// 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.
Savage.plugin(function (Savage, Element, Paper, glob) {
    var elproto = Element.prototype,
        is = Savage.is,
        clone = Savage._.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 function (path, length, onlystart) {
            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;
        };
    }
    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 (!Savage.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 / 5),
            n2 = ~~(l2 / 5),
            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;
        }
        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 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, attr.cy, attr.rx, attr.ry);
        },
        rect: function (el) {
            var attr = unit2px(el);
            return rectPath(attr.x, attr.y, attr.width, attr.height, attr.rx, attr.ry);
        },
        image: function (el) {
            var attr = unit2px(el);
            return rectPath(attr.x, attr.y, attr.width, attr.height);
        },
        text: function (el) {
            var bbox = el.node.getBBox();
            return rectPath(bbox.x, bbox.y, bbox.width, bbox.height);
        },
        g: function (el) {
            var bbox = el.node.getBBox();
            return rectPath(bbox.x, bbox.y, bbox.width, bbox.height);
        },
        symbol: function (el) {
            var bbox = el.getBBox();
            return rectPath(bbox.x, bbox.y, bbox.width, bbox.height);
        }
    };
    function pathToRelative(pathArray) {
        var pth = paths(pathArray);
        if (pth.rel) {
            return pathClone(pth.rel);
        }
        if (!Savage.is(pathArray, "array") || !Savage.is(pathArray && pathArray[0], "array")) {
            pathArray = Savage.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 = Savage.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 = 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 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
        };
    }
    function curveDim(p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y) {
        var a = (c2x - 2 * c1x + p1x) - (p2x - 2 * c2x + c1x),
            b = 2 * (c1x - p1x) - 2 * (c2x - c1x),
            c = p1x - c1x,
            t1 = (-b + math.sqrt(b * b - 4 * a * c)) / 2 / a,
            t2 = (-b - math.sqrt(b * b - 4 * a * c)) / 2 / a,
            y = [p1y, p2y],
            x = [p1x, p2x],
            dot;
        abs(t1) > "1e12" && (t1 = .5);
        abs(t2) > "1e12" && (t2 = .5);
        if (t1 > 0 && t1 < 1) {
            dot = findDotAtSegment(p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y, t1);
            x.push(dot.x);
            y.push(dot.y);
        }
        if (t2 > 0 && t2 < 1) {
            dot = findDotAtSegment(p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y, t2);
            x.push(dot.x);
            y.push(dot.y);
        }
        a = (c2y - 2 * c1y + p1y) - (p2y - 2 * c2y + c1y);
        b = 2 * (c1y - p1y) - 2 * (c2y - c1y);
        c = p1y - c1y;
        t1 = (-b + math.sqrt(b * b - 4 * a * c)) / 2 / a;
        t2 = (-b - math.sqrt(b * b - 4 * a * c)) / 2 / a;
        abs(t1) > "1e12" && (t1 = .5);
        abs(t2) > "1e12" && (t2 = .5);
        if (t1 > 0 && t1 < 1) {
            dot = findDotAtSegment(p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y, t1);
            x.push(dot.x);
            y.push(dot.y);
        }
        if (t2 > 0 && t2 < 1) {
            dot = findDotAtSegment(p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y, t2);
            x.push(dot.x);
            y.push(dot.y);
        }
        return {
            min: {x: mmin.apply(0, x), y: mmin.apply(0, y)},
            max: {x: mmax.apply(0, x), y: mmax.apply(0, y)}
        };
    }
    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) {
                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":
                        nx = d.x + (d.x - (d.bx || d.x));
                        ny = d.y + (d.y - (d.by || d.y));
                        path = ["C", nx, ny].concat(path.slice(1));
                        break;
                    case "T":
