* @copyright Wout Fierens <wout@mick-wout.com.com>
* @license MIT
*
-* BUILT: Sun Nov 13 2016 14:06:31 GMT+0100 (CET)
+* BUILT: Tue Dec 20 2016 04:06:31 GMT-0500 (EST)
*/;
(function(root, factory) {
if (typeof define === 'function' && define.amd) {
return this
}
+ // Test if the passed path array use the same commands as this path array
+, haveSameCommands: function(pathArray) {
+ var i, il, haveSameCommands
+
+ pathArray = new SVG.PathArray(pathArray)
+
+ haveSameCommands = this.value.length === pathArray.value.length
+ for(i = 0, il = this.value.length; haveSameCommands && i < il; i++) {
+ haveSameCommands = this.value[i][0] === pathArray.value[i][0]
+ }
+
+ return haveSameCommands
+ }
+ // Make path array morphable
+, morph: function(pathArray) {
+ var pathsMorphable
+
+ this.destination = new SVG.PathArray(pathArray)
+
+ if(this.haveSameCommands(this.destination)) {
+ this.sourceMorphable = this
+ this.destinationMorphable = this.destination
+ } else {
+ pathsMorphable = SVG.utils.makePathsMorphable(this.value, this.destination)
+ this.sourceMorphable = pathsMorphable[0]
+ this.destinationMorphable = pathsMorphable[1]
+ }
+
+ return this
+ }
+ // Get morphed path array at given position
+, at: function(pos) {
+ if(pos === 1) {
+ return this.destination
+ } else if(pos === 0) {
+ return this
+ } else {
+ var sourceArray = this.sourceMorphable.value
+ , destinationArray = this.destinationMorphable.value
+ , array = [], pathArray = new SVG.PathArray()
+ , i, il, j, jl
+
+ // Animate has specified in the SVG spec
+ // See: https://www.w3.org/TR/SVG11/paths.html#PathElement
+ for (i = 0, il = sourceArray.length; i < il; i++) {
+ array[i] = [sourceArray[i][0]]
+ for(j=1, jl = sourceArray[i].length; j < jl; j++) {
+ array[i][j] = sourceArray[i][j] + (destinationArray[i][j] - sourceArray[i][j]) * pos
+ }
+ // For the two flags of the elliptical arc command, the SVG spec say:
+ // Flags and booleans are interpolated as fractions between zero and one, with any non-zero value considered to be a value of one/true
+ // Elliptical arc command as an array followed by corresponding indexes:
+ // ['A', rx, ry, x-axis-rotation, large-arc-flag, sweep-flag, x, y]
+ // 0 1 2 3 4 5 6 7
+ if(array[i][0] === 'A') {
+ array[i][4] = +(array[i][4] != 0)
+ array[i][5] = +(array[i][5] != 0)
+ }
+ }
+
+ // Directly modify the value of a path array, this is done this way for performance
+ pathArray.value = array
+ return pathArray
+ }
+ }
// Absolutize and parse path to array
, parse: function(array) {
// if it's already a patharray, no need to parse it
}
})
+
// Module for unit convertions
SVG.Number = SVG.invent({
// Initialize
{x:x[0], y:x[1]} :
typeof x === 'object' ?
{x:x.x, y:x.y} :
- y != null ?
- {x:x, y:y} : base
-
+ x != null ?
+ {x:x, y:(y != null ? y : x)} : base // If y has no value, then x is used has its value
+ // This allow element-wise operations to be passed a single number
// merge source
this.x = source.x
this.y = source.y
return new SVG.Point(this)
}
// Morph one point into another
- , morph: function(point) {
+ , morph: function(x, y) {
// store new destination
- this.destination = new SVG.Point(point)
+ this.destination = new SVG.Point(x, y)
return this
}
, transform: function(matrix) {
return new SVG.Point(this.native().matrixTransform(matrix.native()))
}
-
+ // return an array of the x and y coordinates
+ , toArray: function() {
+ return [this.x, this.y]
+ }
+ // perform an element-wise addition with the passed point or number
+ , plus: function(x, y) {
+ var point = new SVG.Point(x, y)
+ return new SVG.Point(this.x + point.x, this.y + point.y)
+ }
+ // perform an element-wise subtraction with the passed point or number
+ , minus: function(x, y) {
+ var point = new SVG.Point(x, y)
+ return new SVG.Point(this.x - point.x, this.y - point.y)
+ }
+ // perform an element-wise multiplication with the passed point or number
+ , times: function(x, y) {
+ var point = new SVG.Point(x, y)
+ return new SVG.Point(this.x * point.x, this.y * point.y)
+ }
+ // perform an element-wise division with the passed point or number
+ , divide: function(x, y) {
+ var point = new SVG.Point(x, y)
+ return new SVG.Point(this.x / point.x, this.y / point.y)
+ }
+ // calculate the Euclidean norm
+ , norm: function() {
+ return Math.sqrt(this.x*this.x + this.y*this.y)
+ }
+ // calculate the distance to the passed point
+ , distance: function(x, y) {
+ return this.minus(x, y).norm()
+ }
}
})
// Create matrix array for looping
var abcdef = 'abcdef'.split('')
+// Take two path array that don't have the same commands (which mean that they
+// cannot be morphed in one another) and return 2 equivalent path array (meaning
+// that they produce the same shape as the passed path array) that have the
+// same commands (moveto and curveto)
+//
+// Algorithm used:
+// First, convert every path segment of the two passed paths into equivalent cubic Bezier curves.
+// Then, calculate the positions relative to the total length of the path of the endpoint of all those cubic Bezier curves.
+// After that, split the Bezier curves of the source at the positions that the destination have that are not common to the source and vice versa.
+// Finally, make the source and destination have the same number of subpaths.
+SVG.utils.makePathsMorphable = function (sourcePathArray, destinationPathArray) {
+ var source, sourcePositions, sourcePositionsToSplitAt
+ , destination, destinationPositions, destinationPositionsToSplitAt
+ , i, il, j, jl
+ , s, d
+ , sourceSubpath, destinationSubpath, lastSegPt
+
+ // Convert every path segments into equivalent cubic Bezier curves
+ source = cubicSuperPath(sourcePathArray)
+ destination = cubicSuperPath(destinationPathArray)
+
+ // The positions relative to the total length of the path is calculated for the endpoint of all those cubic bezier curves
+ sourcePositions = cspPositions(source)
+ destinationPositions = cspPositions(destination)
+
+ // Find the positions that the destination have that are not in the source and vice versa
+ sourcePositionsToSplitAt = []
+ destinationPositionsToSplitAt = []
+ i = 0, il = sourcePositions.length
+ j = 0, jl = destinationPositions.length
+ while(i < il && j < jl) {
+ // Test if the two values are equal taking into account the imprecision of floating point number
+ if (Math.abs(sourcePositions[i] - destinationPositions[j]) < 0.000001) {
+ i++
+ j++
+ } else if(sourcePositions[i] > destinationPositions[j]){
+ sourcePositionsToSplitAt.push(destinationPositions[j++])
+ } else {
+ destinationPositionsToSplitAt.push(sourcePositions[i++])
+ }
+ }
+ // If there are still some destination positions left, they all are not in the source and vice versa
+ sourcePositionsToSplitAt = sourcePositionsToSplitAt.concat(destinationPositions.slice(j))
+ destinationPositionsToSplitAt = destinationPositionsToSplitAt.concat(sourcePositions.slice(i))
+
+ // Split the source and the destination at the positions they don't have in common
+ cspSplitAtPositions(source, sourcePositions, sourcePositionsToSplitAt)
+ cspSplitAtPositions(destination, destinationPositions, destinationPositionsToSplitAt)
+
+
+ // Break paths so that corresponding subpaths have an equal number of segments
+ s = source, source = [], sourceSubpath = s[i = 0]
+ d = destination, destination = [], destinationSubpath = d[j = 0]
+ while (sourceSubpath && destinationSubpath) {
+ // Push REFERENCES to the current subpath arrays in their respective array
+ source.push(sourceSubpath)
+ destination.push(destinationSubpath)
+
+ il = sourceSubpath.length
+ jl = destinationSubpath.length
+
+ // If the current subpath of the source and the current subpath of the destination don't
+ // have the same length, that mean that the biggest of the two must be split in two
+ if(il > jl) {
+ lastSegPt = sourceSubpath[jl-1]
+ // Perform the split using splice that change the content of the array by removing elements and returning them in an array
+ sourceSubpath = sourceSubpath.splice(jl)
+ sourceSubpath.unshift(lastSegPt) // The last segment point is duplicated since these two segments must be joined together
+ destinationSubpath = d[++j] // This subpath has been accounted for, past to the next
+ } else if(il < jl) {
+ lastSegPt = destinationSubpath[il-1]
+ destinationSubpath = destinationSubpath.splice(il)
+ destinationSubpath.unshift(lastSegPt)
+ sourceSubpath = s[++i]
+ } else {
+ sourceSubpath = s[++i]
+ destinationSubpath = d[++j]
+ }
+ }
+
+ // Convert in path array and return
+ return [uncubicSuperPath(source), uncubicSuperPath(destination)]
+}
+
+
+
+
+
+
+// This function converts every segment of a path array into equivalent cubic Bezier curves
+// and return the results in a 3 dimensional array that have the following hierarchy:
+// Cubic super path: [ ]
+// Segments: [ ] ...
+// Segment points: [SVG.Point, SVG.Point, SVG.Point] ...
+//
+// A segment point is a point with the two control points that are attached to it:
+// [First control point, Point, Second control point]
+//
+// If the passed path array cannot be converted in a cubic super path, this function return an empty array.
