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transformation-matrix

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2d transformation matrix functions written in ES6 syntax. Tree shaking ready!

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var __webpack_exports__ = {};
// ESM COMPAT FLAG
__webpack_require__.r(__webpack_exports__);

// EXPORTS
__webpack_require__.d(__webpack_exports__, {
  applyToPoint: () => (/* reexport */ applyToPoint),
  applyToPoints: () => (/* reexport */ applyToPoints),
  compose: () => (/* reexport */ compose),
  decomposeTSR: () => (/* reexport */ decomposeTSR),
  flipOrigin: () => (/* reexport */ flipOrigin),
  flipX: () => (/* reexport */ flipX),
  flipY: () => (/* reexport */ flipY),
  fromDefinition: () => (/* reexport */ fromDefinition),
  fromObject: () => (/* reexport */ fromObject),
  fromOneMovingPoint: () => (/* reexport */ fromOneMovingPoint),
  fromString: () => (/* reexport */ fromString),
  fromStringLegacy: () => (/* reexport */ fromStringLegacy),
  fromTransformAttribute: () => (/* reexport */ fromTransformAttribute),
  fromTriangles: () => (/* reexport */ fromTriangles),
  fromTwoMovingPoints: () => (/* reexport */ fromTwoMovingPoints),
  identity: () => (/* reexport */ identity),
  inverse: () => (/* reexport */ inverse),
  isAffineMatrix: () => (/* reexport */ isAffineMatrix),
  rotate: () => (/* reexport */ rotate),
  rotateDEG: () => (/* reexport */ rotateDEG),
  scale: () => (/* reexport */ scale),
  shear: () => (/* reexport */ shear),
  skew: () => (/* reexport */ skew),
  skewDEG: () => (/* reexport */ skewDEG),
  smoothMatrix: () => (/* reexport */ smoothMatrix),
  toCSS: () => (/* reexport */ toCSS),
  toSVG: () => (/* reexport */ toSVG),
  toString: () => (/* reexport */ toString_toString),
  transform: () => (/* reexport */ transform),
  translate: () => (/* reexport */ translate)
});

;// ./src/applyToPoint.js
/**
 * Calculate a point transformed with an affine matrix
 * @param matrix {Matrix} Affine Matrix
 * @param  point {Point} Point
 * @returns {Point} Point
 */
function applyToPoint(matrix, point) {
  return Array.isArray(point) ? [matrix.a * point[0] + matrix.c * point[1] + matrix.e, matrix.b * point[0] + matrix.d * point[1] + matrix.f] : {
    x: matrix.a * point.x + matrix.c * point.y + matrix.e,
    y: matrix.b * point.x + matrix.d * point.y + matrix.f
  };
}

/**
 * Calculate an array of points transformed with an affine matrix
 * @param matrix {Matrix} Affine Matrix
 * @param points {Point[]} Array of point
 * @returns {Point[]} Array of point
 */
function applyToPoints(matrix, points) {
  return points.map(function (point) {
    return applyToPoint(matrix, point);
  });
}
;// ./src/fromObject.js
/**
 * Extract an affine matrix from an object that contains a,b,c,d,e,f keys
 * Any value could be a float or a string that contains a float
 * @param object {Object} Object that contains a,b,c,d,e,f keys
 * @return {Matrix} Affine Matrix
 */
function fromObject(object) {
  return {
    a: parseFloat(object.a),
    b: parseFloat(object.b),
    c: parseFloat(object.c),
    d: parseFloat(object.d),
    e: parseFloat(object.e),
    f: parseFloat(object.f)
  };
}
;// ./src/fromString.js
/**
 * @ignore
 * @type {RegExp}
 */
var matrixRegex = /^matrix\(\s*([0-9_+-.e]+)\s*,\s*([0-9_+-.e]+)\s*,\s*([0-9_+-.e]+)\s*,\s*([0-9_+-.e]+)\s*,\s*([0-9_+-.e]+)\s*,\s*([0-9_+-.e]+)\s*\)$/i;

/**
 * Parse a string formatted as matrix(a,b,c,d,e,f)
 * @param string {string} String with an affine matrix
 * @returns {Matrix} Affine Matrix
 *
 * @example
 * > fromString('matrix(1,2,3,4,5,6)')
 * {a: 1, b: 2, c: 3, d: 4, c: 5, e: 6}
 */
function fromString(string) {
  var parseFloatOrThrow = function parseFloatOrThrow(number) {
    var n = parseFloat(number);
    if (Number.isFinite(n)) return n; // excludes NaN, +Infinite, -Infinite
    throw new Error("'".concat(string, "' is not a matrix"));
  };
  var prefix = string.substring(0, 7).toLowerCase();
  var suffix = string.substring(string.length - 1);
  var body = string.substring(7, string.length - 1);
  var elements = body.split(',');
  if (prefix === 'matrix(' && suffix === ')' && elements.length === 6) {
    return {
      a: parseFloatOrThrow(elements[0]),
      b: parseFloatOrThrow(elements[1]),
      c: parseFloatOrThrow(elements[2]),
      d: parseFloatOrThrow(elements[3]),
      e: parseFloatOrThrow(elements[4]),
      f: parseFloatOrThrow(elements[5])
    };
  }
  throw new Error("'".concat(string, "' is not a matrix"));
}

/**
 * Parse a string formatted as matrix(a,b,c,d,e,f) - Legacy implementation of `fromString(matrix)`;
 * Read this PR for details {@link https://github.com/chrvadala/transformation-matrix/pull/107}
 * @param string {string} String with an affine matrix
 * @deprecated
 * @returns {Matrix} Affine Matrix
 *
 * @example
 * > fromStringLegacy('matrix(1,2,3,4,5,6)')
 * {a: 1, b: 2, c: 3, d: 4, c: 5, e: 6}
 */
function fromStringLegacy(string) {
  var parsed = string.match(matrixRegex);
  if (parsed === null || parsed.length < 7) throw new Error("'".concat(string, "' is not a matrix"));
  return {
    a: parseFloat(parsed[1]),
    b: parseFloat(parsed[2]),
    c: parseFloat(parsed[3]),
    d: parseFloat(parsed[4]),
    e: parseFloat(parsed[5]),
    f: parseFloat(parsed[6])
  };
}
;// ./src/identity.js
/**
 * Identity matrix
 * @returns {Matrix} Affine Matrix
 */
function identity() {
  return {
    a: 1,
    c: 0,
    e: 0,
    b: 0,
    d: 1,
    f: 0
  };
}
;// ./src/inverse.js
/**
 * Calculate a matrix that is the inverse of the provided matrix
 * @param matrix {Matrix} Affine Matrix
 * @returns {Matrix} Inverted Affine Matrix
 */
function inverse(matrix) {
  // http://www.wolframalpha.com/input/?i=Inverse+%5B%7B%7Ba,c,e%7D,%7Bb,d,f%7D,%7B0,0,1%7D%7D%5D