                        d.qx = d.x + (d.x - (d.qx || d.x));
                        d.qy = d.y + (d.y - (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) {
                        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;
                    a1.x = path1[i][1];
                    a1.y = path1[i][2];
                    ii = mmax(p.length, p2 && p2.length || 0);
                }
            };
        for (var i = 0, ii = mmax(p.length, p2 && p2.length || 0); i < ii; i++) {
            p[i] = processPath(p[i], attrs);
            fixArc(p, i);
            p2 && (p2[i] = processPath(p2[i], attrs2));
            p2 && fixArc(p2, i);
            fixM(p, p2, attrs, attrs2, i);
            fixM(p2, p, attrs2, attrs, i);
            var seg = p[i],
                seg2 = p2 && p2[i],
                seglen = seg.length,
                seg2len = p2 && seg2.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;
            attrs2.bx = p2 && (toFloat(seg2[seg2len - 4]) || attrs2.x);
            attrs2.by = p2 && (toFloat(seg2[seg2len - 3]) || attrs2.y);
            attrs2.x = p2 && seg2[seg2len - 2];
            attrs2.y = p2 && seg2[seg2len - 1];
        }
        if (!p2) {
            pth.curve = pathClone(p);
        }
        return p2 ? [p, p2] : p;
    }
    function mapPath(path, matrix) {
        if (!matrix) {
            return path;
        }
        var x, y, i, j, ii, jj, pathi;
        path = path2curve(path);
        for (i = 0, ii = path.length; i < ii; i++) {
            pathi = path[i];
            for (j = 1, jj = pathi.length; j < jj; j += 2) {
                x = matrix.x(pathi[j], pathi[j + 1]);
                y = matrix.y(pathi[j], pathi[j + 1]);
                pathi[j] = x;
                pathi[j + 1] = y;
            }
        }
        return path;
    }

    // http://schepers.cc/getting-to-the-point
    function catmullRom2bezier(crp, z) {
        var d = [];
        for (var i = 0, iLen = crp.length; iLen - 2 * !z > i; i += 2) {
            var p = [
                        {x: +crp[i - 2], y: +crp[i - 1]},
                        {x: +crp[i],     y: +crp[i + 1]},
                        {x: +crp[i + 2], y: +crp[i + 3]},
                        {x: +crp[i + 4], y: +crp[i + 5]}
                    ];
            if (z) {
                if (!i) {
                    p[0] = {x: +crp[iLen - 2], y: +crp[iLen - 1]};
                } else if (iLen - 4 == i) {
                    p[3] = {x: +crp[0], y: +crp[1]};
                } else if (iLen - 2 == i) {
                    p[2] = {x: +crp[0], y: +crp[1]};
                    p[3] = {x: +crp[2], y: +crp[3]};
                }
            } else {
                if (iLen - 4 == i) {
                    p[3] = p[2];
                } else if (!i) {
                    p[0] = {x: +crp[i], y: +crp[i + 1]};
                }
            }
            d.push(["C",
                  (-p[0].x + 6 * p[1].x + p[2].x) / 6,
                  (-p[0].y + 6 * p[1].y + p[2].y) / 6,
                  (p[1].x + 6 * p[2].x - p[3].x) / 6,
                  (p[1].y + 6*p[2].y - p[3].y) / 6,
                  p[2].x,
                  p[2].y
            ]);
        }

        return d;
    }

    // export
    Savage.path = paths;

    /*\
     * Savage.path.getTotalLength
     [ method ]
     **
     * Returns length of the given path in pixels.
     **
     > Parameters
     **
     - path (string) SVG path string.
     **
     = (number) length.
    \*/
    Savage.path.getTotalLength = getTotalLength;
    /*\
     * Savage.path.getPointAtLength
     [ method ]
     **
     * Return coordinates of the point located at the given length on the given path.
     **
     > Parameters
     **
     - path (string) SVG path string
     - length (number)
     **
     = (object) representation of the point:
     o {
     o     x: (number) x coordinate
     o     y: (number) y coordinate
     o     alpha: (number) angle of derivative
     o }
    \*/
    Savage.path.getPointAtLength = getPointAtLength;
    /*\
     * Savage.path.getSubpath
     [ method ]
     **
     * Return subpath of a given path from given length to given length.
