !subpaths.start) {
point = getPointAtSegmentLength(x, y, p[1], p[2], p[3], p[4], p[5], p[6], length - len);
sp += [
"C" + O(point.start.x),
O(point.start.y),
O(point.m.x),
O(point.m.y),
O(point.x),
O(point.y)
];
if (onlystart) {return sp;}
subpaths.start = sp;
sp = [
"M" + O(point.x),
O(point.y) + "C" + O(point.n.x),
O(point.n.y),
O(point.end.x),
O(point.end.y),
O(p[5]),
O(p[6])
].join();
len += l;
x = +p[5];
y = +p[6];
continue;
}
if (!istotal && !subpath) {
point = getPointAtSegmentLength(x, y, p[1], p[2], p[3], p[4], p[5], p[6], length - len);
return point;
}
}
len += l;
x = +p[5];
y = +p[6];
}
sp += p.shift() + p;
}
subpaths.end = sp;
point = istotal ? len : subpath ? subpaths : findDotsAtSegment(x, y, p[0], p[1], p[2], p[3], p[4], p[5], 1);
return point;
}, null, Snap._.clone);
}
var getTotalLength = getLengthFactory(1),
getPointAtLength = getLengthFactory(),
getSubpathsAtLength = getLengthFactory(0, 1);
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,
mx = p1x + 2 * t * (c1x - p1x) + t2 * (c2x - 2 * c1x + p1x),
my = p1y + 2 * t * (c1y - p1y) + t2 * (c2y - 2 * c1y + p1y),
nx = c1x + 2 * t * (c2x - c1x) + t2 * (p2x - 2 * c2x + c1x),
ny = c1y + 2 * t * (c2y - c1y) + t2 * (p2y - 2 * c2y + c1y),
ax = t1 * p1x + t * c1x,
ay = t1 * p1y + t * c1y,
cx = t1 * c2x + t * p2x,
cy = t1 * c2y + t * p2y,
alpha = 90 - math.atan2(mx - nx, my - ny) * 180 / 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
};
}
function bezierBBox(p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y) {
if (!Snap.is(p1x, "array")) {
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
);
}
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 = 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);
}
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 getTotLen(x1, y1, x2, y2, x3, y3, x4, y4, ll) {
if (ll < 0 || bezlen(x1, y1, x2, y2, x3, y3, x4, y4) < ll) {
return;
}
var t = 1,
step = t / 2,
t2 = t - step,
l,
e = .01;
l = bezlen(x1, y1, x2, y2, x3, y3, x4, y4, t2);
while (abs(l - ll) > e) {
step /= 2;
t2 += (l < ll ? 1 : -1) * step;
l = bezlen(x1, y1, x2, y2, x3, y3, x4, y4, t2);
}
return t2;
}
function intersect(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 = nx / denominator,
py = 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 inter(bez1, bez2) {
return interHelper(bez1, bez2);
}
function interCount(bez1, bez2) {
return interHelper(bez1, bez2, 1);
}
function interHelper(bez1, bez2, justCount) {
var bbox1 = bezierBBox(bez1),
bbox2 = bezierBBox(bez2);
if (!isBBoxIntersect(bbox1, bbox2)) {
return justCount ? 0 : [];
}
var l1 = bezlen.apply(0, bez1),
l2 = bezlen.apply(0, bez2),
n1 = ~~(l1 / 8),
n2 = ~~(l2 / 8),
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) < .001 ? "y" : "x",
cj = abs(dj1.x - dj.x) < .001 ? "y" : "x",
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 + 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;
}
function pathIntersection(path1, path2) {
return interPathHelper(path1, path2);
}
function pathIntersectionNumber(path1, path2) {
return interPathHelper(path1, path2, 1);
}
function interPathHelper(path1, path2, justCount) {
path1 = path2curve(path1);
path2 = path2curve(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 = 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;
}
function isPointInsidePath(path, x, y) {
var bbox = pathBBox(path);
return isPointInsideBBox(bbox, x, y) &&
interPathHelper(path, [["M", x, y], ["H", bbox.x2 + 10]], 1) % 2 == 1;
}
function pathBBox(path) {
var pth = paths(path);
if (pth.bbox) {
return clone(pth.bbox);
}
if (!path) {
return box();
}
path = path2curve(path);
var x = 0,
y = 0,
X = [],
Y = [],
p;
for (var i = 0, ii = path.length; i < ii; i++) {
p = path[i];
if (p[0] == "M") {
x = p[1];
y = p[2];
X.push(x);
Y.push(y);
} else {
var dim = curveDim(x, y, p[1], p[2], p[3], p[4], p[5], p[6]);
X = X.concat(dim.min.x, dim.max.x);