  var a = matrix.a,
    b = matrix.b,
    c = matrix.c,
    d = matrix.d,
    e = matrix.e,
    f = matrix.f;
  var denom = a * d - b * c;
  return {
    a: d / denom,
    b: b / -denom,
    c: c / -denom,
    d: a / denom,
    e: (d * e - c * f) / -denom,
    f: (b * e - a * f) / denom
  };
}
;// ./src/utils.js
function _typeof(o) { "@babel/helpers - typeof"; return _typeof = "function" == typeof Symbol && "symbol" == typeof Symbol.iterator ? function (o) { return typeof o; } : function (o) { return o && "function" == typeof Symbol && o.constructor === Symbol && o !== Symbol.prototype ? "symbol" : typeof o; }, _typeof(o); }
function isUndefined(val) {
  return typeof val === 'undefined';
}
function isNumeric(n) {
  return typeof n === 'number' && !Number.isNaN(n) && Number.isFinite(n);
}
function isObject(obj) {
  return _typeof(obj) === 'object' && obj !== null && !Array.isArray(obj);
}
function matchesShape(obj, keys) {
  return keys.every(function (key) {
    return key in obj;
  });
}
;// ./src/isAffineMatrix.js


/**
 * Check if the object contain an affine matrix
 * @param object {Object} Generic Plain Object
 * @return {boolean} True if is an object and contains an affine matrix
 */

function isAffineMatrix(object) {
  return isObject(object) && 'a' in object && isNumeric(object.a) && 'b' in object && isNumeric(object.b) && 'c' in object && isNumeric(object.c) && 'd' in object && isNumeric(object.d) && 'e' in object && isNumeric(object.e) && 'f' in object && isNumeric(object.f);
}
;// ./src/translate.js
/**
 * Calculate a translate matrix
 * @param tx {number} Translation on axis x
 * @param [ty = 0] {number} Translation on axis y
 * @returns {Matrix} Affine Matrix
 */
function translate(tx) {
  var ty = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : 0;
  return {
    a: 1,
    c: 0,
    e: tx,
    b: 0,
    d: 1,
    f: ty
  };
}
;// ./src/transform.js
function _toConsumableArray(r) { return _arrayWithoutHoles(r) || _iterableToArray(r) || _unsupportedIterableToArray(r) || _nonIterableSpread(); }
function _nonIterableSpread() { throw new TypeError("Invalid attempt to spread non-iterable instance.\nIn order to be iterable, non-array objects must have a [Symbol.iterator]() method."); }
function _arrayWithoutHoles(r) { if (Array.isArray(r)) return _arrayLikeToArray(r); }
function _toArray(r) { return _arrayWithHoles(r) || _iterableToArray(r) || _unsupportedIterableToArray(r) || _nonIterableRest(); }
function _nonIterableRest() { throw new TypeError("Invalid attempt to destructure non-iterable instance.\nIn order to be iterable, non-array objects must have a [Symbol.iterator]() method."); }
function _unsupportedIterableToArray(r, a) { if (r) { if ("string" == typeof r) return _arrayLikeToArray(r, a); var t = {}.toString.call(r).slice(8, -1); return "Object" === t && r.constructor && (t = r.constructor.name), "Map" === t || "Set" === t ? Array.from(r) : "Arguments" === t || /^(?:Ui|I)nt(?:8|16|32)(?:Clamped)?Array$/.test(t) ? _arrayLikeToArray(r, a) : void 0; } }
function _arrayLikeToArray(r, a) { (null == a || a > r.length) && (a = r.length); for (var e = 0, n = Array(a); e < a; e++) n[e] = r[e]; return n; }
function _iterableToArray(r) { if ("undefined" != typeof Symbol && null != r[Symbol.iterator] || null != r["@@iterator"]) return Array.from(r); }
function _arrayWithHoles(r) { if (Array.isArray(r)) return r; }
/**
 * Merge multiple matrices into one
 * @param matrices {...Matrix | Matrix[]} Matrices listed as separate parameters or in an array
 * @returns {Matrix} Affine Matrix
 */
function transform() {
  for (var _len = arguments.length, matrices = new Array(_len), _key = 0; _key < _len; _key++) {
    matrices[_key] = arguments[_key];
  }
  matrices = Array.isArray(matrices[0]) ? matrices[0] : matrices;
  var multiply = function multiply(m1, m2) {
    return {
      a: m1.a * m2.a + m1.c * m2.b,
      c: m1.a * m2.c + m1.c * m2.d,
      e: m1.a * m2.e + m1.c * m2.f + m1.e,
      b: m1.b * m2.a + m1.d * m2.b,
      d: m1.b * m2.c + m1.d * m2.d,
      f: m1.b * m2.e + m1.d * m2.f + m1.f
    };
  };
  switch (matrices.length) {
    case 0:
      throw new Error('no matrices provided');
    case 1:
      return matrices[0];
    case 2:
      return multiply(matrices[0], matrices[1]);
    default:
      {
        var _matrices = matrices,
          _matrices2 = _toArray(_matrices),
          m1 = _matrices2[0],
          m2 = _matrices2[1],
          rest = _matrices2.slice(2);
        var m = multiply(m1, m2);
        return transform.apply(void 0, [m].concat(_toConsumableArray(rest)));
      }
  }
}