+function cubicSuperPath(pathArray) {
+ pathArray = new SVG.PathArray(pathArray)
+
+ var cubicSP = []
+ , subpath = null
+ , subpathStartPt = null
+ , lastPt = null
+ , lastCtrlPt = null
+ , i, il, cmd = null, params, lastCmd
+ , start, control, end
+ , arcSegPoints, segPt
+
+ for (i = 0, il = pathArray.value.length; i < il; i++) {
+ lastCmd = cmd
+ cmd = pathArray.value[i][0]
+ params = pathArray.value[i].slice(1)
+
+ switch (cmd) {
+ case 'M': // moveto
+ // Parameters: x y
+ if (lastPt) {
+ subpath.push([lastCtrlPt, lastPt, lastPt.clone()])
+ }
+ subpath = []
+ cubicSP.push(subpath) // Push a reference to the current subpath array in the cubic super path array
+ subpathStartPt = new SVG.Point(params)
+ lastPt = subpathStartPt.clone()
+ lastCtrlPt = subpathStartPt.clone()
+ break
+
+ case 'L': // lineto
+ // Parameters: x y
+ subpath.push([lastCtrlPt, lastPt, lastPt.clone()])
+ lastPt = new SVG.Point(params)
+ lastCtrlPt = lastPt.clone()
+ break
+
+ case 'H': // horizontal lineto
+ // Parameters: x
+ subpath.push([lastCtrlPt, lastPt, lastPt.clone()])
+ lastPt = new SVG.Point(params[0], lastPt.y)
+ lastCtrlPt = lastPt.clone()
+ break
+
+ case 'V': // vertical lineto
+ // Parameters: y
+ subpath.push([lastCtrlPt, lastPt, lastPt.clone()])
+ lastPt = new SVG.Point(lastPt.x, params[0])
+ lastCtrlPt = lastPt.clone()
+ break
+
+ case 'C': // curveto
+ // Parameters: x1 y1 x2 y2 x y
+ subpath.push([lastCtrlPt, lastPt, new SVG.Point(params.slice(0,2))])
+ lastPt = new SVG.Point(params.slice(4,6))
+ lastCtrlPt = new SVG.Point(params.slice(2,4))
+ break
+
+ case 'S': // shorthand/smooth curveto
+ // Parameters: x2 y2 x y
+ // For this version of curveto, the first control point is the reflection of the second control point on the previous command relative to the current point
+ // If the previous command is not a curveto command, then the first control point is the same as the current point
+ if(lastCmd === 'C' || lastCmd === 'S') {
+ subpath.push([lastCtrlPt, lastPt, lastPt.times(2).minus(lastCtrlPt)])
+ } else {
+ subpath.push([lastCtrlPt, lastPt, lastPt.clone()])
+ }
+ lastPt = new SVG.Point(params.slice(2,4))
+ lastCtrlPt = new SVG.Point(params.slice(0,2))
+ break
+
+ case 'Q': // quadratic Bezier curveto
+ // Parameters: x1 y1 x y
+ // For an explanation of the method used, see: https://pomax.github.io/bezierinfo/#reordering
+ start = lastPt
+ control = new SVG.Point(params.slice(0,2))
+ end = new SVG.Point(params.slice(2,4))
+
+ subpath.push([lastCtrlPt, start, start.times(1/3).plus(control.times(2/3))])
+ lastPt = end
+ lastCtrlPt = control.times(2/3).plus(end.times(1/3))
+ break
+
+ case 'T': // shorthand/smooth quadratic Bézier curveto
+ // Parameters: x y
+ // For this version of quadratic Bézier curveto, the control point is the reflection of the control point on the previous command relative to the current point
+ // If the previous command is not a quadratic Bézier curveto command, then the control point is the same as the current point
+ start = lastPt
+ if(lastCmd === 'Q' || lastCmd === 'T') {
+ control = start.times(2).minus(control)
+ } else {
+ control = start
+ }
+ end = new SVG.Point(params.slice(0,2))
+
+ subpath.push([lastCtrlPt, start, start.times(1/3).plus(control.times(2/3))])
+ lastPt = end
+ lastCtrlPt = control.times(2/3).plus(end.times(1/3))
+ break
+
+ case 'A': // elliptical arc
+ // Parameters: rx ry x-axis-rotation large-arc-flag sweep-flag x y
+ arcSegPoints = arcToPath(lastPt, params)
+ arcSegPoints[0][0] = lastCtrlPt
+ segPt = arcSegPoints.pop()
+ lastPt = segPt[1]
+ lastCtrlPt = segPt[0]
+ Array.prototype.push.apply(subpath, arcSegPoints)
+ break
+
+ case 'Z': // closepath
+ // Parameters: none
+ subpath.push([lastCtrlPt, lastPt, lastPt.clone()])
+ // Close the path only if it is not already closed
+ if(lastPt.x != subpathStartPt.x && lastPt.y != subpathStartPt.y) {
+ lastPt = subpathStartPt
+ lastCtrlPt = subpathStartPt.clone()
+ } else {
+ lastPt = null
+ lastCtrlPt = null
+ }
+ break
+ }
+ }
+
+ // Push final segment point if any
+ if(lastPt) {
+ subpath.push([lastCtrlPt, lastPt, lastPt.clone()])
+ }
+
+ return cubicSP
+}
+
+
+// This function convert a cubic super path into a path array
+function uncubicSuperPath (cubicSP) {
+ var i, il, j, jl, array = [], pathArray = new SVG.PathArray, subpath
+
+ for (i = 0, il = cubicSP.length; i < il; i++) {
+ subpath = cubicSP[i]
+
+ if (subpath.length) {
+ array.push(['M'].concat(subpath[0][1].toArray()))
+
+ for (j = 1, jl = subpath.length; j < jl; j++) {
+ array.push(['C'].concat(subpath[j-1][2].toArray(), subpath[j][0].toArray(), subpath[j][1].toArray()))
+ }
+ }
+ }
+
+ // Directly modify the value of a path array, this is done this way for performance
+ pathArray.value = array
+ return pathArray
+}
+
+// Convert an arc segment into equivalent cubic Bezier curves
+// Depending on the arc, up to 4 curves might be used to represent it since a
+// curve gives a good approximation for only a quarter of an ellipse
+// The curves are returned as an array of segment points:
+// [ [SVG.Point, SVG.Point, SVG.Point] ... ]
+function arcToPath(lastPt, params) {
+ // Parameters extraction, handle out-of-range parameters as specified in the SVG spec
+ // See: https://www.w3.org/TR/SVG11/implnote.html#ArcOutOfRangeParameters
+ var rx = Math.abs(params[0]), ry = Math.abs(params[1]), xAxisRotation = params[2] % 360
+ , largeArcFlag = params[3], sweepFlag = params[4], x2 = params[5], y2 = params[6]
+ , A = lastPt, B = new SVG.Point(x2, y2)
+ , primedCoord, lambda, mat, k, c, cSquare, t, O, OA, OB, tetaStart, tetaEnd
+ , deltaTeta, nbSectors, f, arcSegPoints, angle, sinAngle, cosAngle, pt, i, il
+
+ // Ensure radii are non-zero
+ if(rx === 0 || ry === 0 || (A.x === B.x && A.y === B.y)) {
+ // treat this arc as a straight line segment
+ return [[A, A.clone(), A.clone()], [B, B.clone(), B.clone()]]
+ }
+
+ // Ensure radii are large enough using the algorithm provided in the SVG spec
+ // See: https://www.w3.org/TR/SVG11/implnote.html#ArcCorrectionOutOfRangeRadii
+ primedCoord = A.minus(B).divide(2).transform(new SVG.Matrix().rotate(xAxisRotation))
+ lambda = (primedCoord.x * primedCoord.x) / (rx * rx) + (primedCoord.y * primedCoord.y) / (ry * ry)
+ if(lambda > 1) {
+ lambda = Math.sqrt(lambda)
+ rx = lambda*rx
+ ry = lambda*ry
+ }
+
+ // To simplify calculations, we make the arc part of a unit circle (rayon is 1) instead of an ellipse
+ mat = new SVG.Matrix().rotate(xAxisRotation).scale(1/rx, 1/ry).rotate(-xAxisRotation)
+ A = A.transform(mat)
+ B = B.transform(mat)
+
+ // Calculate the horizontal and vertical distance between the initial and final point of the arc
+ k = [B.x-A.x, B.y-A.y]
+
+ // Find the length of the chord formed by A and B
+ cSquare = k[0]*k[0] + k[1]*k[1]
+ c = Math.sqrt(cSquare)
+
+ // Calculate the ratios of the horizontal and vertical distance on the length of the chord
+ k[0] /= c
+ k[1] /= c
+
+ // Calculate the distance between the circle center and the chord midpoint
+ // using this formula: t = sqrt(r^2 - c^2 / 4)
+ // where t is the distance between the cirle center and the chord midpoint,
+ // r is the rayon of the circle and c is the chord length
+ // From: http://www.ajdesigner.com/phpcircle/circle_segment_chord_t.php
+ // Because of the imprecision of floating point numbers, cSquare might end
+ // up being slightly above 4 which would result in a negative radicand
+ // To prevent that, a test is made before computing the square root
+ t = (cSquare < 4) ? Math.sqrt(1 - cSquare/4) : 0
+
+ // For most situations, there are actually two different ellipses that
+ // satisfy the constraints imposed by the points A and B, the radii rx and ry,
+ // and the xAxisRotation
+ // When the flags largeArcFlag and sweepFlag are equal, it means that the
+ // second ellipse is used as a solution
+ // See: https://www.w3.org/TR/SVG/paths.html#PathDataEllipticalArcCommands
+ if(largeArcFlag === sweepFlag) {
+ t *= -1
+ }
+
+ // Calculate the coordinates of the center of the circle from the midpoint of the chord
+ // This is done by multiplying the ratios calculated previously by the distance between
+ // the circle center and the chord midpoint and using these values to go from the midpoint
+ // to the center of the circle
+ // The negative of the vertical distance ratio is used to modify the x coordinate while
+ // the horizontal distance ratio is used to modify the y coordinate
+ // That is because the center of the circle is perpendicular to the chord and perpendicular
+ // lines are negative reciprocals
+ O = new SVG.Point((B.x+A.x)/2 + t*-k[1], (B.y+A.y)/2 + t*k[0])
+ // Move the center of the circle at the origin
+ OA = A.minus(O)
+ OB = B.minus(O)
+
+ // Calculate the start and end angle
+ tetaStart = Math.acos(OA.x/OA.norm())
+ if (OA.y < 0) {
+ tetaStart *= -1
+ }
+ tetaEnd = Math.acos(OB.x/OB.norm())
+ if (OB.y < 0) {
+ tetaEnd *= -1
+ }
+
+ // If sweep-flag is '1', then the arc will be drawn in a "positive-angle" direction,
+ // make sure that the end angle is above the start angle
+ if (sweepFlag && tetaStart > tetaEnd) {
+ tetaEnd += 2*Math.PI
+ }
+ // If sweep-flag is '0', then the arc will be drawn in a "negative-angle" direction,
+ // make sure that the end angle is below the start angle
+ if (!sweepFlag && tetaStart < tetaEnd) {
+ tetaEnd -= 2*Math.PI
+ }
+
+ // Find the number of Bezier curves that are required to represent the arc
+ // A cubic Bezier curve gives a good enough approximation when representing at most a quarter of a circle
+ nbSectors = Math.ceil(Math.abs(tetaStart-tetaEnd) * 2/Math.PI)
+
+ // Calculate the coordinates of the points of all the Bezier curves required to represent the arc
+ // For an in-depth explanation of this part see: http://pomax.github.io/bezierinfo/#circles_cubic
+ arcSegPoints = []
+ angle = tetaStart
+ deltaTeta = (tetaEnd-tetaStart)/nbSectors
+ f = 4*Math.tan(deltaTeta/4)/3
+ for (i = 0; i <= nbSectors; i++) { // The <= is because a Bezier curve have a start and a endpoint
+ cosAngle = Math.cos(angle)
+ sinAngle = Math.sin(angle)
+
+ pt = O.plus(cosAngle, sinAngle)
+ arcSegPoints[i] = [pt.plus(+f*sinAngle, -f*cosAngle), pt, pt.plus(-f*sinAngle, +f*cosAngle)]
+
+ angle += deltaTeta
+ }
+
+ // Remove the first control point of the first segment point and remove the second control point of the last segment point
+ // These two control points are not used in the approximation of the arc, that is why they are removed
+ arcSegPoints[0][0] = arcSegPoints[0][1].clone()
+ arcSegPoints[arcSegPoints.length-1][2] = arcSegPoints[arcSegPoints.length-1][1].clone()
+
+ // Revert the transformation that was applied to make the arc part of a unit circle instead of an ellipse
+ mat = new SVG.Matrix().rotate(xAxisRotation).scale(rx, ry).rotate(-xAxisRotation)
+ for (i = 0, il = arcSegPoints.length; i < il; i++) {
+ arcSegPoints[i][0] = arcSegPoints[i][0].transform(mat)
+ arcSegPoints[i][1] = arcSegPoints[i][1].transform(mat)
+ arcSegPoints[i][2] = arcSegPoints[i][2].transform(mat)
+ }
+
+ return arcSegPoints
+}
+
+
+// Use de Casteljau's algorithm to split a cubic Bezier curve
+// For a description of the algorithm, see: https://pomax.github.io/bezierinfo/#decasteljau
+// Return an array of 3 segment points
+function cspSegSplit(segPt1, segPt2, t) {
+ segPt1 = [segPt1[0].clone(), segPt1[1].clone(), segPt1[2].clone()]
+ segPt2 = [segPt2[0].clone(), segPt2[1].clone(), segPt2[2].clone()]
+
+ var m1 = segPt1[1].morph(segPt1[2]).at(t)
+ , m2 = segPt1[2].morph(segPt2[0]).at(t)
+ , m3 = segPt2[0].morph(segPt2[1]).at(t)
+ , m4 = m1.morph(m2).at(t)
+ , m5 = m2.morph(m3).at(t)
+ , m = m4.morph(m5).at(t)
+
+ return [[segPt1[0], segPt1[1], m1], [m4, m, m5], [m3, segPt2[1], segPt2[2]]]
+}
+
+
+// Find the length of a cubic Bezier curve using the built-in method getTotalLength of SVGPathElement
+// For more info, see: https://www.w3.org/TR/SVG11/paths.html#InterfaceSVGPathElement
+function cspSegLength(segPt1, segPt2) {
+ var path = document.createElementNS(SVG.ns, "path")
+ , d = ['M', segPt1[1].toArray(), 'C', segPt1[2].toArray(), segPt2[0].toArray(), segPt2[1].toArray()].join(' ')
+
+ path.setAttribute('d', d)
+
+ return path.getTotalLength()
+}
+
+
+// Find the length of all the cubic Bezier curves of a cubic super path and return
+// the results in a 2 dimensional array that have the following hierarchy:
+// Cubic super path lengths: [ ]
+// Segments lengths: [ ] ...
