svg.pathmorphing.js

/*!
* svg.pathmorphing.js - Enables pathmorphing / path animation in svg.js
* @version 0.1.3
*
*
* @copyright (c) 2018 Ulrich-Matthias Schäfer
* @license MIT
*/;
;(function() {
  "use strict";

  SVG.extend(SVG.PathArray, {
    morph: function(array) {

      var startArr = this.value
          ,  destArr = this.parse(array)

      var startOffsetM = 0
          ,  destOffsetM = 0

      var startOffsetNextM = false
          ,  destOffsetNextM = false

      while(true){
        // stop if there is no M anymore
        if(startOffsetM === false && destOffsetM === false) break

        // find the next M in path array
        startOffsetNextM = findNextM(startArr, startOffsetM === false ? false : startOffsetM+1)
        destOffsetNextM = findNextM( destArr,  destOffsetM === false ? false :  destOffsetM+1)

        // We have to add one M to the startArray
        if(startOffsetM === false){
          var bbox = new SVG.PathArray(result.start).bbox()

          // when the last block had no bounding box we simply take the first M we got
          if(bbox.height == 0 || bbox.width == 0){
            startOffsetM =  startArr.push(startArr[0]) - 1
          }else{
            // we take the middle of the bbox instead when we got one
            startOffsetM = startArr.push( ['M', bbox.x + bbox.width/2, bbox.y + bbox.height/2 ] ) - 1
          }
        }

        // We have to add one M to the destArray
        if( destOffsetM === false){
          var bbox = new SVG.PathArray(result.dest).bbox()

          if(bbox.height == 0 || bbox.width == 0){
            destOffsetM =  destArr.push(destArr[0]) - 1
          }else{
            destOffsetM =  destArr.push( ['M', bbox.x + bbox.width/2, bbox.y + bbox.height/2 ] ) - 1
          }
        }

        // handle block from M to next M
        var result = handleBlock(startArr, startOffsetM, startOffsetNextM, destArr, destOffsetM, destOffsetNextM)

        // update the arrays to their new values
        startArr = startArr.slice(0, startOffsetM).concat(result.start, startOffsetNextM === false ? [] : startArr.slice(startOffsetNextM))
        destArr =  destArr.slice(0,  destOffsetM).concat(result.dest ,  destOffsetNextM === false ? [] :  destArr.slice( destOffsetNextM))

        // update offsets
        startOffsetM = startOffsetNextM === false ? false : startOffsetM + result.start.length
        destOffsetM =  destOffsetNextM === false ? false :  destOffsetM + result.dest.length

      }

      // copy back arrays
      this.value = startArr
      this.destination = new SVG.PathArray()
      this.destination.value = destArr

      return this
    }
  })



// sorry for the long declaration
// slices out one block (from M to M) and syncronize it so the types and length match
  function handleBlock(startArr, startOffsetM, startOffsetNextM, destArr, destOffsetM, destOffsetNextM, undefined){

    // slice out the block we need
    var startArrTemp = startArr.slice(startOffsetM, startOffsetNextM || undefined)
        ,  destArrTemp =  destArr.slice( destOffsetM,  destOffsetNextM || undefined)

    var i = 0
        , posStart = {pos:[0,0], start:[0,0]}
        , posDest  = {pos:[0,0], start:[0,0]}

    do{

      // convert shorthand types to long form
      startArrTemp[i] = simplyfy.call(posStart, startArrTemp[i])
      destArrTemp[i] = simplyfy.call(posDest ,  destArrTemp[i])

      // check if both shape types match
      // 2 elliptical arc curve commands ('A'), are considered different if the
      // flags (large-arc-flag, sweep-flag) don't match
      if(startArrTemp[i][0] != destArrTemp[i][0] || startArrTemp[i][0] == 'M' ||
          (startArrTemp[i][0] == 'A' &&
              (startArrTemp[i][4] != destArrTemp[i][4] || startArrTemp[i][5] != destArrTemp[i][5])
          )
      ) {

        // if not, convert shapes to beziere
        Array.prototype.splice.apply(startArrTemp, [i, 1].concat(toBeziere.call(posStart, startArrTemp[i])))
        Array.prototype.splice.apply(destArrTemp, [i, 1].concat(toBeziere.call(posDest, destArrTemp[i])))

      } else {

        // only update positions otherwise
        startArrTemp[i] = setPosAndReflection.call(posStart, startArrTemp[i])
        destArrTemp[i] = setPosAndReflection.call(posDest ,  destArrTemp[i])

      }

      // we are at the end at both arrays. stop here
      if(++i == startArrTemp.length && i == destArrTemp.length) break

      // destArray is longer. Add one element
      if(i == startArrTemp.length){
        startArrTemp.push([
          'C',
          posStart.pos[0],
          posStart.pos[1],
          posStart.pos[0],
          posStart.pos[1],
          posStart.pos[0],
          posStart.pos[1],
        ])
      }

      // startArr is longer. Add one element
      if(i == destArrTemp.length){
        destArrTemp.push([
          'C',
          posDest.pos[0],
          posDest.pos[1],
          posDest.pos[0],
          posDest.pos[1],
          posDest.pos[0],
          posDest.pos[1]
        ])
      }