/**
 * Merge multiple matrices into one
 * @param matrices {...Matrix | Matrix[]} Matrices listed as separate parameters or in an array
 * @returns {Matrix} Affine Matrix
 */
function compose() {
  return transform.apply(void 0, arguments);
}
;// ./src/rotate.js



var cos = Math.cos,
  sin = Math.sin,
  PI = Math.PI;
/**
 * Calculate a rotation matrix
 * @param angle {number} Angle in radians
 * @param [cx] {number} If (cx,cy) are supplied the rotate is about this point
 * @param [cy] {number} If (cx,cy) are supplied the rotate is about this point
 * @returns {Matrix} Affine Matrix
 */
function rotate(angle, cx, cy) {
  var cosAngle = cos(angle);
  var sinAngle = sin(angle);
  var rotationMatrix = {
    a: cosAngle,
    c: -sinAngle,
    e: 0,
    b: sinAngle,
    d: cosAngle,
    f: 0
  };
  if (isUndefined(cx) || isUndefined(cy)) {
    return rotationMatrix;
  }
  return transform([translate(cx, cy), rotationMatrix, translate(-cx, -cy)]);
}

/**
 * Calculate a rotation matrix with a DEG angle
 * @param angle {number} Angle in degree
 * @param [cx] {number} If (cx,cy) are supplied the rotate is about this point
 * @param [cy] {number} If (cx,cy) are supplied the rotate is about this point
 * @returns {Matrix} Affine Matrix
 */
function rotateDEG(angle) {
  var cx = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : undefined;
  var cy = arguments.length > 2 && arguments[2] !== undefined ? arguments[2] : undefined;
  return rotate(angle * PI / 180, cx, cy);
}
;// ./src/scale.js




/**
 * Calculate a scaling matrix
 * @param sx {number} Scaling on axis x
 * @param [sy = sx] {number} Scaling on axis y (default sx)
 * @param [cx] {number} If (cx,cy) are supplied the scaling is about this point
 * @param [cy] {number} If (cx,cy) are supplied the scaling is about this point
 * @returns {Matrix} Affine Matrix
 */
function scale(sx) {
  var sy = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : undefined;
  var cx = arguments.length > 2 && arguments[2] !== undefined ? arguments[2] : undefined;
  var cy = arguments.length > 3 && arguments[3] !== undefined ? arguments[3] : undefined;
  if (isUndefined(sy)) sy = sx;
  var scaleMatrix = {
    a: sx,
    c: 0,
    e: 0,
    b: 0,
    d: sy,
    f: 0
  };
  if (isUndefined(cx) || isUndefined(cy)) {
    return scaleMatrix;
  }
  return transform([translate(cx, cy), scaleMatrix, translate(-cx, -cy)]);
}
;// ./src/shear.js
/**
 * Calculate a shear matrix
 * @param shx {number} Shear on axis x
 * @param shy {number} Shear on axis y
 * @returns {Matrix} Affine Matrix
 */
function shear(shx, shy) {
  return {
    a: 1,
    c: shx,
    e: 0,
    b: shy,
    d: 1,
    f: 0
  };
}
;// ./src/skew.js
// https://developer.mozilla.org/en-US/docs/Web/CSS/transform-function/skew
var tan = Math.tan;

/**
 * Calculate a skew matrix
 * @param ax {number} Skew on axis x
 * @param ay {number} Skew on axis y
 * @returns {Matrix} Affine Matrix
 */
function skew(ax, ay) {
  return {
    a: 1,
    c: tan(ax),
    e: 0,
    b: tan(ay),
    d: 1,
    f: 0
  };
}

/**
 * Calculate a skew matrix using DEG angles
 * @param ax {number} Skew on axis x
 * @param ay {number} Skew on axis y
 * @returns {Matrix} Affine Matrix
 */
function skewDEG(ax, ay) {
  return skew(ax * Math.PI / 180, ay * Math.PI / 180);
}
;// ./src/toString.js
/**
 * Serialize an affine matrix to a string that can be used with CSS or SVG
 * @param matrix {Matrix} Affine Matrix
 * @returns {string} String that contains an affine matrix formatted as matrix(a,b,c,d,e,f)
 */
function toCSS(matrix) {
  return toString_toString(matrix);
}

/**
 * Serialize an affine matrix to a string that can be used with CSS or SVG
 * @param matrix {Matrix} Affine Matrix
 * @returns {string} String that contains an affine matrix formatted as matrix(a,b,c,d,e,f)
 */
function toSVG(matrix) {
  return toString_toString(matrix);
}

/**
 * Serialize an affine matrix to a string that can be used with CSS or SVG
 * @param matrix {Matrix} Affine Matrix
 * @returns {string} String that contains an affine matrix formatted as matrix(a,b,c,d,e,f)
 */
function toString_toString(matrix) {
  return "matrix(".concat(matrix.a, ",").concat(matrix.b, ",").concat(matrix.c, ",").concat(matrix.d, ",").concat(matrix.e, ",").concat(matrix.f, ")");
}
;// ./src/smoothMatrix.js
/**
 * Rounds all elements of the given matrix using the given precision
 * @param matrix {Matrix} An affine matrix to round
 * @param [precision] {number} A precision to use for Math.round. Defaults to 10000000000 (meaning which rounds to the 10th digit after the comma).
 * @returns {Matrix} The rounded Affine Matrix
 */
function smoothMatrix(matrix) {
  var precision = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : 10000000000;
  return {
    a: Math.round(matrix.a * precision) / precision,
    b: Math.round(matrix.b * precision) / precision,
    c: Math.round(matrix.c * precision) / precision,
    d: Math.round(matrix.d * precision) / precision,
    e: Math.round(matrix.e * precision) / precision,
    f: Math.round(matrix.f * precision) / precision
  };
}
;// ./src/fromTriangles.js




/**
 * Returns a matrix that transforms a triangle t1 into another triangle t2, or throws an exception if it is impossible.
 * @param t1 {Point[]} Array of points containing the three points for the first triangle
 * @param t2 {Point[]} Array of points containing the three points for the second triangle
 * @returns {Matrix} Matrix which transforms t1 to t2
 * @throws Exception if the matrix becomes not invertible
 */
function fromTriangles(t1, t2) {
  // point p = first point of the triangle
  var px1 = t1[0].x != null ? t1[0].x : t1[0][0];
  var py1 = t1[0].y != null ? t1[0].y : t1[0][1];
  var px2 = t2[0].x != null ? t2[0].x : t2[0][0];
  var py2 = t2[0].y != null ? t2[0].y : t2[0][1];