+// Cubic Bezier curves length: Number ...
+//
+// On the returned array, the property total is set to the sum of all the lengths
+function cspLengths(cubicSP) {
+ var total = 0
+ , subpath, lengths = [], lengthsSubpath, length
+ , i, il, j, jl
+
+ for (i = 0, il = cubicSP.length; i < il; i++) {
+ subpath = cubicSP[i]
+ lengthsSubpath = []
+ lengths[i] = lengthsSubpath // Save a reference to the current subpath lengths array in the cubic super path lengths array
+
+ for (j = 1, jl = subpath.length; j < jl; j++) {
+ length = cspSegLength(subpath[j-1], subpath[j])
+ lengthsSubpath[j-1] = length
+ total += length
+ }
+ }
+
+ lengths.total = total
+ return lengths
+}
+
+
+// Split a cubic Bezier curve at the given length ratio
+// Return an array of 3 segment points
+function cspSegSplitAtLengthRatio(segPt1, segPt2, lengthRatio) {
+ var t = 1.0
+ , tdiv = t
+ , currentLength = cspSegLength(segPt1, segPt2)
+ , targetLength = lengthRatio * currentLength
+ , diff = currentLength - targetLength
+ , split = cspSegSplit(segPt1, segPt2, t)
+ , maxNbLoops = 4096 // For not getting stuck in an infinite loop
+
+ while (Math.abs(diff) > 0.001 && maxNbLoops--) {
+ tdiv /= 2
+ t += (diff < 0) ? tdiv : -tdiv
+ split = cspSegSplit(segPt1, segPt2, t)
+ currentLength = cspSegLength(split[0], split[1])
+ diff = currentLength - targetLength
+ }
+
+ return split
+}
+
+
+
+// Find the position relative to the total length of the endpoint of all the cubic Bezier curves
+// of a cubic super path and return the results in a 1 dimensional array
+function cspPositions(cubicSP) {
+ var lengths = cspLengths(cubicSP), total = lengths.total
+ , pos = 0, positions = []
+ , i, il, j, jl
+
+ for (i = 0, il = lengths.length; i < il; i++) {
+ for (j = 0, jl = lengths[i].length; j < jl; j++) {
+ pos += lengths[i][j] / total
+ positions.push(pos)
+ }
+ }
+
+ return positions
+}
+
+// Split the passed cubic super path at the specified positions and return the results as a new cubic super path
+// For performance reasons, the positions of the passed cubic super path must also be provided
+function cspSplitAtPositions(cubicSP, positions, positionsToSplitAt){
+ var subpath, newSubpath
+ , accumNbPositions = 0, segPt, lengthRatio, split, pos, prevPos
+ , i, il, j, jl // indexes on the cubicSP array
+ , k = 0 // index on the positions array
+ , l = 0, ll = positionsToSplitAt.length
+
+ for (i = 0, il = cubicSP.length; i < il && l < ll; i++) {
+ subpath = cubicSP[i]
+ // The positions are only for the endpoints of the cubic Bezier curves, so
+ // a subpath need at least 2 segment points for a position to be on it
+ if(subpath.length < 2) {continue}
+ // Test if there are splits to be performed on the current subpath
+ if(positionsToSplitAt[l] < positions[accumNbPositions + subpath.length-2]) {
+ k = accumNbPositions
+ newSubpath = []
+ cubicSP[i] = newSubpath // Save a reference to the new current subpath array in the cubic super path array
+ pos = positions[k-1] || 0
+
+ // Recopy the content of the current subpath, performing splits where necessary
+ newSubpath.push(subpath[0])
+ for (j = 1, jl = subpath.length; j < jl; j++) {
+ prevPos = pos
+ pos = positions[k++]
+ segPt = subpath[j]
+
+ while(l < ll && positionsToSplitAt[l] < pos) {
+ lengthRatio = (positionsToSplitAt[l] - prevPos) / (pos - prevPos)
+ split = cspSegSplitAtLengthRatio(newSubpath[newSubpath.length-1], segPt, lengthRatio)
+ newSubpath[newSubpath.length-1] = split[0]
+ newSubpath.push(split[1])
+ segPt = split[2]
+ prevPos = positionsToSplitAt[l++]
+ }
+
+ newSubpath.push(segPt)
+ }
+ }
+
+ // -1 because positions are only for endpoints of Bezier curves
+ accumNbPositions += subpath.length - 1
+ }
+}
+
// Add CustomEvent to IE9 and IE10
if (typeof CustomEvent !== 'function') {
// Code from: https://developer.mozilla.org/en-US/docs/Web/API/CustomEvent
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s=i.extract();t.scaleX=1*t.scaleX/s.scaleX,t.scaleY=1*t.scaleY/s.scaleY}i=i.scale(t.scaleX,t.scaleY,t.cx,t.cy)}else if(null!=t.skew||null!=t.skewX||null!=t.skewY){if(f(t,n),t.skewX=null!=t.skew?t.skew:null!=t.skewX?t.skewX:0,t.skewY=null!=t.skew?t.skew:null!=t.skewY?t.skewY:0,!e){var s=i.extract();i=i.multiply((new g.Matrix).skew(s.skewX,s.skewY,t.cx,t.cy).inverse())}i=i.skew(t.skewX,t.skewY,t.cx,t.cy)}else t.flip?i=i.flip(t.flip,null==t.offset?n.bbox()["c"+t.flip]:t.offset):null==t.x&&null==t.y||(e?i=i.translate(t.x,t.y):(null!=t.x&&(i.e=t.x),null!=t.y&&(i.f=t.y)));return this.attr("transform",i)}}),g.extend(g.FX,{transform:function(t,e){var i,n=this.target();return"object"!=typeof t?(i=new g.Matrix(n).extract(),"string"==typeof t?i[t]:i):(e=!!e||!!t.relative,null!=t.a?i=new g.Matrix(t):null!=t.rotation?(f(t,n),i=new g.Rotate(t.rotation,t.cx,t.cy)):null!=t.scale||null!=t.scaleX||null!=t.scaleY?(f(t,n),t.scaleX=null!=t.scale?t.scale:null!=t.scaleX?t.scaleX:1,t.scaleY=null!=t.scale?t.scale:null!=t.scaleY?t.scaleY:1,i=new g.Scale(t.scaleX,t.scaleY,t.cx,t.cy)):null!=t.skewX||null!=t.skewY?(f(t,n),t.skewX=null!=t.skewX?t.skewX:0,t.skewY=null!=t.skewY?t.skewY:0,i=new g.Skew(t.skewX,t.skewY,t.cx,t.cy)):t.flip?i=(new g.Matrix).morph((new g.Matrix).flip(t.flip,null==t.offset?n.bbox()["c"+t.flip]:t.offset)):null==t.x&&null==t.y||(i=new g.Translate(t.x,t.y)),i?(i.relative=e,this.last().transforms.push(i),setTimeout(function(){this.start()}.bind(this),0),this):this)}}),g.extend(g.Element,{untransform:function(){return this.attr("transform",null)},matrixify:function(){var t=(this.attr("transform")||"").split(/\)\s*,?\s*/).slice(0,-1).map(function(t){var e=t.trim().split("(");return[e[0],e[1].split(g.regex.matrixElements).map(function(t){return parseFloat(t)})]}).reduce(function(t,e){return"matrix"==e[0]?t.multiply(l(e[1])):t[e[0]].apply(t,e[1])},new g.Matrix);return t},toParent:function(t){if(this==t)return this;var e=this.screenCTM(),i=t.rect(1,1),n=i.screenCTM().inverse();return i.remove(),this.addTo(t).untransform().transform(n.multiply(e)),this},toDoc:function(){return this.toParent(this.doc())}}),g.Transformation=g.invent({create:function(t,e){if(arguments.length>1&&"boolean"!=typeof e)return this.create([].slice.call(arguments));if("object"==typeof t)for(var i=0,n=this.arguments.length;i<n;++i)this[this.arguments[i]]=t[this.arguments[i]];if(Array.isArray(t))for(var i=0,n=this.arguments.length;i<n;++i)this[this.arguments[i]]=t[i];this.inversed=!1,e===!0&&(this.inversed=!0)},extend:{at:function(t){for(var e=[],i=0,n=this.arguments.length;i<n;++i)e.push(this[this.arguments[i]]);var s=this._undo||new g.Matrix;return s=(new g.Matrix).morph(g.Matrix.prototype[this.method].apply(s,e)).at(t),this.inversed?s.inverse():s},undo:function(t){for(var e=0,i=this.arguments.length;e<i;++e)t[this.arguments[e]]="undefined"==typeof this[this.arguments[e]]?0:t[this.arguments[e]];return t.cx=this.cx,t.cy=this.cy,this._undo=new(g[r(this.method)])(t,(!0)).at(1),this}}}),g.Translate=g.invent({parent:g.Matrix,inherit:g.Transformation,create:function(t,e){"object"==typeof t?this.constructor.call(this,t,e):this.constructor.call(this,[].slice.call(arguments))},extend:{arguments:["transformedX","transformedY"],method:"translate"}}),g.Rotate=g.invent({parent:g.Matrix,inherit:g.Transformation,create:function(t,e){"object"==typeof t?this.constructor.call(this,t,e):this.constructor.call(this,[].slice.call(arguments))},extend:{arguments:["rotation","cx","cy"],method:"rotate",at:function(t){var e=(new g.Matrix).rotate((new g.Number).morph(this.rotation-(this._undo?this._undo.rotation:0)).at(t),this.cx,this.cy);return this.inversed?e.inverse():e},undo:function(t){this._undo=t}}}),g.Scale=g.invent({parent:g.Matrix,inherit:g.Transformation,create:function(t,e){"object"==typeof t?this.constructor.call(this,t,e):this.constructor.call(this,[].slice.call(arguments))},extend:{arguments:["scaleX","scaleY","cx","cy"],method:"scale"}}),g.Skew=g.invent({parent:g.Matrix,inherit:g.Transformation,create:function(t,e){"object"==typeof t?this.constructor.call(this,t,e):this.constructor.call(this,[].slice.call(arguments))},extend:{arguments:["skewX","skewY","cx","cy"],method:"skew"}}),g.extend(g.Element,{style:function(t,e){if(0==arguments.length)return this.node.style.cssText||"";if(arguments.length<2)if("object"==typeof t)for(e in t)this.style(e,t[e]);else{if(!g.regex.isCss.test(t))return this.node.style[s(t)];t=t.split(";");for(var i=0;i<t.length;i++)e=t[i].split(":"),this.style(e[0].replace(/\s+/g,""),e[1])}else this.node.style[s(t)]=null===e||g.regex.isBlank.test(e)?"":e;return this}}),g.Parent=g.invent({create:function(t){this.constructor.call(this,t)},inherit:g.Element,extend:{children:function(){return g.utils.map(g.utils.filterSVGElements(this.node.childNodes),function(t){return g.adopt(t)})},add:function(t,e){return null==e?this.node.appendChild(t.node):t.node!=this.node.childNodes[e]&&this.node.insertBefore(t.node,this.node.childNodes[e]),this},put:function(t,e){return this.add(t,e),t},has:function(t){return this.index(t)>=0},index:function(t){return[].slice.call(this.node.childNodes).indexOf(t.node)},get:function(t){return g.adopt(this.node.childNodes[t])},first:function(){return this.get(0)},last:function(){return this.get(this.node.childNodes.length-1)},each:function(t,e){var i,n,s=this.children();for(i=0,n=s.length;i<n;i++)s[i]instanceof g.Element&&t.apply(s[i],[i,s]),e&&s[i]instanceof g.Container&&s[i].each(t,e);return this},removeElement:function(t){return this.node.removeChild(t.node),this},clear:function(){for(;this.node.hasChildNodes();)this.node.removeChild(this.node.lastChild);return delete this._defs,this},defs:function(){return this.doc().defs()}}}),g.extend(g.Parent,{ungroup:function(t,e){return 0===e||this instanceof g.Defs?this:(t=t||(this instanceof g.Doc?this:this.parent(g.Parent)),e=e||1/0,this.each(function(){return this instanceof g.Defs?this:this instanceof g.Parent?this.ungroup(t,e-1):this.toParent(t)}),this.node.firstChild||this.remove(),this)},flatten:function(t,e){return this.ungroup(t,e)}}),g.Container=g.invent({create:function(t){this.constructor.call(this,t)},inherit:g.Parent}),g.ViewBox=g.invent({create:function(t){var e,i,n,s,r,a,o,h,u=[0,0,0,0],l=1,c=1,f=/[+-]?