Y = Y.concat(dim.min.y, dim.max.y);
x = p[5];
y = p[6];
}
}
var xmin = mmin.apply(0, X),
ymin = mmin.apply(0, Y),
xmax = mmax.apply(0, X),
ymax = mmax.apply(0, Y),
bb = box(xmin, ymin, xmax - xmin, ymax - ymin);
pth.bbox = clone(bb);
return bb;
}
function rectPath(x, y, w, h, r) {
if (r) {
return [
["M", +x + +r, y],
["l", w - r * 2, 0],
["a", r, r, 0, 0, 1, r, r],
["l", 0, h - r * 2],
["a", r, r, 0, 0, 1, -r, r],
["l", r * 2 - w, 0],
["a", r, r, 0, 0, 1, -r, -r],
["l", 0, r * 2 - h],
["a", r, r, 0, 0, 1, r, -r],
["z"]
];
}
var res = [["M", x, y], ["l", w, 0], ["l", 0, h], ["l", -w, 0], ["z"]];
res.toString = toString;
return res;
}
function ellipsePath(x, y, rx, ry, a) {
if (a == null && ry == null) {
ry = rx;
}
x = +x;
y = +y;
rx = +rx;
ry = +ry;
if (a != null) {
var rad = Math.PI / 180,
x1 = x + rx * Math.cos(-ry * rad),
x2 = x + rx * Math.cos(-a * rad),
y1 = y + rx * Math.sin(-ry * rad),
y2 = y + rx * Math.sin(-a * rad),
res = [["M", x1, y1], ["A", rx, rx, 0, +(a - ry > 180), 0, x2, y2]];
} else {
res = [
["M", x, y],
["m", 0, -ry],
["a", rx, ry, 0, 1, 1, 0, 2 * ry],
["a", rx, ry, 0, 1, 1, 0, -2 * ry],
["z"]
];
}
res.toString = toString;
return res;
}
var unit2px = Snap._unit2px,
getPath = {
path: function (el) {
return el.attr("path");
},
circle: function (el) {
var attr = unit2px(el);
return ellipsePath(attr.cx, attr.cy, attr.r);
},
ellipse: function (el) {
var attr = unit2px(el);
return ellipsePath(attr.cx || 0, attr.cy || 0, attr.rx, attr.ry);
},
rect: function (el) {
var attr = unit2px(el);
return rectPath(attr.x || 0, attr.y || 0, attr.width, attr.height, attr.rx, attr.ry);
},
image: function (el) {
var attr = unit2px(el);
return rectPath(attr.x || 0, attr.y || 0, attr.width, attr.height);
},
line: function (el) {
return "M" + [el.attr("x1") || 0, el.attr("y1") || 0, el.attr("x2"), el.attr("y2")];
},
polyline: function (el) {
return "M" + el.attr("points");
},
polygon: function (el) {
return "M" + el.attr("points") + "z";
},
deflt: function (el) {
var bbox = el.node.getBBox();
return rectPath(bbox.x, bbox.y, bbox.width, bbox.height);
}
};
function pathToRelative(pathArray) {
var pth = paths(pathArray),
lowerCase = String.prototype.toLowerCase;
if (pth.rel) {
return pathClone(pth.rel);
}
if (!Snap.is(pathArray, "array") || !Snap.is(pathArray && pathArray[0], "array")) {
pathArray = Snap.parsePathString(pathArray);
}
var res = [],
x = 0,
y = 0,
mx = 0,
my = 0,
start = 0;
if (pathArray[0][0] == "M") {
x = pathArray[0][1];
y = pathArray[0][2];
mx = x;
my = y;
start++;
res.push(["M", x, y]);
}
for (var i = start, ii = pathArray.length; i < ii; i++) {
var r = res[i] = [],
pa = pathArray[i];
if (pa[0] != lowerCase.call(pa[0])) {
r[0] = lowerCase.call(pa[0]);
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).toFixed(3);
r[7] = +(pa[7] - y).toFixed(3);
break;
case "v":
r[1] = +(pa[1] - y).toFixed(3);
break;
case "m":
mx = pa[1];
my = pa[2];
default:
for (var j = 1, jj = pa.length; j < jj; j++) {
r[j] = +(pa[j] - (j % 2 ? x : y)).toFixed(3);
}
}
} else {
r = res[i] = [];
if (pa[0] == "m") {
mx = pa[1] + x;
my = pa[2] + y;
}
for (var k = 0, kk = pa.length; k < kk; k++) {
res[i][k] = pa[k];
}
}
var len = res[i].length;
switch (res[i][0]) {
case "z":
x = mx;
y = my;
break;
case "h":
x += +res[i][len - 1];
break;
case "v":
y += +res[i][len - 1];
break;
default:
x += +res[i][len - 2];
y += +res[i][len - 1];
}
}
res.toString = toString;
pth.rel = pathClone(res);
return res;
}
function pathToAbsolute(pathArray) {
var pth = paths(pathArray);
if (pth.abs) {
return pathClone(pth.abs);
}
if (!is(pathArray, "array") || !is(pathArray && pathArray[0], "array")) { // rough assumption
pathArray = Snap.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];
}
var crz = pathArray.length == 3 &&
pathArray[0][0] == "M" &&
pathArray[1][0].toUpperCase() == "R" &&
pathArray[2][0].toUpperCase() == "Z";
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 "R":