     **
     > Parameters
     **
     - path (string) SVG path string
     - from (number) position of the start of the segment
     - to (number) position of the end of the segment
     **
     = (string) pathstring for the segment
    \*/
    Savage.path.getSubpath = function (path, from, to) {
        if (this.getTotalLength(path) - to < 1e-6) {
            return getSubpathsAtLength(path, from).end;
        }
        var a = getSubpathsAtLength(path, to, 1);
        return from ? getSubpathsAtLength(a, from).end : a;
    };
    /*\
     * Element.getTotalLength
     [ method ]
     **
     * Returns length of the path in pixels. Only works for element of “path” type.
     = (number) length.
    \*/
    elproto.getTotalLength = function () {
        if (this.node.getTotalLength) {
            return this.node.getTotalLength();
        }
    };
    /*\
     * Element.getPointAtLength
     [ method ]
     **
     * Return coordinates of the point located at the given length on the given path. Only works for element of “path” type.
     **
     > Parameters
     **
     - length (number)
     **
     = (object) representation of the point:
     o {
     o     x: (number) x coordinate
     o     y: (number) y coordinate
     o     alpha: (number) angle of derivative
     o }
    \*/
    elproto.getPointAtLength = function (length) {
        return getPointAtLength(this.attr("d"), length);
    };
    /*\
     * Element.getSubpath
     [ method ]
     **
     * Return subpath of a given element from given length to given length. Only works for element of “path” type.
     **
     > Parameters
     **
     - from (number) position of the start of the segment
     - to (number) position of the end of the segment
     **
     = (string) pathstring for the segment
    \*/
    elproto.getSubpath = function (from, to) {
        return getSubpath(this.attr("d"), from, to);
    };
    Savage._.box = box;
    /*\
     * Savage.findDotsAtSegment
     [ method ]
     **
     * Utility method
     **
     * Find dot coordinates on the given cubic bezier curve at the given t.
     > Parameters
     - p1x (number) x of the first point of the curve
     - p1y (number) y of the first point of the curve
     - c1x (number) x of the first anchor of the curve
     - c1y (number) y of the first anchor of the curve
     - c2x (number) x of the second anchor of the curve
     - c2y (number) y of the second anchor of the curve
     - p2x (number) x of the second point of the curve
     - p2y (number) y of the second point of the curve
     - t (number) position on the curve (0..1)
     = (object) point information in format:
     o {
     o     x: (number) x coordinate of the point
     o     y: (number) y coordinate of the point
     o     m: {
     o         x: (number) x coordinate of the left anchor
     o         y: (number) y coordinate of the left anchor
     o     }
     o     n: {
     o         x: (number) x coordinate of the right anchor
     o         y: (number) y coordinate of the right anchor
     o     }
     o     start: {
     o         x: (number) x coordinate of the start of the curve
     o         y: (number) y coordinate of the start of the curve
     o     }
     o     end: {
     o         x: (number) x coordinate of the end of the curve
     o         y: (number) y coordinate of the end of the curve
     o     }
     o     alpha: (number) angle of the curve derivative at the point
     o }
    \*/
    Savage.path.findDotsAtSegment = findDotsAtSegment;
    /*\
     * Savage.path.bezierBBox
     [ method ]
     **
     * Utility method
     **
     * Return bounding box of a given cubic bezier curve
     > Parameters
     - p1x (number) x of the first point of the curve
     - p1y (number) y of the first point of the curve
     - c1x (number) x of the first anchor of the curve
     - c1y (number) y of the first anchor of the curve
     - c2x (number) x of the second anchor of the curve
     - c2y (number) y of the second anchor of the curve
     - p2x (number) x of the second point of the curve
     - p2y (number) y of the second point of the curve
     * or
     - bez (array) array of six points for bezier curve
     = (object) point information in format:
     o {
     o     min: {
     o         x: (number) x coordinate of the left point
     o         y: (number) y coordinate of the top point
     o     }
     o     max: {
     o         x: (number) x coordinate of the right point
     o         y: (number) y coordinate of the bottom point
     o     }
     o }
    \*/
    Savage.path.bezierBBox = bezierBBox;
    /*\
     * Savage.path.isPointInsideBBox
     [ method ]
     **
     * Utility method
     **
     * Returns `true` if given point is inside bounding box.