(?:\d+(?:\.\d*)?|\.\d+)(?:e[+-]?\d+)?/gi;if(t instanceof g.Element){for(o=t,h=t,a=(t.attr("viewBox")||"").match(f),r=t.bbox,n=new g.Number(t.width()),s=new g.Number(t.height());"%"==n.unit;)l*=n.value,n=new g.Number(o instanceof 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g.ViewBox([this.x+(this.destination.x-this.x)*t,this.y+(this.destination.y-this.y)*t,this.width+(this.destination.width-this.width)*t,this.height+(this.destination.height-this.height)*t]):this}},parent:g.Container,construct:{viewbox:function(t){return 0==arguments.length?new g.ViewBox(this):(t=1==arguments.length?[t.x,t.y,t.width,t.height]:[].slice.call(arguments),this.attr("viewBox",t))}}}),["click","dblclick","mousedown","mouseup","mouseover","mouseout","mousemove","touchstart","touchmove","touchleave","touchend","touchcancel"].forEach(function(t){g.Element.prototype[t]=function(e){var i=this;return this.node["on"+t]="function"==typeof e?function(){return e.apply(i,arguments)}:null,this}}),g.listeners=[],g.handlerMap=[],g.listenerId=0,g.on=function(t,e,i,n){var s=i.bind(n||t.instance||t),r=(g.handlerMap.indexOf(t)+1||g.handlerMap.push(t))-1,a=e.split(".")[0],o=e.split(".")[1]||"*";g.listeners[r]=g.listeners[r]||{},g.listeners[r][a]=g.listeners[r][a]||{},g.listeners[r][a][o]=g.listeners[r][a][o]||{},i._svgjsListenerId||(i._svgjsListenerId=++g.listenerId),g.listeners[r][a][o][i._svgjsListenerId]=s,t.addEventListener(a,s,!1)},g.off=function(t,e,i){var n=g.handlerMap.indexOf(t),s=e&&e.split(".")[0],r=e&&e.split(".")[1];if(n!=-1)if(i){if("function"==typeof i&&(i=i._svgjsListenerId),!i)return;g.listeners[n][s]&&g.listeners[n][s][r||"*"]&&(t.removeEventListener(s,g.listeners[n][s][r||"*"][i],!1),delete g.listeners[n][s][r||"*"][i])}else if(r&&s){if(g.listeners[n][s]&&g.listeners[n][s][r]){for(i in g.listeners[n][s][r])g.off(t,[s,r].join("."),i);delete g.listeners[n][s][r]}}else if(r)for(e in g.listeners[n])for(namespace in g.listeners[n][e])r===namespace&&g.off(t,[e,r].join("."));else if(s){if(g.listeners[n][s]){for(namespace in g.listeners[n][s])g.off(t,[s,namespace].join("."));delete g.listeners[n][s]}}else{for(e in g.listeners[n])g.off(t,e);delete g.listeners[n]}},g.extend(g.Element,{on:function(t,e,i){return g.on(this.node,t,e,i),this},off:function(t,e){return g.off(this.node,t,e),this},fire:function(t,e){return t instanceof Event?this.node.dispatchEvent(t):this.node.dispatchEvent(new b(t,{detail:e})),this}}),g.Defs=g.invent({create:"defs",inherit:g.Container}),g.G=g.invent({create:"g",inherit:g.Container,extend:{x:function(t){return null==t?this.transform("x"):this.transform({x:t-this.x()},!0)},y:function(t){return null==t?this.transform("y"):this.transform({y:t-this.y()},!0)},cx:function(t){return null==t?this.gbox().cx:this.x(t-this.gbox().width/2)},cy:function(t){return null==t?this.gbox().cy:this.y(t-this.gbox().height/2)},gbox:function(){var t=this.bbox(),e=this.transform();return t.x+=e.x,t.x2+=e.x,t.cx+=e.x,t.y+=e.y,t.y2+=e.y,t.cy+=e.y,t}},construct:{group:function(){return this.put(new g.G)}}}),g.extend(g.Element,{siblings:function(){return this.parent().children()},position:function(){return this.parent().index(this)},next:function(){return this.siblings()[this.position()+1]},previous:function(){return this.siblings()[this.position()-1]},forward:function(){var t=this.position()+1,e=this.parent();return e.removeElement(this).add(this,t),e instanceof g.Doc&&e.node.appendChild(e.defs().node),this},backward:function(){var t=this.position();return t>0&&this.parent().removeElement(this).add(this,t-1),this},front:function(){var t=this.parent();return t.node.appendChild(this.node),t instanceof g.Doc&&t.node.appendChild(t.defs().node),this},back:function(){return this.position()>0&&this.parent().removeElement(this).add(this,0),this},before:function(t){t.remove();var e=this.position();return this.parent().add(t,e),this},after:function(t){t.remove();var e=this.position();return this.parent().add(t,e+1),this}}),g.Mask=g.invent({create:function(){this.constructor.call(this,g.create("mask")),this.targets=[]},inherit:g.Container,extend:{remove:function(){for(var t=this.targets.length-1;t>=0;t--)this.targets[t]&&this.targets[t].unmask();return this.targets=[],this.parent().removeElement(this),this}},construct:{mask:function(){return this.defs().put(new g.Mask)}}}),g.extend(g.Element,{maskWith:function(t){return this.masker=t instanceof g.Mask?t:this.parent().mask().add(t),this.masker.targets.push(this),this.attr("mask",'url("#'+this.masker.attr("id")+'")')},unmask:function(){return delete this.masker,this.attr("mask",null)}}),g.ClipPath=g.invent({create:function(){this.constructor.call(this,g.create("clipPath")),this.targets=[]},inherit:g.Container,extend:{remove:function(){for(var t=this.targets.length-1;t>=0;t--)this.targets[t]&&this.targets[t].unclip();return this.targets=[],this.parent().removeElement(this),this}},construct:{clip:function(){return this.defs().put(new g.ClipPath)}}}),g.extend(g.Element,{clipWith:function(t){return this.clipper=t instanceof g.ClipPath?t:this.parent().clip().add(t),this.clipper.targets.push(this),this.attr("clip-path",'url("#'+this.clipper.attr("id")+'")')},unclip:function(){return delete this.clipper,this.attr("clip-path",null)}}),g.Gradient=g.invent({create:function(t){this.constructor.call(this,g.create(t+"Gradient")),this.type=t},inherit:g.Container,extend:{at:function(t,e,i){return this.put(new g.Stop).update(t,e,i)},update:function(t){return this.clear(),"function"==typeof t&&t.call(this,this),this},fill:function(){return"url(#"+this.id()+")"},toString:function(){return this.fill()},attr:function(t,e,i){return"transform"==t&&(t="gradientTransform"),g.Container.prototype.attr.call(this,t,e,i)}},construct:{gradient:function(t,e){return this.defs().gradient(t,e)}}}),g.extend(g.Gradient,g.FX,{from:function(t,e){return"radial"==(this._target||this).type?this.attr({fx:new g.Number(t),fy:new g.Number(e)}):this.attr({x1:new g.Number(t),y1:new g.Number(e)})},to:function(t,e){return"radial"==(this._target||this).type?this.attr({cx:new g.Number(t),cy:new g.Number(e)}):this.attr({x2:new g.Number(t),y2:new g.Number(e)})}}),g.extend(g.Defs,{gradient:function(t,e){return this.put(new g.Gradient(t)).update(e)}}),g.Stop=g.invent({create:"stop",inherit:g.Element,extend:{update:function(t){return("number"==typeof t||t instanceof g.Number)&&(t={offset:arguments[0],color:arguments[1],opacity:arguments[2]}),null!=t.opacity&&this.attr("stop-opacity",t.opacity),null!=t.color&&this.attr("stop-color",t.color),null!=t.offset&&this.attr("offset",new g.Number(t.offset)),this}}}),g.Pattern=g.invent({create:"pattern",inherit:g.Container,extend:{fill:function(){return"url(#"+this.id()+")"},update:function(t){return this.clear(),"function"==typeof t&&t.call(this,this),this},toString:function(){return this.fill()},attr:function(t,e,i){return"transform"==t&&(t="patternTransform"),g.Container.prototype.attr.call(this,t,e,i)}},construct:{pattern:function(t,e,i){return this.defs().pattern(t,e,i)}}}),g.extend(g.Defs,{pattern:function(t,e,i){return this.put(new g.Pattern).update(i).attr({x:0,y:0,width:t,height:e,patternUnits:"userSpaceOnUse"})}}),g.Doc=g.invent({create:function(t){t&&(t="string"==typeof t?e.getElementById(t):t,"svg"==t.nodeName?this.constructor.call(this,t):(this.constructor.call(this,g.create("svg")),t.appendChild(this.node),this.size("100%","100%")),this.namespace().defs())},inherit:g.Container,extend:{namespace:function(){return this.attr({xmlns:g.ns,version:"1.1"}).attr("xmlns:xlink",g.xlink,g.xmlns).attr("xmlns:svgjs",g.svgjs,g.xmlns)},defs:function(){if(!this._defs){var t;(t=this.node.getElementsByTagName("defs")[0])?this._defs=g.adopt(t):this._defs=new g.Defs,this.node.appendChild(this._defs.node)}return this._defs},parent:function(){return"#document"==this.node.parentNode.nodeName?null:this.node.parentNode},spof:function(t){var e=this.node.getScreenCTM();return e&&this.style("left",-e.e%1+"px").style("top",-e.f%1+"px"),this},remove:function(){return this.parent()&&this.parent().removeChild(this.node),this}}}),g.Shape=g.invent({create:function(t){this.constructor.call(this,t)},inherit:g.Element}),g.Bare=g.invent({create:function(t,e){if(this.constructor.call(this,g.create(t)),e)for(var i in e.prototype)"function"==typeof e.prototype[i]&&(this[i]=e.prototype[i])},inherit:g.Element,extend:{words:function(t){for(;this.node.hasChildNodes();)this.node.removeChild(this.node.lastChild);return this.node.appendChild(e.createTextNode(t)),this}}}),g.extend(g.Parent,{element:function(t,e){return this.put(new g.Bare(t,e))},symbol:function(){return this.defs().element("symbol",g.Container)}}),g.Use=g.invent({create:"use",inherit:g.Shape,extend:{element:function(t,e){return this.attr("href",(e||"")+"#"+t,g.xlink)}},construct:{use:function(t,e){return this.put(new g.Use).element(t,e)}}}),g.Rect=g.invent({create:"rect",inherit:g.Shape,construct:{rect:function(t,e){return this.put(new g.Rect).size(t,e)}}}),g.Circle=g.invent({create:"circle",inherit:g.Shape,construct:{circle:function(t){return this.put(new g.Circle).rx(new g.Number(t).divide(2)).move(0,0)}}}),g.extend(g.Circle,g.FX,{rx:function(t){return this.attr("r",t)},ry:function(t){return this.rx(t)}}),g.Ellipse=g.invent({create:"ellipse",inherit:g.Shape,construct:{ellipse:function(t,e){return this.put(new g.Ellipse).size(t,e).move(0,0)}}}),g.extend(g.Ellipse,g.Rect,g.FX,{rx:function(t){return this.attr("rx",t)},ry:function(t){return this.attr("ry",t)}}),g.extend(g.Circle,g.Ellipse,{x:function(t){return null==t?this.cx()-this.rx():this.cx(t+this.rx())},y:function(t){return null==t?this.cy()-this.ry():this.cy(t+this.ry())},cx:function(t){return 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A.Point(t,e).transform(this.screenCTM().inverse())}}),A.extend(A.Element,{attr:function(t,e,i){if(null==t){for(t={},e=this.node.attributes,i=e.length-1;i>=0;i--)t[e[i].nodeName]=A.regex.isNumber.test(e[i].nodeValue)?parseFloat(e[i].nodeValue):e[i].nodeValue;return t}if("object"==typeof t)for(e in t)this.attr(e,t[e]);else if(null===e)this.node.removeAttribute(t);else{if(null==e)return e=this.node.getAttribute(t),null==e?A.defaults.attrs[t]:A.regex.isNumber.test(e)?parseFloat(e):e;"stroke-width"==t?this.attr("stroke",parseFloat(e)>0?this._stroke:null):"stroke"==t&&(this._stroke=e),"fill"!