var dots = [x, y].concat(pa.slice(1));
for (var j = 2, jj = dots.length; j < jj; j++) {
dots[j] = +dots[j] + x;
dots[++j] = +dots[j] + y;
}
res.pop();
res = res.concat(catmullRom2bezier(dots, crz));
break;
case "O":
res.pop();
dots = ellipsePath(x, y, pa[1], pa[2]);
dots.push(dots[0]);
res = res.concat(dots);
break;
case "U":
res.pop();
res = res.concat(ellipsePath(x, y, pa[1], pa[2], pa[3]));
r = ["U"].concat(res[res.length - 1].slice(-2));
break;
case "M":
mx = +pa[1] + x;
my = +pa[2] + y;
default:
for (j = 1, jj = pa.length; j < jj; j++) {
r[j] = +pa[j] + (j % 2 ? x : y);
}
}
} else if (pa0 == "R") {
dots = [x, y].concat(pa.slice(1));
res.pop();
res = res.concat(catmullRom2bezier(dots, crz));
r = ["R"].concat(pa.slice(-2));
} else if (pa0 == "O") {
res.pop();
dots = ellipsePath(x, y, pa[1], pa[2]);
dots.push(dots[0]);
res = res.concat(dots);
} else if (pa0 == "U") {
res.pop();
res = res.concat(ellipsePath(x, y, pa[1], pa[2], pa[3]));
r = ["U"].concat(res[res.length - 1].slice(-2));
} else {
for (var k = 0, kk = pa.length; k < kk; k++) {
r[k] = pa[k];
}
}
pa0 = pa0.toUpperCase();
if (pa0 != "O") {
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 = toString;
pth.abs = pathClone(res);
return res;
}
function l2c(x1, y1, x2, y2) {
return [x1, y1, x2, y2, x2, y2];
}
function q2c(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 a2c(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 = Snap._.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 (!rx || !ry) {
return [x1, y1, x2, y2, x2, y2];
}
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 cos = math.cos(PI / 180 * angle),
sin = math.sin(PI / 180 * angle),
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 = a2c(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;
}
}
function findDotAtSegment(p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y, t) {
var t1 = 1 - t;
return {
x: pow(t1, 3) * p1x + pow(t1, 2) * 3 * t * c1x + t1 * 3 * t * t * c2x + pow(t, 3) * p2x,
y: pow(t1, 3) * p1y + pow(t1, 2) * 3 * t * c1y + t1 * 3 * t * t * c2y + pow(t, 3) * p2y
};
}
// 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 curveDim(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 x, y, 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 {
min: {x: mmin.apply(0, bounds[0]), y: mmin.apply(0, bounds[1])},
max: {x: mmax.apply(0, bounds[0]), y: mmax.apply(0, bounds[1])}
};
}
function path2curve(path, path2) {
var pth = !path2 && paths(path);
if (!path2 && pth.curve) {
return pathClone(pth.curve);
}
var p = pathToAbsolute(path),
p2 = path2 && pathToAbsolute(path2),
attrs = {x: 0, y: 0, bx: 0, by: 0, X: 0, Y: 0, qx: null, qy: null},
attrs2 = {x: 0, y: 0, bx: 0, by: 0, X: 0, Y: 0, qx: null, qy: null},
processPath = function (path, d, pcom) {
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(a2c.apply(0, [d.x, d.y].concat(path.slice(1))));
break;
case "S":
if (pcom == "C" || pcom == "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 (pcom == "Q" || pcom == "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(q2c(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(q2c(d.x, d.y, path[1], path[2], path[3], path[4]));
break;
case "L":
path = ["C"].concat(l2c(d.x, d.y, path[1], path[2]));
break;
case "H":
path = ["C"].concat(l2c(d.x, d.y, path[1], d.y));
break;
case "V":
path = ["C"].concat(l2c(d.x, d.y, d.x, path[1]));
break;
case "Z":
path = ["C"].concat(l2c(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) {
pcoms1[i] = "A"; // if created multiple C:s, their original seg is saved
p2 && (pcoms2[i] = "A"); // the same as above
pp.splice(i++, 0, ["C"].concat(pi.splice(0, 6)));
}
pp.splice(i, 1);
ii = mmax(p.length, p2 && p2.length || 0);
}
},
fixM = function (path1, path2, a1, a2, i) {
if (path1 && path2 && path1[i][0] == "M" && path2[i][0] != "M") {
path2.splice(i, 0, ["M", a2.x, a2.y]);
a1.bx = 0;
a1.by = 0;