* @copyright Wout Fierens <wout@mick-wout.com.com>
* @license MIT
*
-* BUILT: Tue Dec 20 2016 04:06:31 GMT-0500 (EST)
+* BUILT: Tue Dec 20 2016 21:29:40 GMT-0500 (EST)
*/;
(function(root, factory) {
if (typeof define === 'function' && define.amd) {
}
// Make path array morphable
, morph: function(pathArray) {
- var pathsMorphable
-
- this.destination = new SVG.PathArray(pathArray)
+ pathArray = new SVG.PathArray(pathArray)
- if(this.haveSameCommands(this.destination)) {
- this.sourceMorphable = this
- this.destinationMorphable = this.destination
+ if(this.haveSameCommands(pathArray)) {
+ this.destination = pathArray
} else {
- pathsMorphable = SVG.utils.makePathsMorphable(this.value, this.destination)
- this.sourceMorphable = pathsMorphable[0]
- this.destinationMorphable = pathsMorphable[1]
+ this.destination = undefined
}
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)
- }
- }
+ // make sure a destination is defined
+ if (!this.destination) return this
- // Directly modify the value of a path array, this is done this way for performance
- pathArray.value = array
- return pathArray
+ var sourceArray = this.value
+ , destinationArray = this.destination.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) {
{x:x.x, y:x.y} :
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
, 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
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t=u(this,0,1),e=u(this,1,0),i=180/Math.PI*Math.atan2(t.y,t.x)-90;return{x:this.e,y:this.f,transformedX:(this.e*Math.cos(i*Math.PI/180)+this.f*Math.sin(i*Math.PI/180))/Math.sqrt(this.a*this.a+this.b*this.b),transformedY:(this.f*Math.cos(i*Math.PI/180)+this.e*Math.sin(-i*Math.PI/180))/Math.sqrt(this.c*this.c+this.d*this.d),skewX:-i,skewY:180/Math.PI*Math.atan2(e.y,e.x),scaleX:Math.sqrt(this.a*this.a+this.b*this.b),scaleY:Math.sqrt(this.c*this.c+this.d*this.d),rotation:i,a:this.a,b:this.b,c:this.c,d:this.d,e:this.e,f:this.f,matrix:new A.Matrix(this)}},clone:function(){return new A.Matrix(this)},morph:function(t){return this.destination=new A.Matrix(t),this},at:function(t){if(!this.destination)return this;var e=new A.Matrix({a:this.a+(this.destination.a-this.a)*t,b:this.b+(this.destination.b-this.b)*t,c:this.c+(this.destination.c-this.c)*t,d:this.d+(this.destination.d-this.d)*t,e:this.e+(this.destination.e-this.e)*t,f:this.f+(this.destination.f-this.f)*t});if(this.param&&this.param.to){var i={rotation:this.param.from.rotation+(this.param.to.rotation-this.param.from.rotation)*t,cx:this.param.from.cx,cy:this.param.from.cy};e=e.rotate((this.param.to.rotation-2*this.param.from.rotation)*t,i.cx,i.cy),e.param=i}return e},multiply:function(t){return new A.Matrix(this.native().multiply(c(t).native()))},inverse:function(){return new A.Matrix(this.native().inverse())},translate:function(t,e){return new A.Matrix(this.native().translate(t||0,e||0))},scale:function(t,e,i,n){return 1==arguments.length?e=t:3==arguments.length&&(n=i,i=e,e=t),this.around(i,n,new A.Matrix(t,0,0,e,0,0))},rotate:function(t,e,i){return t=A.utils.radians(t),this.around(e,i,new A.Matrix(Math.cos(t),Math.sin(t),(-Math.sin(t)),Math.cos(t),0,0))},flip:function(t,e){return"x"==t?this.scale(-1,1,e,0):this.scale(1,-1,0,e)},skew:function(t,e,i,n){return 1==arguments.length?e=t:3==arguments.length&&(n=i,i=e,e=t),t=A.utils.radians(t),e=A.utils.radians(e),this.around(i,n,new A.Matrix(1,Math.tan(e),Math.tan(t),1,0,0))},skewX:function(t,e,i){return this.skew(t,0,e,i)},skewY:function(t,e,i){return this.skew(0,t,e,i)},around:function(t,e,i){return