  // point q = second point of the triangle
  var qx1 = t1[1].x != null ? t1[1].x : t1[1][0];
  var qy1 = t1[1].y != null ? t1[1].y : t1[1][1];
  var qx2 = t2[1].x != null ? t2[1].x : t2[1][0];
  var qy2 = t2[1].y != null ? t2[1].y : t2[1][1];

  // point r = third point of the triangle
  var rx1 = t1[2].x != null ? t1[2].x : t1[2][0];
  var ry1 = t1[2].y != null ? t1[2].y : t1[2][1];
  var rx2 = t2[2].x != null ? t2[2].x : t2[2][0];
  var ry2 = t2[2].y != null ? t2[2].y : t2[2][1];
  var r1 = {
    a: px1 - rx1,
    b: py1 - ry1,
    c: qx1 - rx1,
    d: qy1 - ry1,
    e: rx1,
    f: ry1
  };
  var r2 = {
    a: px2 - rx2,
    b: py2 - ry2,
    c: qx2 - rx2,
    d: qy2 - ry2,
    e: rx2,
    f: ry2
  };
  var inverseR1 = inverse(r1);
  var affineMatrix = transform([r2, inverseR1]);

  // round the matrix elements to smooth the finite inversion
  return smoothMatrix(affineMatrix);
}
;// ./src/fromDefinition.js







/**
 * Converts array of matrix descriptor to array of matrix
 * @param definitionOrArrayOfDefinition {Object[]} Array of object describing the matrix
 * @returns {Matrix[]} Array of matrix
 *
 * @example
 * > fromDefinition([
 *  { type: 'matrix', a:1, b:2, c:3, d:4, e:5, f:6 },
 *  { type: 'translate', tx: 10, ty: 20 },
 *  { type: 'scale', sx: 2, sy: 4 },
 *  { type: 'rotate', angle: 90, cx: 50, cy: 25 },
 *  { type: 'skewX', angle: 45 },
 *  { type: 'skewY',  angle: 45 },
 *  { type: 'shear', shx: 10, shy: 20}
 * ])
 *
 * [
 *  { a: 1, b: 2, c: 3, d: 4, e: 5, f: 6 },
 *  { a: 1, c: 0, e: 10, b: 0, d: 1, f: 20 },
 *  { a: 2, c: 0, e: 0, b: 0, d: 4, f: 0 },
 *  { a: 6.123, c: -1, e: 0, b: 1, d: 6.123, f: 0 },
 *  { a: 1, c: 0.99.., e: 0, b: 0, d: 1, f: 0 },
 *  { a: 1, c: 0, e: 0, b: 0.99, d: 1, f: 0 },
 *  { a: 1, c: 10, e: 0, b: 20, d: 1, f: 0 }
 * ]
 **/
function fromDefinition(definitionOrArrayOfDefinition) {
  return Array.isArray(definitionOrArrayOfDefinition) ? definitionOrArrayOfDefinition.map(mapper) : mapper(definitionOrArrayOfDefinition);
  function mapper(descriptor) {
    switch (descriptor.type) {
      case 'matrix':
        if ('a' in descriptor && 'b' in descriptor && 'c' in descriptor && 'd' in descriptor && 'e' in descriptor && 'f' in descriptor) {
          return fromObject(descriptor);
        } else {
          throw new Error('MISSING_MANDATORY_PARAM');
        }
      case 'translate':
        if (!('tx' in descriptor)) throw new Error('MISSING_MANDATORY_PARAM');
        if ('ty' in descriptor) return translate(descriptor.tx, descriptor.ty);
        return translate(descriptor.tx);
      case 'scale':
        if (!('sx' in descriptor)) throw new Error('MISSING_MANDATORY_PARAM');
        if ('sy' in descriptor) return scale(descriptor.sx, descriptor.sy);
        return scale(descriptor.sx);
      case 'rotate':
        if (!('angle' in descriptor)) throw new Error('MISSING_MANDATORY_PARAM');
        if ('cx' in descriptor && 'cy' in descriptor) {
          return rotateDEG(descriptor.angle, descriptor.cx, descriptor.cy);
        }
        return rotateDEG(descriptor.angle);
      case 'skewX':
        if (!('angle' in descriptor)) throw new Error('MISSING_MANDATORY_PARAM');
        return skewDEG(descriptor.angle, 0);
      case 'skewY':
        if (!('angle' in descriptor)) throw new Error('MISSING_MANDATORY_PARAM');
        return skewDEG(0, descriptor.angle);
      case 'shear':
        if (!('shx' in descriptor && 'shy' in descriptor)) throw new Error('MISSING_MANDATORY_PARAM');
        return shear(descriptor.shx, descriptor.shy);
      default:
        throw new Error('UNSUPPORTED_DESCRIPTOR');
    }
  }
}
;// ./src/fromTransformAttribute.autogenerated.js
// @generated by Peggy 4.2.0.
//
// https://peggyjs.org/