    }while(true)

    // return the updated block
    return {start:startArrTemp, dest:destArrTemp}
  }

// converts shorthand types to long form
  function simplyfy(val){

    switch(val[0]){
      case 'z': // shorthand line to start
      case 'Z':
        val[0] = 'L'
        val[1] = this.start[0]
        val[2] = this.start[1]
        break
      case 'H': // shorthand horizontal line
        val[0] = 'L'
        val[2] = this.pos[1]
        break
      case 'V': // shorthand vertical line
        val[0] = 'L'
        val[2] = val[1]
        val[1] = this.pos[0]
        break
      case 'T': // shorthand quadratic beziere
        val[0] = 'Q'
        val[3] = val[1]
        val[4] = val[2]
        val[1] = this.reflection[1]
        val[2] = this.reflection[0]
        break
      case 'S': // shorthand cubic beziere
        val[0] = 'C'
        val[6] = val[4]
        val[5] = val[3]
        val[4] = val[2]
        val[3] = val[1]
        val[2] = this.reflection[1]
        val[1] = this.reflection[0]
        break
    }

    return val

  }

// updates reflection point and current position
  function setPosAndReflection(val){

    var len = val.length

    this.pos = [ val[len-2], val[len-1] ]

    if('SCQT'.indexOf(val[0]) != -1)
      this.reflection = [ 2 * this.pos[0] - val[len-4], 2 * this.pos[1] - val[len-3] ]

    return val
  }

// converts all types to cubic beziere
  function toBeziere(val){
    var retVal = [val]

    switch(val[0]){
      case 'M': // special handling for M
        this.pos = this.start = [val[1], val[2]]
        return retVal
      case 'L':
        val[5] = val[3] = val[1]
        val[6] = val[4] = val[2]
        val[1] = this.pos[0]
        val[2] = this.pos[1]
        break
      case 'Q':
        val[6] = val[4]
        val[5] = val[3]
        val[4] = val[4] * 1/3 + val[2] * 2/3
        val[3] = val[3] * 1/3 + val[1] * 2/3
        val[2] = this.pos[1] * 1/3 + val[2] * 2/3
        val[1] = this.pos[0] * 1/3 + val[1] * 2/3
        break
      case 'A':
        retVal = arcToBeziere(this.pos, val)
        val = retVal[0]
        break
    }

    val[0] = 'C'
    this.pos = [val[5], val[6]]
    this.reflection = [2 * val[5] - val[3], 2 * val[6] - val[4]]

    return retVal

  }

// finds the next position of type M
  function findNextM(arr, offset){

    if(offset === false) return false

    for(var i = offset, len = arr.length;i < len;++i){

      if(arr[i][0] == 'M') return i

    }

    return false
  }



// 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 SVG curve commands:
// [ ['C', x1, y1, x2, y2, x, y] ... ]
  function arcToBeziere(pos, val) {
    // 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(val[1]), ry = Math.abs(val[2]), xAxisRotation = val[3] % 360
        , largeArcFlag = val[4], sweepFlag = val[5], x = val[6], y = val[7]
        , A = new SVG.Point(pos), B = new SVG.Point(x, y)
        , primedCoord, lambda, mat, k, c, cSquare, t, O, OA, OB, tetaStart, tetaEnd
        , deltaTeta, nbSectors, f, arcSegPoints, angle, sinAngle, cosAngle, pt, i, il
        , retVal = [], x1, y1, x2, y2

    // 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 [['C', A.x, A.y, B.x, B.y, B.x, B.y]]
    }

    // Ensure radii are large enough using the algorithm provided in the SVG spec
    // See: https://www.w3.org/TR/SVG11/implnote.html#ArcCorrectionOutOfRangeRadii
    primedCoord = new SVG.Point((A.x-B.x)/2, (A.y-B.y)/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 = new SVG.Point(A.x-O.x, A.y-O.y)
    OB = new SVG.Point(B.x-O.x, B.y-O.y)

    // Calculate the start and end angle
    tetaStart = Math.acos(OA.x/Math.sqrt(OA.x*OA.x + OA.y*OA.y))
    if (OA.y < 0) {
      tetaStart *= -1
    }
    tetaEnd = Math.acos(OB.x/Math.sqrt(OB.x*OB.x + OB.y*OB.y))
    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 = new SVG.Point(O.x+cosAngle, O.y+sinAngle)
      arcSegPoints[i] = [new SVG.Point(pt.x+f*sinAngle, pt.y-f*cosAngle), pt, new SVG.Point(pt.x-f*sinAngle, pt.y+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)
    }


    // Convert the segments points to SVG curve commands
    for (i = 1, il = arcSegPoints.length; i < il; i++) {
      pt = arcSegPoints[i-1][2]
      x1 = pt.x
      y1 = pt.y

      pt = arcSegPoints[i][0]
      x2 = pt.x
      y2 = pt.y

      pt = arcSegPoints[i][1]
      x = pt.x
      y = pt.y

      retVal.push(['C', x1, y1, x2, y2, x, y])
    }

    return retVal
  }
}());