this.multiply(new A.Matrix(1,0,0,1,t||0,e||0)).multiply(i).multiply(new A.Matrix(1,0,0,1,-t||0,-e||0))},native:function(){for(var t=A.parser.native.createSVGMatrix(),e=E.length-1;e>=0;e--)t[E[e]]=this[E[e]];return t},toString:function(){return"matrix("+this.a+","+this.b+","+this.c+","+this.d+","+this.e+","+this.f+")"}},parent:A.Element,construct:{ctm:function(){return new A.Matrix(this.node.getCTM())},screenCTM:function(){return new A.Matrix(this.node.getScreenCTM())}}}),A.Point=A.invent({create:function(t,e){var i,n={x:0,y:0};i=Array.isArray(t)?{x:t[0],y:t[1]}:"object"==typeof t?{x:t.x,y:t.y}:null!=t?{x:t,y:null!=e?e:t}:n,this.x=i.x,this.y=i.y},extend:{clone:function(){return new A.Point(this)},morph:function(t,e){return this.destination=new A.Point(t,e),this},at:function(t){if(!this.destination)return this;var e=new A.Point({x:this.x+(this.destination.x-this.x)*t,y:this.y+(this.destination.y-this.y)*t});return e},native:function(){var t=A.parser.native.createSVGPoint();return t.x=this.x,t.y=this.y,t},transform:function(t){return new A.Point(this.native().matrixTransform(t.native()))},toArray:function(){return[this.x,this.y]},plus:function(t,e){var i=new A.Point(t,e);return new A.Point(this.x+i.x,this.y+i.y)},minus:function(t,e){var i=new A.Point(t,e);return new A.Point(this.x-i.x,this.y-i.y)},times:function(t,e){var i=new A.Point(t,e);return new A.Point(this.x*i.x,this.y*i.y)},divide:function(t,e){var i=new A.Point(t,e);return new A.Point(this.x/i.x,this.y/i.y)},norm:function(){return Math.sqrt(this.x*this.x+this.y*this.y)},distance:function(t,e){return this.minus(t,e).norm()}}}),A.extend(A.Element,{point:function(t,e){return new 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 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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 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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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this._array||(this._array=new A.PointArray(this.attr("points")))},plot:function(t){return this.attr("points",this._array=new A.PointArray(t))},move:function(t,e){return this.attr("points",this.array().move(t,e))},size:function(t,e){var i=h(this,t,e);return this.attr("points",this.array().size(i.width,i.height))}}),A.extend(A.Line,A.Polyline,A.Polygon,{morphArray:A.PointArray,x:function(t){return null==t?this.bbox().x:this.move(t,this.bbox().y)},y:function(t){return null==t?this.bbox().y:this.move(this.bbox().x,t)},width:function(t){var e=this.bbox();return null==t?e.width:this.size(t,e.height)},height:function(t){var e=this.bbox();return null==t?e.height:this.size(e.width,t)}}),A.Path=A.invent({create:"path",inherit:A.Shape,extend:{morphArray:A.PathArray,array:function(){return this._array||(this._array=new A.PathArray(this.attr("d")))},plot:function(t){return this.attr("d",this._array=new A.PathArray(t))},move:function(t,e){return this.attr("d",this.array().move(t,e))},x:function(t){return null==t?this.bbox().x:this.move(t,this.bbox().y)},y:function(t){return null==t?this.bbox().y:this.move(this.bbox().x,t)},size:function(t,e){var i=h(this,t,e);return this.attr("d",this.array().size(i.width,i.height))},width:function(t){return null==t?this.bbox().width:this.size(t,this.bbox().height)},height:function(t){return null==t?this.bbox().height:this.size(this.bbox().width,t)}},construct:{path:function(t){return this.put(new A.Path).plot(t)}}}),A.Image=A.invent({create:"image",inherit:A.Shape,extend:{load:function(t){if(!t)return this;var i=this,n=e.createElement("img");return n.onload=function(){var e=i.parent(A.Pattern);null!