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}
function peg$SyntaxError(message, expected, found, location) {
  var self = Error.call(this, message);
  // istanbul ignore next Check is a necessary evil to support older environments
  if (Object.setPrototypeOf) {
    Object.setPrototypeOf(self, peg$SyntaxError.prototype);
  }
  self.expected = expected;
  self.found = found;
  self.location = location;
  self.name = "SyntaxError";
  return self;
}
peg$subclass(peg$SyntaxError, Error);
function peg$padEnd(str, targetLength, padString) {
  padString = padString || " ";
  if (str.length > targetLength) {
    return str;
  }
  targetLength -= str.length;
  padString += padString.repeat(targetLength);
  return str + padString.slice(0, targetLength);
}
peg$SyntaxError.prototype.format = function (sources) {
  var str = "Error: " + this.message;
  if (this.location) {
    var src = null;
    var k;
    for (k = 0; k < sources.length; k++) {
      if (sources[k].source === this.location.source) {
        src = sources[k].text.split(/\r\n|\n|\r/g);
        break;
      }
    }
    var s = this.location.start;
    var offset_s = this.location.source && typeof this.location.source.offset === "function" ? this.location.source.offset(s) : s;
    var loc = this.location.source + ":" + offset_s.line + ":" + offset_s.column;
    if (src) {
      var e = this.location.end;
      var filler = peg$padEnd("", offset_s.line.toString().length, ' ');
      var line = src[s.line - 1];
      var last = s.line === e.line ? e.column : line.length + 1;
      var hatLen = last - s.column || 1;
      str += "\n --> " + loc + "\n" + filler + " |\n" + offset_s.line + " | " + line + "\n" + filler + " | " + peg$padEnd("", s.column - 1, ' ') + peg$padEnd("", hatLen, "^");
    } else {
      str += "\n at " + loc;
    }
  }
  return str;
};
peg$SyntaxError.buildMessage = function (expected, found) {
  var DESCRIBE_EXPECTATION_FNS = {
    literal: function literal(expectation) {
      return "\"" + literalEscape(expectation.text) + "\"";
    },
    "class": function _class(expectation) {
      var escapedParts = expectation.parts.map(function (part) {
        return Array.isArray(part) ? classEscape(part[0]) + "-" + classEscape(part[1]) : classEscape(part);
      });
      return "[" + (expectation.inverted ? "^" : "") + escapedParts.join("") + "]";
    },
    any: function any() {
      return "any character";
    },
    end: function end() {
      return "end of input";
    },
    other: function other(expectation) {
      return expectation.description;
    }
  };
  function hex(ch) {
    return ch.charCodeAt(0).toString(16).toUpperCase();
  }
  function literalEscape(s) {
    return s.replace(/\\/g, "\\\\").replace(/"/g, "\\\"").replace(/\0/g, "\\0").replace(/\t/g, "\\t").replace(/\n/g, "\\n").replace(/\r/g, "\\r").replace(/[\x00-\x0F]/g, function (ch) {
      return "\\x0" + hex(ch);
    }).replace(/[\x10-\x1F\x7F-\x9F]/g, function (ch) {
      return "\\x" + hex(ch);
    });
  }
  function classEscape(s) {
    return s.replace(/\\/g, "\\\\").replace(/\]/g, "\\]").replace(/\^/g, "\\^").replace(/-/g, "\\-").replace(/\0/g, "\\0").replace(/\t/g, "\\t").replace(/\n/g, "\\n").replace(/\r/g, "\\r").replace(/[\x00-\x0F]/g, function (ch) {
      return "\\x0" + hex(ch);
    }).replace(/[\x10-\x1F\x7F-\x9F]/g, function (ch) {
      return "\\x" + hex(ch);
    });
  }
  function describeExpectation(expectation) {
    return DESCRIBE_EXPECTATION_FNS[expectation.type](expectation);
  }
  function describeExpected(expected) {
    var descriptions = expected.map(describeExpectation);
    var i, j;
    descriptions.sort();
    if (descriptions.length > 0) {
      for (i = 1, j = 1; i < descriptions.length; i++) {
        if (descriptions[i - 1] !== descriptions[i]) {
          descriptions[j] = descriptions[i];
          j++;
        }
      }
      descriptions.length = j;
    }
    switch (descriptions.length) {
      case 1:
        return descriptions[0];
      case 2:
        return descriptions[0] + " or " + descriptions[1];
      default:
        return descriptions.slice(0, -1).join(", ") + ", or " + descriptions[descriptions.length - 1];
    }
  }
  function describeFound(found) {
    return found ? "\"" + literalEscape(found) + "\"" : "end of input";
  }
  return "Expected " + describeExpected(expected) + " but " + describeFound(found) + " found.";
};
function peg$parse(input, options) {
  options = options !== undefined ? options : {};
  var peg$FAILED = {};
  var peg$source = options.grammarSource;
  var peg$startRuleFunctions = {
    transformList: peg$parsetransformList
  };
  var peg$startRuleFunction = peg$parsetransformList;
  var peg$c0 = "matrix";
  var peg$c1 = "(";
  var peg$c2 = ")";
  var peg$c3 = "translate";
  var peg$c4 = "scale";
  var peg$c5 = "rotate";
  var peg$c6 = "skewX";
  var peg$c7 = "skewY";
  var peg$c8 = ",";
  var peg$c9 = ".";
  var peg$r0 = /^[eE]/;
  var peg$r1 = /^[+\-]/;
  var peg$r2 = /^[0-9]/;
  var peg$r3 = /^[ \t\r\n]/;
  var peg$e0 = peg$literalExpectation("matrix", false);
  var peg$e1 = peg$literalExpectation("(", false);
  var peg$e2 = peg$literalExpectation(")", false);
  var peg$e3 = peg$literalExpectation("translate", false);
  var peg$e4 = peg$literalExpectation("scale", false);
  var peg$e5 = peg$literalExpectation("rotate", false);
  var peg$e6 = peg$literalExpectation("skewX", false);
  var peg$e7 = peg$literalExpectation("skewY", false);
  var peg$e8 = peg$literalExpectation(",", false);
  var peg$e9 = peg$otherExpectation("fractionalConstant");
  var peg$e10 = peg$literalExpectation(".", false);
  var peg$e11 = peg$classExpectation(["e", "E"], false, false);
  var peg$e12 = peg$classExpectation(["+", "-"], false, false);
  var peg$e13 = peg$classExpectation([["0", "9"]], false, false);
  var peg$e14 = peg$classExpectation([" ", "\t", "\r", "\n"], false, false);
  var peg$f0 = function peg$f0(ts) {
    return ts;
  };
  var peg$f1 = function peg$f1(t, ts) {
    return t.concat(ts);
  };
  var peg$f2 = function peg$f2(a, b, c, d, e, f) {