     > Parameters
     - bbox (string) bounding box
     - x (string) x coordinate of the point
     - y (string) y coordinate of the point
     = (boolean) `true` if point inside
    \*/
    Savage.path.isPointInsideBBox = isPointInsideBBox;
    /*\
     * Savage.path.isBBoxIntersect
     [ method ]
     **
     * Utility method
     **
     * Returns `true` if two bounding boxes intersect
     > Parameters
     - bbox1 (string) first bounding box
     - bbox2 (string) second bounding box
     = (boolean) `true` if they intersect
    \*/
    Savage.path.isBBoxIntersect = isBBoxIntersect;
    /*\
     * Savage.path.intersection
     [ method ]
     **
     * Utility method
     **
     * Finds intersections of two paths
     > Parameters
     - path1 (string) path string
     - path2 (string) path string
     = (array) dots of intersection
     o [
     o     {
     o         x: (number) x coordinate of the point
     o         y: (number) y coordinate of the point
     o         t1: (number) t value for segment of path1
     o         t2: (number) t value for segment of path2
     o         segment1: (number) order number for segment of path1
     o         segment2: (number) order number for segment of path2
     o         bez1: (array) eight coordinates representing beziér curve for the segment of path1
     o         bez2: (array) eight coordinates representing beziér curve for the segment of path2
     o     }
     o ]
    \*/
    Savage.path.intersection = pathIntersection;
    Savage.path.intersectionNumber = pathIntersectionNumber;
    /*\
     * Savage.path.isPointInside
     [ method ]
     **
     * Utility method
     **
     * Returns `true` if given point is inside a given closed path.
     > Parameters
     - path (string) path string
     - x (number) x of the point
     - y (number) y of the point
     = (boolean) true, if point is inside the path
    \*/
    Savage.path.isPointInside = isPointInsidePath;
    /*\
     * Savage.pathBBox
     [ method ]
     **
     * Utility method
     **
     * Return bounding box of a given path
     > Parameters
     - path (string) path string
     = (object) bounding box
     o {
     o     x: (number) x coordinate of the left top point of the box
     o     y: (number) y coordinate of the left top point of the box
     o     x2: (number) x coordinate of the right bottom point of the box
     o     y2: (number) y coordinate of the right bottom point of the box
     o     width: (number) width of the box
     o     height: (number) height of the box
     o }
    \*/
    Savage.path.getBBox = pathBBox;
    Savage.path.get = getPath;
    /*\
     * Savage.path.toRelative
     [ method ]
     **
     * Utility method
     **
     * Converts path coordinates into relative values.
     > Parameters
     - path (string) path string
     = (array) path string
    \*/
    Savage.path.toRelative = pathToRelative;
    /*\
     * Savage.path.toAbsolute
     [ method ]
     **
     * Utility method
     **
     * Converts path coordinates into absolute values.
     > Parameters
     - path (string) path string
     = (array) path string
    \*/
    Savage.path.toAbsolute = pathToAbsolute;
    /*\
     * Savage.path.toCubic
     [ method ]
     **
     * Utility method
     **
     * Converts path to a new path where all segments are cubic bezier curves.
     > Parameters
     - pathString (string|array) path string or array of segments
     = (array) array of segments.
    \*/
    Savage.path.toCubic = path2curve;
    /*\
     * Savage.path.map
     [ method ]
     **
     * Transform the path string with given matrix.
     > Parameters
     - path (string) path string
     - matrix (object) see @Matrix
     = (string) transformed path string
    \*/
    Savage.path.map = mapPath;
    Savage.path.toString = toString;
    Savage.path.clone = pathClone;
});