==e&&(0==i.width()&&0==i.height()&&i.size(n.width,n.height),e&&0==e.width()&&0==e.height()&&e.size(i.width(),i.height()),"function"==typeof i._loaded&&i._loaded.call(i,{width:n.width,height:n.height,ratio:n.width/n.height,url:t}))},n.onerror=function(t){"function"==typeof i._error&&i._error.call(i,t)},this.attr("href",n.src=this.src=t,A.xlink)},loaded:function(t){return this._loaded=t,this},error:function(t){return this._error=t,this}},construct:{image:function(t,e,i){return this.put(new A.Image).load(t).size(e||0,i||e||0)}}}),A.Text=A.invent({create:function(){this.constructor.call(this,A.create("text")),this.dom.leading=new A.Number(1.3),this._rebuild=!0,this._build=!1,this.attr("font-family",A.defaults.attrs["font-family"])},inherit:A.Shape,extend:{x:function(t){return null==t?this.attr("x"):(this.textPath||this.lines().each(function(){this.dom.newLined&&this.x(t)}),this.attr("x",t))},y:function(t){var e=this.attr("y"),i="number"==typeof e?e-this.bbox().y:0;return null==t?"number"==typeof e?e-i:e:this.attr("y","number"==typeof t?t+i:t)},cx:function(t){return null==t?this.bbox().cx:this.x(t-this.bbox().width/2)},cy:function(t){return null==t?this.bbox().cy:this.y(t-this.bbox().height/2)},text:function(t){if("undefined"==typeof t){for(var t="",e=this.node.childNodes,i=0,n=e.length;i<n;++i)0!=i&&3!=e[i].nodeType&&1==A.adopt(e[i]).dom.newLined&&(t+="\n"),t+=e[i].textContent;return t}if(this.clear().build(!0),"function"==typeof t)t.call(this,this);else{t=t.split("\n");for(var i=0,r=t.length;i<r;i++)this.tspan(t[i]).newLine()}return this.build(!1).rebuild()},size:function(t){return this.attr("font-size",t).rebuild()},leading:function(t){return null==t?this.dom.leading:(this.dom.leading=new A.Number(t),this.rebuild())},lines:function(){var t=(this.textPath&&this.textPath()||this).node,e=A.utils.map(A.utils.filterSVGElements(t.childNodes),function(t){return A.adopt(t)});return new A.Set(e)},rebuild:function(t){if("boolean"==typeof t&&(this._rebuild=t),this._rebuild){var e=this,i=0,n=this.dom.leading*new A.Number(this.attr("font-size"));this.lines().each(function(){this.dom.newLined&&(this.textPath||this.attr("x",e.attr("x")),"\n"==this.text()?i+=n:(this.attr("dy",n+i),i=0))}),this.fire("rebuild")}return this},build:function(t){return this._build=!!t,this},setData:function(t){return this.dom=t,this.dom.leading=new A.Number(t.leading||1.3),this}},construct:{text:function(t){return this.put(new A.Text).text(t)},plain:function(t){return this.put(new A.Text).plain(t)}}}),A.Tspan=A.invent({create:"tspan",inherit:A.Shape,extend:{text:function(t){return null==t?this.node.textContent+(this.dom.newLined?"\n":""):("function"==typeof t?t.call(this,this):this.plain(t),this)},dx:function(t){return this.attr("dx",t)},dy:function(t){return this.attr("dy",t)},newLine:function(){var t=this.parent(A.Text);return this.dom.newLined=!0,this.dy(t.dom.leading*t.attr("font-size")).attr("x",t.x())}}}),A.extend(A.Text,A.Tspan,{plain:function(t){return this._build===!1&&this.clear(),this.node.appendChild(e.createTextNode(t)),this},tspan:function(t){var e=(this.textPath&&this.textPath()||this).node,i=new A.Tspan;return this._build===!1&&this.clear(),e.appendChild(i.node),i.text(t)},clear:function(){for(var t=(this.textPath&&this.textPath()||this).node;t.hasChildNodes();)t.removeChild(t.lastChild);return this},length:function(){return