    return [{
      type: 'matrix',
      a: a,
      b: b,
      c: c,
      d: d,
      e: e,
      f: f
    }];
  };
  var peg$f3 = function peg$f3(tx, ty) {
    var t = {
      type: 'translate',
      tx: tx
    };
    if (ty) t.ty = ty;
    return [t];
  };
  var peg$f4 = function peg$f4(sx, sy) {
    var s = {
      type: 'scale',
      sx: sx
    };
    if (sy) s.sy = sy;
    return [s];
  };
  var peg$f5 = function peg$f5(angle, c) {
    var r = {
      type: 'rotate',
      angle: angle
    };
    if (c) {
      r.cx = c[0];
      r.cy = c[1];
    }
    return [r];
  };
  var peg$f6 = function peg$f6(angle) {
    return [{
      type: 'skewX',
      angle: angle
    }];
  };
  var peg$f7 = function peg$f7(angle) {
    return [{
      type: 'skewY',
      angle: angle
    }];
  };
  var peg$f8 = function peg$f8(f) {
    return parseFloat(f.join(""));
  };
  var peg$f9 = function peg$f9(i) {
    return parseInt(i.join(""));
  };
  var peg$f10 = function peg$f10(n) {
    return n;
  };
  var peg$f11 = function peg$f11(n1, n2) {
    return [n1, n2];
  };
  var peg$f12 = function peg$f12(ds) {
    return ds.join("");
  };
  var peg$f13 = function peg$f13(f, e) {
    return [f, e || null].join("");
  };
  var peg$f14 = function peg$f14(d, e) {
    return [d, e].join("");
  };
  var peg$f15 = function peg$f15(d1, d2) {
    return [d1 ? d1.join("") : null, ".", d2.join("")].join("");
  };
  var peg$f16 = function peg$f16(d) {
    return d.join("");
  };
  var peg$f17 = function peg$f17(s, d) {
    return ['e', s, d.join("")].join("");
  };
  var peg$currPos = options.peg$currPos | 0;
  var peg$savedPos = peg$currPos;
  var peg$posDetailsCache = [{
    line: 1,
    column: 1
  }];
  var peg$maxFailPos = peg$currPos;
  var peg$maxFailExpected = options.peg$maxFailExpected || [];
  var peg$silentFails = options.peg$silentFails | 0;
  var peg$result;
  if (options.startRule) {
    if (!(options.startRule in peg$startRuleFunctions)) {
      throw new Error("Can't start parsing from rule \"" + options.startRule + "\".");
    }
    peg$startRuleFunction = peg$startRuleFunctions[options.startRule];
  }
  function text() {
    return input.substring(peg$savedPos, peg$currPos);
  }
  function offset() {
    return peg$savedPos;
  }
  function range() {
    return {
      source: peg$source,
      start: peg$savedPos,
      end: peg$currPos
    };
  }
  function location() {
    return peg$computeLocation(peg$savedPos, peg$currPos);
  }
  function expected(description, location) {
    location = location !== undefined ? location : peg$computeLocation(peg$savedPos, peg$currPos);
    throw peg$buildStructuredError([peg$otherExpectation(description)], input.substring(peg$savedPos, peg$currPos), location);
  }
  function error(message, location) {
    location = location !== undefined ? location : peg$computeLocation(peg$savedPos, peg$currPos);
    throw peg$buildSimpleError(message, location);
  }
  function peg$literalExpectation(text, ignoreCase) {
    return {
      type: "literal",
      text: text,
      ignoreCase: ignoreCase
    };
  }
  function peg$classExpectation(parts, inverted, ignoreCase) {
    return {
      type: "class",
      parts: parts,
      inverted: inverted,
      ignoreCase: ignoreCase
    };
  }
  function peg$anyExpectation() {
    return {
      type: "any"
    };
  }
  function peg$endExpectation() {
    return {
      type: "end"
    };
  }
  function peg$otherExpectation(description) {
    return {
      type: "other",
      description: description
    };
  }
  function peg$computePosDetails(pos) {
    var details = peg$posDetailsCache[pos];
    var p;
    if (details) {
      return details;
    } else {
      if (pos >= peg$posDetailsCache.length) {
        p = peg$posDetailsCache.length - 1;
      } else {
        p = pos;
        while (!peg$posDetailsCache[--p]) {}
      }
      details = peg$posDetailsCache[p];
      details = {
        line: details.line,
        column: details.column
      };
      while (p < pos) {
        if (input.charCodeAt(p) === 10) {
          details.line++;
          details.column = 1;
        } else {
          details.column++;
        }
        p++;
      }
      peg$posDetailsCache[pos] = details;
      return details;
    }
  }
  function peg$computeLocation(startPos, endPos, offset) {
    var startPosDetails = peg$computePosDetails(startPos);
    var endPosDetails = peg$computePosDetails(endPos);
    var res = {
      source: peg$source,
      start: {
        offset: startPos,
        line: startPosDetails.line,
        column: startPosDetails.column
      },
      end: {
        offset: endPos,
        line: endPosDetails.line,
        column: endPosDetails.column
      }
    };
    if (offset && peg$source && typeof peg$source.offset === "function") {
      res.start = peg$source.offset(res.start);
      res.end = peg$source.offset(res.end);
    }
    return res;
  }
  function peg$fail(expected) {
    if (peg$currPos < peg$maxFailPos) {
      return;
    }
    if (peg$currPos > peg$maxFailPos) {
      peg$maxFailPos = peg$currPos;
      peg$maxFailExpected = [];
    }
    peg$maxFailExpected.push(expected);
  }
  function peg$buildSimpleError(message, location) {
    return new peg$SyntaxError(message, null, null, location);
  }
  function peg$buildStructuredError(expected, found, location) {
    return new peg$SyntaxError(peg$SyntaxError.buildMessage(expected, found), expected, found, location);
  }
  function peg$parsetransformList() {
    var s0, s1, s2, s3, s4;
    s0 = peg$currPos;
    s1 = [];
    s2 = peg$parsewsp();
    while (s2 !== peg$FAILED) {
      s1.push(s2);
      s2 = peg$parsewsp();
    }
    s2 = peg$parsetransforms();
    if (s2 === peg$FAILED) {
      s2 = null;
    }
    s3 = [];
    s4 = peg$parsewsp();
    while (s4 !== peg$FAILED) {
      s3.push(s4);
      s4 = peg$parsewsp();
    }
    peg$savedPos = s0;
    s0 = peg$f0(s2);
    return s0;
  }
  function peg$parsetransforms() {
    var s0, s1, s2, s3;
    s0 = peg$currPos;