=t&&"stroke"!=t||(A.regex.isImage.test(e)&&(e=this.doc().defs().image(e,0,0)),e instanceof A.Image&&(e=this.doc().defs().pattern(0,0,function(){this.add(e)}))),"number"==typeof e?e=new A.Number(e):A.Color.isColor(e)?e=new A.Color(e):Array.isArray(e)?e=new A.Array(e):e instanceof A.Matrix&&e.param&&(this.param=e.param),"leading"==t?this.leading&&this.leading(e):"string"==typeof i?this.node.setAttributeNS(i,t,e.toString()):this.node.setAttribute(t,e.toString()),!this.rebuild||"font-size"!=t&&"x"!=t||this.rebuild(t,e)}return this}}),A.extend(A.Element,{transform:function(t,e){var i,n=this;if("object"!=typeof t)return i=new A.Matrix(n).extract(),"string"==typeof t?i[t]:i;if(i=new A.Matrix(n),e=!!e||!!t.relative,null!=t.a)i=e?i.multiply(new A.Matrix(t)):new A.Matrix(t);else if(null!=t.rotation)f(t,n),i=e?i.rotate(t.rotation,t.cx,t.cy):i.rotate(t.rotation-i.extract().rotation,t.cx,t.cy);else if(null!=t.scale||null!=t.scaleX||null!=t.scaleY){if(f(t,n),t.scaleX=null!=t.scale?t.scale:null!=t.scaleX?t.scaleX:1,t.scaleY=null!=t.scale?t.scale:null!=t.scaleY?t.scaleY:1,!e){var r=i.extract();t.scaleX=1*t.scaleX/r.scaleX,t.scaleY=1*t.scaleY/r.scaleY}i=i.scale(t.scaleX,t.scaleY,t.cx,t.cy)}else if(null!=t.skew||null!=t.skewX||null!=t.skewY){if(f(t,n),t.skewX=null!=t.skew?t.skew:null!=t.skewX?t.skewX:0,t.skewY=null!=t.skew?t.skew:null!=t.skewY?t.skewY:0,!e){var r=i.extract();i=i.multiply((new A.Matrix).skew(r.skewX,r.skewY,t.cx,t.cy).inverse())}i=i.skew(t.skewX,t.skewY,t.cx,t.cy)}else t.flip?i=i.flip(t.flip,null==t.offset?n.bbox()["c"+t.flip]:t.offset):null==t.x&&null==t.y||(e?i=i.translate(t.x,t.y):(null!=t.x&&(i.e=t.x),null!=t.y&&(i.f=t.y)));return this.attr("transform",i)}}),A.extend(A.FX,{transform:function(t,e){var i,n=this.target();return"object"!=typeof t?(i=new A.Matrix(n).extract(),"string"==typeof t?i[t]:i):(e=!!e||!!t.relative,null!=t.a?i=new A.Matrix(t):null!=t.rotation?(f(t,n),i=new A.Rotate(t.rotation,t.cx,t.cy)):null!=t.scale||null!=t.scaleX||null!=t.scaleY?(f(t,n),t.scaleX=null!=t.scale?t.scale:null!=t.scaleX?t.scaleX:1,t.scaleY=null!=t.scale?t.scale:null!=t.scaleY?t.scaleY:1,i=new A.Scale(t.scaleX,t.scaleY,t.cx,t.cy)):null!=t.skewX||null!=t.skewY?(f(t,n),t.skewX=null!=t.skewX?t.skewX:0,t.skewY=null!=t.skewY?t.skewY:0,i=new A.Skew(t.skewX,t.skewY,t.cx,t.cy)):t.flip?i=(new A.Matrix).morph((new A.Matrix).flip(t.flip,null==t.offset?n.bbox()["c"+t.flip]:t.offset)):null==t.x&&null==t.y||(i=new A.Translate(t.x,t.y)),i?(i.relative=e,this.last().transforms.push(i),setTimeout(function(){this.start()}.bind(this),0),this):this)}}),A.extend(A.Element,{untransform:function(){return this.attr("transform",null)},matrixify:function(){var t=(this.attr("transform")||"").split(/\)\s*,?\s*/).slice(0,-1).map(function(t){var e=t.trim().split("(");return[e[0],e[1].split(A.regex.matrixElements).map(function(t){return parseFloat(t)})]}).reduce(function(t,e){return"matrix"==e[0]?t.multiply(l(e[1])):t[e[0]].apply(t,e[1])},new A.Matrix);return t},toParent:function(t){if(this==t)return this;var e=this.screenCTM(),i=t.rect(1,1),n=i.screenCTM().inverse();return i.remove(),this.addTo(t).untransform().transform(n.multiply(e)),this},toDoc:function(){return this.toParent(this.doc())}}),A.Transformation=A.invent({create:function(t,e){if(arguments.length>1&&"boolean"!=typeof e)return this.create([].slice.call(arguments));if("object"==typeof t)for(var i=0,n=this.arguments.length;i<n;++i)this[this.arguments[i]]=t[this.arguments[i]];if(Array.isArray(t))for(var i=0,n=this.arguments.length;i<n;++i)this[this.arguments[i]]=t[i];this.inversed=!1,e===!0&&(this.inversed=!0)},extend:{at:function(t){for(var e=[],i=0,n=this.arguments.length;i<n;++i)e.push(this[this.arguments[i]]);var r=this._undo||new A.Matrix;return r=(new A.Matrix).morph(A.Matrix.prototype[this.method].apply(r,e)).at(t),this.inversed?r.inverse():r},undo:function(t){for(var e=0,i=this.arguments.length;e<i;++e)t[this.arguments[e]]="undefined"==typeof this[this.arguments[e]]?0:t[this.arguments[e]];return t.cx=this.cx,t.cy=this.cy,this._undo=new(A[s(this.method)])(t,(!0)).at(1),this}}}),A.Translate=A.invent({parent:A.Matrix,inherit:A.Transformation,create:function(t,e){"object"==typeof t?this.constructor.call(this,t,e):this.constructor.call(this,[].slice.call(arguments))},extend:{arguments:["transformedX","transformedY"],method:"translate"}}),A.Rotate=A.invent({parent:A.Matrix,inherit:A.Transformation,create:function(t,e){"object"==typeof t?this.constructor.call(this,t,e):this.constructor.call(this,[].slice.call(arguments))},extend:{arguments:["rotation","cx","cy"],method:"rotate",at:function(t){var e=(new A.Matrix).rotate((new A.Number).morph(this.rotation-(this._undo?this._undo.rotation:0)).at(t),this.cx,this.cy);return this.inversed?e.inverse():e},undo:function(t){this._undo=t}}}),A.Scale=A.invent({parent:A.Matrix,inherit:A.Transformation,create:function(t,e){"object"==typeof t?this.constructor.call(this,t,e):this.constructor.call(this,[].slice.call(arguments))},extend:{arguments:["scaleX","scaleY","cx","cy"],method:"scale"}}),A.Skew=A.invent({parent:A.Matrix,inherit:A.Transformation,create:function(t,e){"object"==typeof t?this.constructor.call(this,t,e):this.constructor.call(this,[].slice.call(arguments))},extend:{arguments:["skewX","skewY","cx","cy"],method:"skew"}}),A.extend(A.Element,{style:function(t,e){if(0==arguments.length)return this.node.style.cssText||"";if(arguments.length<2)if("object"==typeof t)for(e in t)this.style(e,t[e]);else{if(!A.regex.isCss.test(t))return this.node.style[r(t)];t=t.split(";");for(var i=0;i<t.length;i++)e=t[i].split(":"),this.style(e[0].replace(/\s+/g,""),e[1])}else this.node.style[r(t)]=null===e||A.regex.isBlank.test(e)?"":e;return this}}),A.Parent=A.invent({create:function(t){this.constructor.call(this,t)},inherit:A.Element,extend:{children:function(){return A.utils.map(A.utils.filterSVGElements(this.node.childNodes),function(t){return A.adopt(t)})},add:function(t,e){return null==e?this.node.appendChild(t.node):t.node!=this.node.childNodes[e]&&this.node.insertBefore(t.node,this.node.childNodes[e]),this},put:function(t,e){return this.add(t,e),t},has:function(t){return this.index(t)>=0},index:function(t){return[].slice.call(this.node.childNodes).indexOf(t.node)},get:function(t){return A.adopt(this.node.childNodes[t])},first:function(){return this.get(0)},last:function(){return this.get(this.node.childNodes.length-1)},each:function(t,e){var i,n,r=this.children();for(i=0,n=r.length;i<n;i++)r[i]instanceof A.Element&&t.apply(r[i],[i,r]),e&&r[i]instanceof A.Container&&r[i].each(t,e);return this},removeElement:function(t){return this.node.removeChild(t.node),this},clear:function(){for(;this.node.hasChildNodes();)this.node.removeChild(this.node.lastChild);return delete this._defs,this},defs:function(){return this.doc().defs()}}}),A.extend(A.Parent,{ungroup:function(t,e){return 0===e||this instanceof A.Defs?this:(t=t||(this instanceof A.Doc?this:this.parent(A.Parent)),e=e||1/0,this.each(function(){return this instanceof A.Defs?this:this instanceof A.Parent?this.ungroup(t,e-1):this.toParent(t)}),this.node.firstChild||this.remove(),this)},flatten:function(t,e){return this.ungroup(t,e)}}),A.Container=A.invent({create:function(t){this.constructor.call(this,t)},inherit:A.Parent}),A.ViewBox=A.invent({create:function(t){var e,i,n,r,s,a,o,h,u=[0,0,0,0],l=1,c=1,f=/[+-]?(?:\d+(?:\.\d*)?|\.\d+)(?:e[+-]?\d+)?/gi;if(t instanceof A.Element){for(o=t,h=t,a=(t.attr("viewBox")||"").match(f),s=t.bbox,n=new A.Number(t.width()),r=new A.Number(t.height());"%"==n.unit;)l*=n.value,n=new A.Number(o instanceof A.Doc?o.parent().offsetWidth:o.parent().width()),o=o.parent();for(;"%"==r.unit;)c*=r.value,r=new A.Number(h instanceof A.Doc?h.parent().offsetHeight:h.parent().height()),h=h.parent();this.x=0,this.y=0,this.width=n*l,this.height=r*c,this.zoom=1,a&&(e=parseFloat(a[0]),i=parseFloat(a[1]),n=parseFloat(a[2]),r=parseFloat(a[3]),this.zoom=this.width/this.height>n/r?this.height/r:this.width/n,this.x=e,this.y=i,this.width=n,this.height=r)}else t="string"==typeof t?t.match(f).map(function(t){return parseFloat(t)}):Array.isArray(t)?t:"object"==typeof t?[t.x,t.y,t.width,t.height]:4==arguments.length?[].slice.call(arguments):u,this.x=t[0],this.y=t[1],this.width=t[2],this.height=t[3]},extend:{toString:function(){return this.x+" "+this.y+" "+this.width+" "+this.height},morph:function(t){var t=1==arguments.length?[t.x,t.y,t.width,t.height]:[].slice.call(arguments);return this.destination=new A.ViewBox(t),this},at:function(t){return this.destination?new A.ViewBox([this.x+(this.destination.x-this.x)*t,this.y+(this.destination.y-this.y)*t,this.width+(this.destination.width-this.width)*t,this.height+(this.destination.height-this.height)*t]):this}},parent:A.Container,construct:{viewbox:function(t){return 0==arguments.length?new A.ViewBox(this):(t=1==arguments.length?