this.node.getComputedTextLength()}}),A.TextPath=A.invent({create:"textPath",inherit:A.Parent,parent:A.Text,construct:{path:function(t){for(var e=new A.TextPath,i=this.doc().defs().path(t);this.node.hasChildNodes();)e.node.appendChild(this.node.firstChild);return this.node.appendChild(e.node),e.attr("href","#"+i,A.xlink),this},plot:function(t){var e=this.track();return e&&e.plot(t),this},track:function(){var t=this.textPath();if(t)return t.reference("href")},textPath:function(){if(this.node.firstChild&&"textPath"==this.node.firstChild.nodeName)return A.adopt(this.node.firstChild)}}}),A.Nested=A.invent({create:function(){this.constructor.call(this,A.create("svg")),this.style("overflow","visible")},inherit:A.Container,construct:{nested:function(){return this.put(new A.Nested)}}}),A.A=A.invent({create:"a",inherit:A.Container,extend:{to:function(t){return this.attr("href",t,A.xlink)},show:function(t){return this.attr("show",t,A.xlink)},target:function(t){return this.attr("target",t)}},construct:{link:function(t){return this.put(new A.A).to(t)}}}),A.extend(A.Element,{linkTo:function(t){var e=new A.A;return"function"==typeof t?t.call(e,e):e.to(t),this.parent().put(e).put(this)}}),A.Marker=A.invent({create:"marker",inherit:A.Container,extend:{width:function(t){return this.attr("markerWidth",t)},height:function(t){return this.attr("markerHeight",t)},ref:function(t,e){return this.attr("refX",t).attr("refY",e)},update:function(t){return this.clear(),"function"==typeof t&&t.call(this,this),this},toString:function(){return"url(#"+this.id()+")"}},construct:{marker:function(t,e,i){return this.defs().marker(t,e,i)}}}),A.extend(A.Defs,{marker:function(t,e,i){return this.put(new A.Marker).size(t,e).ref(t/2,e/2).viewbox(0,0,t,e).attr("orient","auto").update(i)}}),A.extend(A.Line,A.Polyline,A.Polygon,A.Path,{marker:function(t,e,i,n){var r=["marker"];return"all"!=t&&r.push(t),r=r.join("-"),t=arguments[1]instanceof A.Marker?arguments[1]:this.doc().marker(e,i,n),this.attr(r,t)}});var S={stroke:["color","width","opacity","linecap","linejoin","miterlimit","dasharray","dashoffset"],fill:["color","opacity","rule"],prefix:function(t,e){return"color"==e?t:t+"-"+e}};["fill","stroke"].forEach(function(t){var e,i={};i[t]=function(i){if("undefined"==typeof i)return this;if("string"==typeof i||A.Color.isRgb(i)||i&&"function"==typeof i.fill)this.attr(t,i);else for(e=S[t].length-1;e>=0;e--)null!=i[S[t][e]]&&this.attr(S.prefix(t,S[t][e]),i[S[t][e]]);return this},A.extend(A.Element,A.FX,i)}),A.extend(A.Element,A.FX,{rotate:function(t,e,i){return this.transform({rotation:t,cx:e,cy:i})},skew:function(t,e,i,n){
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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 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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 g.Doc?o.parent().offsetWidth:o.parent().width()),o=o.parent();for(;"%"==s.unit;)c*=s.value,s=new g.Number(h instanceof g.Doc?h.parent().offsetHeight:h.parent().height()),h=h.parent();this.x=0,this.y=0,this.width=n*l,this.height=s*c,this.zoom=1,a&&(e=parseFloat(a[0]),i=parseFloat(a[1]),n=parseFloat(a[2]),s=parseFloat(a[3]),this.zoom=this.width/this.height>n/s?this.height/s:this.width/n,this.x=e,this.y=i,this.width=n,this.height=s)}else 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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 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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 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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