    s1 = peg$parsetransform();
    if (s1 !== peg$FAILED) {
      s2 = [];
      s3 = peg$parsecommaWsp();
      if (s3 !== peg$FAILED) {
        while (s3 !== peg$FAILED) {
          s2.push(s3);
          s3 = peg$parsecommaWsp();
        }
      } else {
        s2 = peg$FAILED;
      }
      if (s2 !== peg$FAILED) {
        s3 = peg$parsetransforms();
        if (s3 !== peg$FAILED) {
          peg$savedPos = s0;
          s0 = peg$f1(s1, s3);
        } else {
          peg$currPos = s0;
          s0 = peg$FAILED;
        }
      } else {
        peg$currPos = s0;
        s0 = peg$FAILED;
      }
    } else {
      peg$currPos = s0;
      s0 = peg$FAILED;
    }
    if (s0 === peg$FAILED) {
      s0 = peg$parsetransform();
    }
    return s0;
  }
  function peg$parsetransform() {
    var s0;
    s0 = peg$parsematrix();
    if (s0 === peg$FAILED) {
      s0 = peg$parsetranslate();
      if (s0 === peg$FAILED) {
        s0 = peg$parsescale();
        if (s0 === peg$FAILED) {
          s0 = peg$parserotate();
          if (s0 === peg$FAILED) {
            s0 = peg$parseskewX();
            if (s0 === peg$FAILED) {
              s0 = peg$parseskewY();
            }
          }
        }
      }
    }
    return s0;
  }
  function peg$parsematrix() {
    var s0, s1, s2, s3, s4, s5, s6, s7, s8, s9, s10, s11, s12, s13, s14, s15, s16, s17;
    s0 = peg$currPos;
    if (input.substr(peg$currPos, 6) === peg$c0) {
      s1 = peg$c0;
      peg$currPos += 6;
    } else {
      s1 = peg$FAILED;
      if (peg$silentFails === 0) {
        peg$fail(peg$e0);
      }
    }
    if (s1 !== peg$FAILED) {
      s2 = [];
      s3 = peg$parsewsp();
      while (s3 !== peg$FAILED) {
        s2.push(s3);
        s3 = peg$parsewsp();
      }
      if (input.charCodeAt(peg$currPos) === 40) {
        s3 = peg$c1;
        peg$currPos++;
      } else {
        s3 = peg$FAILED;
        if (peg$silentFails === 0) {
          peg$fail(peg$e1);
        }
      }
      if (s3 !== peg$FAILED) {
        s4 = [];
        s5 = peg$parsewsp();
        while (s5 !== peg$FAILED) {
          s4.push(s5);
          s5 = peg$parsewsp();
        }
        s5 = peg$parsenumber();
        if (s5 !== peg$FAILED) {
          s6 = peg$parsecommaWsp();
          if (s6 !== peg$FAILED) {
            s7 = peg$parsenumber();
            if (s7 !== peg$FAILED) {
              s8 = peg$parsecommaWsp();
              if (s8 !== peg$FAILED) {
                s9 = peg$parsenumber();
                if (s9 !== peg$FAILED) {
                  s10 = peg$parsecommaWsp();
                  if (s10 !== peg$FAILED) {
                    s11 = peg$parsenumber();
                    if (s11 !== peg$FAILED) {
                      s12 = peg$parsecommaWsp();
                      if (s12 !== peg$FAILED) {
                        s13 = peg$parsenumber();
                        if (s13 !== peg$FAILED) {
                          s14 = peg$parsecommaWsp();
                          if (s14 !== peg$FAILED) {
                            s15 = peg$parsenumber();
                            if (s15 !== peg$FAILED) {
                              s16 = [];
                              s17 = peg$parsewsp();
                              while (s17 !== peg$FAILED) {
                                s16.push(s17);
                                s17 = peg$parsewsp();
                              }
                              if (input.charCodeAt(peg$currPos) === 41) {
                                s17 = peg$c2;
                                peg$currPos++;
                              } else {
                                s17 = peg$FAILED;
                                if (peg$silentFails === 0) {
                                  peg$fail(peg$e2);
                                }
                              }
                              if (s17 !== peg$FAILED) {
                                peg$savedPos = s0;
                                s0 = peg$f2(s5, s7, s9, s11, s13, s15);
                              } else {
                                peg$currPos = s0;
                                s0 = peg$FAILED;
                              }
                            } else {
                              peg$currPos = s0;
                              s0 = peg$FAILED;
                            }
                          } else {
                            peg$currPos = s0;
                            s0 = peg$FAILED;
                          }
                        } else {
                          peg$currPos = s0;
                          s0 = peg$FAILED;
                        }
                      } else {
                        peg$currPos = s0;
                        s0 = peg$FAILED;
                      }
                    } else {
                      peg$currPos = s0;
                      s0 = peg$FAILED;
                    }
                  } else {
                    peg$currPos = s0;
                    s0 = peg$FAILED;
                  }
                } else {
                  peg$currPos = s0;
                  s0 = peg$FAILED;
                }
              } else {
                peg$currPos = s0;
                s0 = peg$FAILED;
              }
            } else {
              peg$currPos = s0;
              s0 = peg$FAILED;
            }
          } else {
            peg$currPos = s0;
            s0 = peg$FAILED;
          }
        } else {
          peg$currPos = s0;
          s0 = peg$FAILED;
        }
      } else {
        peg$currPos = s0;
        s0 = peg$FAILED;
      }
    } else {
      peg$currPos = s0;
      s0 = peg$FAILED;
    }
    return s0;
  }
  function peg$parsetranslate() {
    var s0, s1, s2, s3, s4, s5, s6, s7, s8;
    s0 = peg$currPos;
    if (input.substr(peg$currPos, 9) === peg$c3) {
      s1 = peg$c3;
      peg$currPos += 9;
    } else {
      s1 = peg$FAILED;
      if (peg$silentFails === 0) {
        peg$fail(peg$e3);
      }
    }
    if (s1 !== peg$FAILED) {
      s2 = [];
      s3 = peg$parsewsp();