[t.x,t.y,t.width,t.height]:[].slice.call(arguments),this.attr("viewBox",t))}}}),["click","dblclick","mousedown","mouseup","mouseover","mouseout","mousemove","touchstart","touchmove","touchleave","touchend","touchcancel"].forEach(function(t){A.Element.prototype[t]=function(e){var i=this;return this.node["on"+t]="function"==typeof e?function(){return e.apply(i,arguments)}:null,this}}),A.listeners=[],A.handlerMap=[],A.listenerId=0,A.on=function(t,e,i,n){var r=i.bind(n||t.instance||t),s=(A.handlerMap.indexOf(t)+1||A.handlerMap.push(t))-1,a=e.split(".")[0],o=e.split(".")[1]||"*";A.listeners[s]=A.listeners[s]||{},A.listeners[s][a]=A.listeners[s][a]||{},A.listeners[s][a][o]=A.listeners[s][a][o]||{},i._svgjsListenerId||(i._svgjsListenerId=++A.listenerId),A.listeners[s][a][o][i._svgjsListenerId]=r,t.addEventListener(a,r,!1)},A.off=function(t,e,i){var n=A.handlerMap.indexOf(t),r=e&&e.split(".")[0],s=e&&e.split(".")[1];if(n!=-1)if(i){if("function"==typeof i&&(i=i._svgjsListenerId),!i)return;A.listeners[n][r]&&A.listeners[n][r][s||"*"]&&(t.removeEventListener(r,A.listeners[n][r][s||"*"][i],!1),delete A.listeners[n][r][s||"*"][i])}else if(s&&r){if(A.listeners[n][r]&&A.listeners[n][r][s]){for(i in A.listeners[n][r][s])A.off(t,[r,s].join("."),i);delete A.listeners[n][r][s]}}else if(s)for(e in A.listeners[n])for(namespace in A.listeners[n][e])s===namespace&&A.off(t,[e,s].join("."));else if(r){if(A.listeners[n][r]){for(namespace in A.listeners[n][r])A.off(t,[r,namespace].join("."));delete A.listeners[n][r]}}else{for(e in A.listeners[n])A.off(t,e);delete A.listeners[n]}},A.extend(A.Element,{on:function(t,e,i){return A.on(this.node,t,e,i),this},off:function(t,e){return A.off(this.node,t,e),this},fire:function(t,e){return t instanceof Event?this.node.dispatchEvent(t):this.node.dispatchEvent(new T(t,{detail:e})),this}}),A.Defs=A.invent({create:"defs",inherit:A.Container}),A.G=A.invent({create:"g",inherit:A.Container,extend:{x:function(t){return null==t?this.transform("x"):this.transform({x:t-this.x()},!0)},y:function(t){return null==t?this.transform("y"):this.transform({y:t-this.y()},!0)},cx:function(t){return null==t?this.gbox().cx:this.x(t-this.gbox().width/2)},cy:function(t){return null==t?this.gbox().cy:this.y(t-this.gbox().height/2)},gbox:function(){var t=this.bbox(),e=this.transform();return t.x+=e.x,t.x2+=e.x,t.cx+=e.x,t.y+=e.y,t.y2+=e.y,t.cy+=e.y,t}},construct:{group:function(){return this.put(new A.G)}}}),A.extend(A.Element,{siblings:function(){return this.parent().children()},position:function(){return this.parent().index(this)},next:function(){return this.siblings()[this.position()+1]},previous:function(){return this.siblings()[this.position()-1]},forward:function(){var t=this.position()+1,e=this.parent();return e.removeElement(this).add(this,t),e instanceof A.Doc&&e.node.appendChild(e.defs().node),this},backward:function(){var t=this.position();return t>0&&this.parent().removeElement(this).add(this,t-1),this},front:function(){var t=this.parent();return t.node.appendChild(this.node),t instanceof A.Doc&&t.node.appendChild(t.defs().node),this},back:function(){return this.position()>0&&this.parent().removeElement(this).add(this,0),this},before:function(t){t.remove();var e=this.position();return this.parent().add(t,e),this},after:function(t){t.remove();var e=this.position();return this.parent().add(t,e+1),this}}),A.Mask=A.invent({create:function(){this.constructor.call(this,A.create("mask")),this.targets=[]},inherit:A.Container,extend:{remove:function(){for(var t=this.targets.length-1;t>=0;t--)this.targets[t]&&this.targets[t].unmask();return this.targets=[],this.parent().removeElement(this),this}},construct:{mask:function(){return this.defs().put(new A.Mask)}}}),A.extend(A.Element,{maskWith:function(t){return this.masker=t instanceof A.Mask?t:this.parent().mask().add(t),this.masker.targets.push(this),this.attr("mask",'url("#'+this.masker.attr("id")+'")')},unmask:function(){return delete this.masker,this.attr("mask",null)}}),A.ClipPath=A.invent({create:function(){this.constructor.call(this,A.create("clipPath")),this.targets=[]},inherit:A.Container,extend:{remove:function(){for(var t=this.targets.length-1;t>=0;t--)this.targets[t]&&this.targets[t].unclip();return this.targets=[],this.parent().removeElement(this),this}},construct:{clip:function(){return this.defs().put(new A.ClipPath)}}}),A.extend(A.Element,{clipWith:function(t){return this.clipper=t instanceof A.ClipPath?t:this.parent().clip().add(t),this.clipper.targets.push(this),this.attr("clip-path",'url("#'+this.clipper.attr("id")+'")')},unclip:function(){return delete this.clipper,this.attr("clip-path",null)}}),A.Gradient=A.invent({create:function(t){this.constructor.call(this,A.create(t+"Gradient")),this.type=t},inherit:A.Container,extend:{at:function(t,e,i){return this.put(new A.Stop).update(t,e,i)},update:function(t){return this.clear(),"function"==typeof t&&t.call(this,this),this},fill:function(){return"url(#"+this.id()+")"},toString:function(){return this.fill()},attr:function(t,e,i){return"transform"==t&&(t="gradientTransform"),A.Container.prototype.attr.call(this,t,e,i)}},construct:{gradient:function(t,e){return this.defs().gradient(t,e)}}}),A.extend(A.Gradient,A.FX,{from:function(t,e){return"radial"==(this._target||this).type?this.attr({fx:new A.Number(t),fy:new A.Number(e)}):this.attr({x1:new A.Number(t),y1:new A.Number(e)})},to:function(t,e){return"radial"==(this._target||this).type?this.attr({cx:new A.Number(t),cy:new A.Number(e)}):this.attr({x2:new A.Number(t),y2:new A.Number(e)})}}),A.extend(A.Defs,{gradient:function(t,e){return this.put(new A.Gradient(t)).update(e)}}),A.Stop=A.invent({create:"stop",inherit:A.Element,extend:{update:function(t){return("number"==typeof t||t instanceof A.Number)&&(t={offset:arguments[0],color:arguments[1],opacity:arguments[2]}),null!=t.opacity&&this.attr("stop-opacity",t.opacity),null!=t.color&&this.attr("stop-color",t.color),null!=t.offset&&this.attr("offset",new A.Number(t.offset)),this}}}),A.Pattern=A.invent({create:"pattern",inherit:A.Container,extend:{fill:function(){return"url(#"+this.id()+")"},update:function(t){return this.clear(),"function"==typeof t&&t.call(this,this),this},toString:function(){return this.fill()},attr:function(t,e,i){return"transform"==t&&(t="patternTransform"),A.Container.prototype.attr.call(this,t,e,i)}},construct:{pattern:function(t,e,i){return this.defs().pattern(t,e,i)}}}),A.extend(A.Defs,{pattern:function(t,e,i){return this.put(new A.Pattern).update(i).attr({x:0,y:0,width:t,height:e,patternUnits:"userSpaceOnUse"})}}),A.Doc=A.invent({create:function(t){t&&(t="string"==typeof t?e.getElementById(t):t,"svg"==t.nodeName?this.constructor.call(this,t):(this.constructor.call(this,A.create("svg")),t.appendChild(this.node),this.size("100%","100%")),this.namespace().defs())},inherit:A.Container,extend:{namespace:function(){return this.attr({xmlns:A.ns,version:"1.1"}).attr("xmlns:xlink",A.xlink,A.xmlns).attr("xmlns:svgjs",A.svgjs,A.xmlns)},defs:function(){if(!this._defs){var t;(t=this.node.getElementsByTagName("defs")[0])?this._defs=A.adopt(t):this._defs=new A.Defs,this.node.appendChild(this._defs.node)}return this._defs},parent:function(){return"#document"==this.node.parentNode.nodeName?null:this.node.parentNode},spof:function(t){var e=this.node.getScreenCTM();return e&&this.style("left",-e.e%1+"px").style("top",-e.f%1+"px"),this},remove:function(){return this.parent()&&this.parent().removeChild(this.node),this}}}),A.Shape=A.invent({create:function(t){this.constructor.call(this,t)},inherit:A.Element}),A.Bare=A.invent({create:function(t,e){if(this.constructor.call(this,A.create(t)),e)for(var i in e.prototype)"function"==typeof e.prototype[i]&&(this[i]=e.prototype[i])},inherit:A.Element,extend:{words:function(t){for(;this.node.hasChildNodes();)this.node.removeChild(this.node.lastChild);return this.node.appendChild(e.createTextNode(t)),this}}}),A.extend(A.Parent,{element:function(t,e){return this.put(new A.Bare(t,e))},symbol:function(){return this.defs().element("symbol",A.Container)}}),A.Use=A.invent({create:"use",inherit:A.Shape,extend:{element:function(t,e){return this.attr("href",(e||"")+"#"+t,A.xlink)}},construct:{use:function(t,e){return this.put(new A.Use).element(t,e)}}}),A.Rect=A.invent({create:"rect",inherit:A.Shape,construct:{rect:function(t,e){return this.put(new A.Rect).size(t,e)}}}),A.Circle=A.invent({create:"circle",inherit:A.Shape,construct:{circle:function(t){return this.put(new A.Circle).rx(new A.Number(t).divide(2)).move(0,0)}}}),A.extend(A.Circle,A.FX,{rx:function(t){return this.attr("r",t)},ry:function(t){return this.rx(t)}}),A.Ellipse=A.invent({create:"ellipse",inherit:A.Shape,construct:{ellipse:function(t,e){return this.put(new A.Ellipse).size(t,e).move(0,0)}}}),A.extend(A.Ellipse,A.Rect,A.FX,{rx:function(t){return this.attr("rx",t)},ry:function(t){return this.attr("ry",t)}}),A.extend(A.Circle,A.Ellipse,{x:function(t){return null==t?this.cx()-this.rx():this.cx(t+this.rx())},y:function(t){return null==t?this.cy()-this.ry():this.cy(t+this.ry())},cx:function(t){return null==t?this.attr("cx"):this.attr("cx",t)},cy:function(t){return null==t?this.attr("cy"):this.attr("cy",t)},width:function(t){return null==t?2*this.rx():this.rx(new A.Number(t).divide(2))},height:function(t){return null==t?2*this.ry():this.ry(new 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--- /dev/null
+// Take two path array that don't have the same commands (which mean that they
+// cannot be morphed in one another) and return 2 equivalent path array (meaning
+// that they produce the same shape as the passed path array) that have the
+// same commands (moveto and curveto)
+//
+// Algorithm used:
+// First, convert every path segment of the two passed paths into equivalent cubic Bezier curves.
+// Then, calculate the positions relative to the total length of the path of the endpoint of all those cubic Bezier curves.
+// After that, split the Bezier curves of the source at the positions that the destination have that are not common to the source and vice versa.
+// Finally, make the source and destination have the same number of subpaths.
+SVG.utils.makePathsMorphable = function (sourcePathArray, destinationPathArray) {
+ var source, sourcePositions, sourcePositionsToSplitAt
+ , destination, destinationPositions, destinationPositionsToSplitAt
+ , i, il, j, jl
+ , s, d
+ , sourceSubpath, destinationSubpath, lastSegPt
+
+ // Convert every path segments into equivalent cubic Bezier curves
+ source = cubicSuperPath(sourcePathArray)
+ destination = cubicSuperPath(destinationPathArray)
+
+ // The positions relative to the total length of the path is calculated for the endpoint of all those cubic bezier curves
+ sourcePositions = cspPositions(source)
+ destinationPositions = cspPositions(destination)
+
+ // Find the positions that the destination have that are not in the source and vice versa
+ sourcePositionsToSplitAt = []
+ destinationPositionsToSplitAt = []
+ i = 0, il = sourcePositions.length
+ j = 0, jl = destinationPositions.length
+ while(i < il && j < jl) {
+ // Test if the two values are equal taking into account the imprecision of floating point number
+ if (Math.abs(sourcePositions[i] - destinationPositions[j]) < 0.000001) {
+ i++
+ j++
+ } else if(sourcePositions[i] > destinationPositions[j]){
+ sourcePositionsToSplitAt.push(destinationPositions[j++])
+ } else {
+ destinationPositionsToSplitAt.push(sourcePositions[i++])
+ }
+ }
+ // If there are still some destination positions left, they all are not in the source and vice versa
+ sourcePositionsToSplitAt = sourcePositionsToSplitAt.concat(destinationPositions.slice(j))
+ destinationPositionsToSplitAt = destinationPositionsToSplitAt.concat(sourcePositions.slice(i))
+
+ // Split the source and the destination at the positions they don't have in common
+ cspSplitAtPositions(source, sourcePositions, sourcePositionsToSplitAt)
+ cspSplitAtPositions(destination, destinationPositions, destinationPositionsToSplitAt)
+
+
+ // Break paths so that corresponding subpaths have an equal number of segments
+ s = source, source = [], sourceSubpath = s[i = 0]
+ d = destination, destination = [], destinationSubpath = d[j = 0]
+ while (sourceSubpath && destinationSubpath) {
+ // Push REFERENCES to the current subpath arrays in their respective array
+ source.push(sourceSubpath)
+ destination.push(destinationSubpath)
+
+ il = sourceSubpath.length
+ jl = destinationSubpath.length
+
+ // If the current subpath of the source and the current subpath of the destination don't
+ // have the same length, that mean that the biggest of the two must be split in two
+ if(il > jl) {
+ lastSegPt = sourceSubpath[jl-1]
+ // Perform the split using splice that change the content of the array by removing elements and returning them in an array
+ sourceSubpath = sourceSubpath.splice(jl)
+ sourceSubpath.unshift(lastSegPt) // The last segment point is duplicated since these two segments must be joined together
+ destinationSubpath = d[++j] // This subpath has been accounted for, past to the next
+ } else if(il < jl) {
+ lastSegPt = destinationSubpath[il-1]
+ destinationSubpath = destinationSubpath.splice(il)
+ destinationSubpath.unshift(lastSegPt)
+ sourceSubpath = s[++i]
+ } else {
+ sourceSubpath = s[++i]
+ destinationSubpath = d[++j]
+ }
+ }
+
+ // Convert in path array and return
+ return [uncubicSuperPath(source), uncubicSuperPath(destination)]
+}
+
+
+
+
+
+
+// This function converts every segment of a path array into equivalent cubic Bezier curves
+// and return the results in a 3 dimensional array that have the following hierarchy:
+// Cubic super path: [ ]
+// Segments: [ ] ...
+// Segment points: [SVG.Point, SVG.Point, SVG.Point] ...
+//
+// A segment point is a point with the two control points that are attached to it:
+// [First control point, Point, Second control point]
+//
+// If the passed path array cannot be converted in a cubic super path, this function return an empty array.
+function cubicSuperPath(pathArray) {
+ pathArray = new SVG.PathArray(pathArray)
+
+ var cubicSP = []
+ , subpath = null
+ , subpathStartPt = null
+ , lastPt = null
+ , lastCtrlPt = null
+ , i, il, cmd = null, params, lastCmd
+ , start, control, end
+ , arcSegPoints, segPt
+
+ for (i = 0, il = pathArray.value.length; i < il; i++) {
+ lastCmd = cmd
+ cmd = pathArray.value[i][0]
+ params = pathArray.value[i].slice(1)
+
+ switch (cmd) {
+ case 'M': // moveto
+ // Parameters: x y
+ if (lastPt) {
+ subpath.push([lastCtrlPt, lastPt, lastPt.clone()])
+ }
+ subpath = []
+ cubicSP.push(subpath) // Push a reference to the current subpath array in the cubic super path array
+ subpathStartPt = new SVG.Point(params)
+ lastPt = subpathStartPt.clone()
+ lastCtrlPt = subpathStartPt.clone()
+ break
+
+ case 'L': // lineto
+ // Parameters: x y
+ subpath.push([lastCtrlPt, lastPt, lastPt.clone()])
+ lastPt = new SVG.Point(params)
+ lastCtrlPt = lastPt.clone()
+ break
+
+ case 'H': // horizontal lineto
+ // Parameters: x
+ subpath.push([lastCtrlPt, lastPt, lastPt.clone()])
+ lastPt = new SVG.Point(params[0], lastPt.y)
+ lastCtrlPt = lastPt.clone()
+ break
+
+ case 'V': // vertical lineto
+ // Parameters: y
+ subpath.push([lastCtrlPt, lastPt, lastPt.clone()])
+ lastPt = new SVG.Point(lastPt.x, params[0])
+ lastCtrlPt = lastPt.clone()
+ break
+
+ case 'C': // curveto
+ // Parameters: x1 y1 x2 y2 x y
+ subpath.push([lastCtrlPt, lastPt, new SVG.Point(params.slice(0,2))])
+ lastPt = new SVG.Point(params.slice(4,6))
+ lastCtrlPt = new SVG.Point(params.slice(2,4))
+ break
+
+ case 'S': // shorthand/smooth curveto
+ // Parameters: x2 y2 x y
+ // For this version of curveto, the first control point is the reflection of the second control point on the previous command relative to the current point
+ // If the previous command is not a curveto command, then the first control point is the same as the current point
+ if(lastCmd === 'C' || lastCmd === 'S') {
+ subpath.push([lastCtrlPt, lastPt, lastPt.times(2).minus(lastCtrlPt)])
+ } else {
+ subpath.push([lastCtrlPt, lastPt, lastPt.clone()])
+ }
+ lastPt = new SVG.Point(params.slice(2,4))
+ lastCtrlPt = new SVG.Point(params.slice(0,2))
+ break
+
+ case 'Q': // quadratic Bezier curveto
+ // Parameters: x1 y1 x y
+ // For an explanation of the method used, see: https://pomax.github.io/bezierinfo/#reordering
+ start = lastPt
+ control = new SVG.Point(params.slice(0,2))
+ end = new SVG.Point(params.slice(2,4))
+
+ subpath.push([lastCtrlPt, start, start.times(1/3).plus(control.times(2/3))])
+ lastPt = end
+ lastCtrlPt = control.times(2/3).plus(end.times(1/3))
+ break
+
+ case 'T': // shorthand/smooth quadratic Bézier curveto
+ // Parameters: x y
+ // For this version of quadratic Bézier curveto, the control point is the reflection of the control point on the previous command relative to the current point
+ // If the previous command is not a quadratic Bézier curveto command, then the control point is the same as the current point
+ start = lastPt
+ if(lastCmd === 'Q' || lastCmd === 'T') {
+ control = start.times(2).minus(control)
+ } else {
+ control = start
+ }
+ end = new SVG.Point(params.slice(0,2))
+
+ subpath.push([lastCtrlPt, start, start.times(1/3).plus(control.times(2/3))])
+ lastPt = end
+ lastCtrlPt = control.times(2/3).plus(end.times(1/3))
+ break
+
+ case 'A': // elliptical arc
+ // Parameters: rx ry x-axis-rotation large-arc-flag sweep-flag x y
+ arcSegPoints = arcToPath(lastPt, params)
+ arcSegPoints[0][0] = lastCtrlPt
+ segPt = arcSegPoints.pop()
+ lastPt = segPt[1]
+ lastCtrlPt = segPt[0]
+ Array.prototype.push.apply(subpath, arcSegPoints)
+ break
+
+ case 'Z': // closepath
+ // Parameters: none
+ subpath.push([lastCtrlPt, lastPt, lastPt.clone()])
+ // Close the path only if it is not already closed
+ if(lastPt.x != subpathStartPt.x && lastPt.y != subpathStartPt.y) {
+ lastPt = subpathStartPt
+ lastCtrlPt = subpathStartPt.clone()
+ } else {
+ lastPt = null
+ lastCtrlPt = null
+ }
+ break
+ }
+ }
+
+ // Push final segment point if any
+ if(lastPt) {
+ subpath.push([lastCtrlPt, lastPt, lastPt.clone()])
+ }
+
+ return cubicSP
+}
+
+
+// This function convert a cubic super path into a path array
+function uncubicSuperPath (cubicSP) {
+ var i, il, j, jl, array = [], pathArray = new SVG.PathArray, subpath
+
+ for (i = 0, il = cubicSP.length; i < il; i++) {
+ subpath = cubicSP[i]
+
+ if (subpath.length) {
+ array.push(['M'].concat(subpath[0][1].toArray()))
+
+ for (j = 1, jl = subpath.length; j < jl; j++) {
+ array.push(['C'].concat(subpath[j-1][2].toArray(), subpath[j][0].toArray(), subpath[j][1].toArray()))
+ }
+ }
+ }
+
+ // Directly modify the value of a path array, this is done this way for performance
+ pathArray.value = array
+ return pathArray
+}
+
+// Convert an arc segment into equivalent cubic Bezier curves
+// Depending on the arc, up to 4 curves might be used to represent it since a
+// curve gives a good approximation for only a quarter of an ellipse
+// The curves are returned as an array of segment points:
+// [ [SVG.Point, SVG.Point, SVG.Point] ... ]
+function arcToPath(lastPt, params) {
+ // Parameters extraction, handle out-of-range parameters as specified in the SVG spec
+ // See: https://www.w3.org/TR/SVG11/implnote.html#ArcOutOfRangeParameters
+ var rx = Math.abs(params[0]), ry = Math.abs(params[1]), xAxisRotation = params[2] % 360
+ , largeArcFlag = params[3], sweepFlag = params[4], x2 = params[5], y2 = params[6]
+ , A = lastPt, B = new SVG.Point(x2, y2)
+ , primedCoord, lambda, mat, k, c, cSquare, t, O, OA, OB, tetaStart, tetaEnd
+ , deltaTeta, nbSectors, f, arcSegPoints, angle, sinAngle, cosAngle, pt, i, il
+
+ // Ensure radii are non-zero
+ if(rx === 0 || ry === 0 || (A.x === B.x && A.y === B.y)) {
+ // treat this arc as a straight line segment
+ return [[A, A.clone(), A.clone()], [B, B.clone(), B.clone()]]
+ }
+
+ // Ensure radii are large enough using the algorithm provided in the SVG spec
+ // See: https://www.w3.org/TR/SVG11/implnote.html#ArcCorrectionOutOfRangeRadii
+ primedCoord = A.minus(B).divide(2).transform(new SVG.Matrix().rotate(xAxisRotation))
+ lambda = (primedCoord.x * primedCoord.x) / (rx * rx) + (primedCoord.y * primedCoord.y) / (ry * ry)
+ if(lambda > 1) {
+ lambda = Math.sqrt(lambda)
+ rx = lambda*rx
+ ry = lambda*ry
+ }
+
+ // To simplify calculations, we make the arc part of a unit circle (rayon is 1) instead of an ellipse
+ mat = new SVG.Matrix().rotate(xAxisRotation).scale(1/rx, 1/ry).rotate(-xAxisRotation)
+ A = A.transform(mat)
+ B = B.transform(mat)
+
+ // Calculate the horizontal and vertical distance between the initial and final point of the arc
+ k = [B.x-A.x, B.y-A.y]
+
+ // Find the length of the chord formed by A and B
+ cSquare = k[0]*k[0] + k[1]*k[1]
+ c = Math.sqrt(cSquare)
+
+ // Calculate the ratios of the horizontal and vertical distance on the length of the chord
+ k[0] /= c
+ k[1] /= c
+
+ // Calculate the distance between the circle center and the chord midpoint
+ // using this formula: t = sqrt(r^2 - c^2 / 4)
+ // where t is the distance between the cirle center and the chord midpoint,
+ // r is the rayon of the circle and c is the chord length
+ // From: http://www.ajdesigner.com/phpcircle/circle_segment_chord_t.php
+ // Because of the imprecision of floating point numbers, cSquare might end
+ // up being slightly above 4 which would result in a negative radicand
+ // To prevent that, a test is made before computing the square root
+ t = (cSquare < 4) ? Math.sqrt(1 - cSquare/4) : 0
+
+ // For most situations, there are actually two different ellipses that
+ // satisfy the constraints imposed by the points A and B, the radii rx and ry,
+ // and the xAxisRotation
+ // When the flags largeArcFlag and sweepFlag are equal, it means that the
+ // second ellipse is used as a solution
+ // See: https://www.w3.org/TR/SVG/paths.html#PathDataEllipticalArcCommands
+ if(largeArcFlag === sweepFlag) {
+ t *= -1
+ }
+
+ // Calculate the coordinates of the center of the circle from the midpoint of the chord
+ // This is done by multiplying the ratios calculated previously by the distance between
+ // the circle center and the chord midpoint and using these values to go from the midpoint
+ // to the center of the circle
+ // The negative of the vertical distance ratio is used to modify the x coordinate while
+ // the horizontal distance ratio is used to modify the y coordinate
+ // That is because the center of the circle is perpendicular to the chord and perpendicular
+ // lines are negative reciprocals
+ O = new SVG.Point((B.x+A.x)/2 + t*-k[1], (B.y+A.y)/2 + t*k[0])
+ // Move the center of the circle at the origin
+ OA = A.minus(O)
+ OB = B.minus(O)
+
+ // Calculate the start and end angle
+ tetaStart = Math.acos(OA.x/OA.norm())
+ if (OA.y < 0) {
+ tetaStart *= -1
+ }
+ tetaEnd = Math.acos(OB.x/OB.norm())
+ if (OB.y < 0) {
+ tetaEnd *= -1
+ }
+
+ // If sweep-flag is '1', then the arc will be drawn in a "positive-angle" direction,
+ // make sure that the end angle is above the start angle
+ if (sweepFlag && tetaStart > tetaEnd) {
+ tetaEnd += 2*Math.PI
+ }
+ // If sweep-flag is '0', then the arc will be drawn in a "negative-angle" direction,
+ // make sure that the end angle is below the start angle
+ if (!sweepFlag && tetaStart < tetaEnd) {
+ tetaEnd -= 2*Math.PI
+ }
+
+ // Find the number of Bezier curves that are required to represent the arc
+ // A cubic Bezier curve gives a good enough approximation when representing at most a quarter of a circle
+ nbSectors = Math.ceil(Math.abs(tetaStart-tetaEnd) * 2/Math.PI)
+
+ // Calculate the coordinates of the points of all the Bezier curves required to represent the arc
+ // For an in-depth explanation of this part see: http://pomax.github.io/bezierinfo/#circles_cubic
+ arcSegPoints = []
+ angle = tetaStart
+ deltaTeta = (tetaEnd-tetaStart)/nbSectors
+ f = 4*Math.tan(deltaTeta/4)/3
+ for (i = 0; i <= nbSectors; i++) { // The <= is because a Bezier curve have a start and a endpoint
+ cosAngle = Math.cos(angle)
+ sinAngle = Math.sin(angle)
+
+ pt = O.plus(cosAngle, sinAngle)
+ arcSegPoints[i] = [pt.plus(+f*sinAngle, -f*cosAngle), pt, pt.plus(-f*sinAngle, +f*cosAngle)]
+
+ angle += deltaTeta
+ }
+
+ // Remove the first control point of the first segment point and remove the second control point of the last segment point
+ // These two control points are not used in the approximation of the arc, that is why they are removed
+ arcSegPoints[0][0] = arcSegPoints[0][1].clone()
+ arcSegPoints[arcSegPoints.length-1][2] = arcSegPoints[arcSegPoints.length-1][1].clone()
+
+ // Revert the transformation that was applied to make the arc part of a unit circle instead of an ellipse
+ mat = new SVG.Matrix().rotate(xAxisRotation).scale(rx, ry).rotate(-xAxisRotation)
+ for (i = 0, il = arcSegPoints.length; i < il; i++) {
+ arcSegPoints[i][0] = arcSegPoints[i][0].transform(mat)
+ arcSegPoints[i][1] = arcSegPoints[i][1].transform(mat)
+ arcSegPoints[i][2] = arcSegPoints[i][2].transform(mat)
+ }
+
+ return arcSegPoints
+}
+
+
+// Use de Casteljau's algorithm to split a cubic Bezier curve
+// For a description of the algorithm, see: https://pomax.github.io/bezierinfo/#decasteljau
+// Return an array of 3 segment points
+function cspSegSplit(segPt1, segPt2, t) {
+ segPt1 = [segPt1[0].clone(), segPt1[1].clone(), segPt1[2].clone()]
+ segPt2 = [segPt2[0].clone(), segPt2[1].clone(), segPt2[2].clone()]
+
+ var m1 = segPt1[1].morph(segPt1[2]).at(t)
+ , m2 = segPt1[2].morph(segPt2[0]).at(t)
+ , m3 = segPt2[0].morph(segPt2[1]).at(t)
+ , m4 = m1.morph(m2).at(t)
+ , m5 = m2.morph(m3).at(t)
+ , m = m4.morph(m5).at(t)
+
+ return [[segPt1[0], segPt1[1], m1], [m4, m, m5], [m3, segPt2[1], segPt2[2]]]
+}
+
+
+// Find the length of a cubic Bezier curve using the built-in method getTotalLength of SVGPathElement
+// For more info, see: https://www.w3.org/TR/SVG11/paths.html#InterfaceSVGPathElement
+function cspSegLength(segPt1, segPt2) {
+ var path = document.createElementNS(SVG.ns, "path")
+ , d = ['M', segPt1[1].toArray(), 'C', segPt1[2].toArray(), segPt2[0].toArray(), segPt2[1].toArray()].join(' ')
+
+ path.setAttribute('d', d)
+
+ return path.getTotalLength()
+}
+
+
+// Find the length of all the cubic Bezier curves of a cubic super path and return
+// the results in a 2 dimensional array that have the following hierarchy:
+// Cubic super path lengths: [ ]
+// Segments lengths: [ ] ...
+// Cubic Bezier curves length: Number ...
+//
+// On the returned array, the property total is set to the sum of all the lengths
+function cspLengths(cubicSP) {
+ var total = 0
+ , subpath, lengths = [], lengthsSubpath, length
+ , i, il, j, jl
+
+ for (i = 0, il = cubicSP.length; i < il; i++) {
+ subpath = cubicSP[i]
+ lengthsSubpath = []
+ lengths[i] = lengthsSubpath // Save a reference to the current subpath lengths array in the cubic super path lengths array
+
+ for (j = 1, jl = subpath.length; j < jl; j++) {
+ length = cspSegLength(subpath[j-1], subpath[j])
+ lengthsSubpath[j-1] = length
+ total += length
+ }
+ }
+
+ lengths.total = total
+ return lengths
+}
+
+
+// Split a cubic Bezier curve at the given length ratio
+// Return an array of 3 segment points
+function cspSegSplitAtLengthRatio(segPt1, segPt2, lengthRatio) {
+ var t = 1.0
+ , tdiv = t
+ , currentLength = cspSegLength(segPt1, segPt2)
+ , targetLength = lengthRatio * currentLength
+ , diff = currentLength - targetLength
+ , split = cspSegSplit(segPt1, segPt2, t)
+ , maxNbLoops = 4096 // For not getting stuck in an infinite loop
+
+ while (Math.abs(diff) > 0.001 && maxNbLoops--) {
+ tdiv /= 2
+ t += (diff < 0) ? tdiv : -tdiv
+ split = cspSegSplit(segPt1, segPt2, t)
+ currentLength = cspSegLength(split[0], split[1])
+ diff = currentLength - targetLength
+ }
+
+ return split
+}
+
+
+
+// Find the position relative to the total length of the endpoint of all the cubic Bezier curves
+// of a cubic super path and return the results in a 1 dimensional array
+function cspPositions(cubicSP) {
+ var lengths = cspLengths(cubicSP), total = lengths.total
+ , pos = 0, positions = []
+ , i, il, j, jl
+
+ for (i = 0, il = lengths.length; i < il; i++) {
+ for (j = 0, jl = lengths[i].length; j < jl; j++) {
+ pos += lengths[i][j] / total
+ positions.push(pos)
+ }
+ }
+
+ return positions
+}
+
+// Split the passed cubic super path at the specified positions and return the results as a new cubic super path
+// For performance reasons, the positions of the passed cubic super path must also be provided
+function cspSplitAtPositions(cubicSP, positions, positionsToSplitAt){
+ var subpath, newSubpath
+ , accumNbPositions = 0, segPt, lengthRatio, split, pos, prevPos
+ , i, il, j, jl // indexes on the cubicSP array
+ , k = 0 // index on the positions array
+ , l = 0, ll = positionsToSplitAt.length
+
+ for (i = 0, il = cubicSP.length; i < il && l < ll; i++) {
+ subpath = cubicSP[i]
+ // The positions are only for the endpoints of the cubic Bezier curves, so
+ // a subpath need at least 2 segment points for a position to be on it
+ if(subpath.length < 2) {continue}
+ // Test if there are splits to be performed on the current subpath
+ if(positionsToSplitAt[l] < positions[accumNbPositions + subpath.length-2]) {
+ k = accumNbPositions
+ newSubpath = []
+ cubicSP[i] = newSubpath // Save a reference to the new current subpath array in the cubic super path array
+ pos = positions[k-1] || 0
+
+ // Recopy the content of the current subpath, performing splits where necessary
+ newSubpath.push(subpath[0])
+ for (j = 1, jl = subpath.length; j < jl; j++) {
+ prevPos = pos
+ pos = positions[k++]
+ segPt = subpath[j]
+
+ while(l < ll && positionsToSplitAt[l] < pos) {
+ lengthRatio = (positionsToSplitAt[l] - prevPos) / (pos - prevPos)
+ split = cspSegSplitAtLengthRatio(newSubpath[newSubpath.length-1], segPt, lengthRatio)
+ newSubpath[newSubpath.length-1] = split[0]
+ newSubpath.push(split[1])
+ segPt = split[2]
+ prevPos = positionsToSplitAt[l++]
+ }
+
+ newSubpath.push(segPt)
+ }
+ }
+
+ // -1 because positions are only for endpoints of Bezier curves
+ accumNbPositions += subpath.length - 1
+ }
+}
projects / svg.js.git / commitdiff