      while (s3 !== peg$FAILED) {
        s2.push(s3);
        s3 = peg$parsewsp();
      }
      if (input.charCodeAt(peg$currPos) === 40) {
        s3 = peg$c1;
        peg$currPos++;
      } else {
        s3 = peg$FAILED;
        if (peg$silentFails === 0) {
          peg$fail(peg$e1);
        }
      }
      if (s3 !== peg$FAILED) {
        s4 = [];
        s5 = peg$parsewsp();
        while (s5 !== peg$FAILED) {
          s4.push(s5);
          s5 = peg$parsewsp();
        }
        s5 = peg$parsenumber();
        if (s5 !== peg$FAILED) {
          s6 = peg$parsecommaWspNumber();
          if (s6 === peg$FAILED) {
            s6 = null;
          }
          s7 = [];
          s8 = peg$parsewsp();
          while (s8 !== peg$FAILED) {
            s7.push(s8);
            s8 = peg$parsewsp();
          }
          if (input.charCodeAt(peg$currPos) === 41) {
            s8 = peg$c2;
            peg$currPos++;
          } else {
            s8 = peg$FAILED;
            if (peg$silentFails === 0) {
              peg$fail(peg$e2);
            }
          }
          if (s8 !== peg$FAILED) {
            peg$savedPos = s0;
            s0 = peg$f3(s5, s6);
          } else {
            peg$currPos = s0;
            s0 = peg$FAILED;
          }
        } else {
          peg$currPos = s0;
          s0 = peg$FAILED;
        }
      } else {
        peg$currPos = s0;
        s0 = peg$FAILED;
      }
    } else {
      peg$currPos = s0;
      s0 = peg$FAILED;
    }
    return s0;
  }
  function peg$parsescale() {
    var s0, s1, s2, s3, s4, s5, s6, s7, s8;
    s0 = peg$currPos;
    if (input.substr(peg$currPos, 5) === peg$c4) {
      s1 = peg$c4;
      peg$currPos += 5;
    } else {
      s1 = peg$FAILED;
      if (peg$silentFails === 0) {
        peg$fail(peg$e4);
      }
    }
    if (s1 !== peg$FAILED) {
      s2 = [];
      s3 = peg$parsewsp();
      while (s3 !== peg$FAILED) {
        s2.push(s3);
        s3 = peg$parsewsp();
      }
      if (input.charCodeAt(peg$currPos) === 40) {
        s3 = peg$c1;
        peg$currPos++;
      } else {
        s3 = peg$FAILED;
        if (peg$silentFails === 0) {
          peg$fail(peg$e1);
        }
      }
      if (s3 !== peg$FAILED) {
        s4 = [];
        s5 = peg$parsewsp();
        while (s5 !== peg$FAILED) {
          s4.push(s5);
          s5 = peg$parsewsp();
        }
        s5 = peg$parsenumber();
        if (s5 !== peg$FAILED) {
          s6 = peg$parsecommaWspNumber();
          if (s6 === peg$FAILED) {
            s6 = null;
          }
          s7 = [];
          s8 = peg$parsewsp();
          while (s8 !== peg$FAILED) {
            s7.push(s8);
            s8 = peg$parsewsp();
          }
          if (input.charCodeAt(peg$currPos) === 41) {
            s8 = peg$c2;
            peg$currPos++;
          } else {
            s8 = peg$FAILED;
            if (peg$silentFails === 0) {
              peg$fail(peg$e2);
            }
          }
          if (s8 !== peg$FAILED) {
            peg$savedPos = s0;
            s0 = peg$f4(s5, s6);
          } else {
            peg$currPos = s0;
            s0 = peg$FAILED;
          }
        } else {
          peg$currPos = s0;
          s0 = peg$FAILED;
        }
      } else {
        peg$currPos = s0;
        s0 = peg$FAILED;
      }
    } else {
      peg$currPos = s0;
      s0 = peg$FAILED;
    }
    return s0;
  }
  function peg$parserotate() {
    var s0, s1, s2, s3, s4, s5, s6, s7, s8;
    s0 = peg$currPos;
    if (input.substr(peg$currPos, 6) === peg$c5) {
      s1 = peg$c5;
      peg$currPos += 6;
    } else {
      s1 = peg$FAILED;
      if (peg$silentFails === 0) {
        peg$fail(peg$e5);
      }
    }
    if (s1 !== peg$FAILED) {
      s2 = [];
      s3 = peg$parsewsp();
      while (s3 !== peg$FAILED) {
        s2.push(s3);
        s3 = peg$parsewsp();
      }
      if (input.charCodeAt(peg$currPos) === 40) {
        s3 = peg$c1;
        peg$currPos++;
      } else {
        s3 = peg$FAILED;
        if (peg$silentFails === 0) {
          peg$fail(peg$e1);
        }
      }
      if (s3 !== peg$FAILED) {
        s4 = [];
        s5 = peg$parsewsp();
        while (s5 !== peg$FAILED) {
          s4.push(s5);
          s5 = peg$parsewsp();
        }
        s5 = peg$parsenumber();
        if (s5 !== peg$FAILED) {
          s6 = peg$parsecommaWspTwoNumbers();
          if (s6 === peg$FAILED) {
            s6 = null;
          }
          s7 = [];
          s8 = peg$parsewsp();
          while (s8 !== peg$FAILED) {
            s7.push(s8);
            s8 = peg$parsewsp();
          }
          if (input.charCodeAt(peg$currPos) === 41) {
            s8 = peg$c2;
            peg$currPos++;
          } else {
            s8 = peg$FAILED;
            if (peg$silentFails === 0) {
              peg$fail(peg$e2);
            }
          }
          if (s8 !== peg$FAILED) {
            peg$savedPos = s0;
            s0 = peg$f5(s5, s6);
          } else {
            peg$currPos = s0;
            s0 = peg$FAILED;
          }
        } else {
          peg$currPos = s0;
          s0 = peg$FAILED;
        }
      } else {
        peg$currPos = s0;
        s0 = peg$FAILED;
      }
    } else {
      peg$currPos = s0;
      s0 = peg$FAILED;
    }
    return s0;
  }
  function peg$parseskewX() {
    var s0, s1, s2, s3, s4, s5, s6, s7;
    s0 = peg$currPos;
    if (input.substr(peg$currPos, 5) === peg$c6) {
      s1 = peg$c6;
      peg$currPos += 5;
    } else {
      s1 = peg$FAILED;
      if (peg$silentFails === 0) {
        peg$fail(peg$e6);
      }
    }
    if (s1 !== peg$FAILED) {
      s2 = [];
      s3 = peg$parsewsp();
      while (s3 !== peg$FAILED) {
        s2.push(s3);
        s3 = peg$parsewsp();
      }
      if (input.charCodeAt(peg$currPos) === 40) {
        s3 = peg$c1;
        peg$currPos++;
      } else {
        s3 = peg$FAILED;
        if (peg$silentFails === 0) {
          peg$fail(peg$e1);
        }
      }
      if (s3 !== peg$FAILED) {
        s4 = [];
        s5 = peg$parsewsp();
        while (s5 !== peg$FAILED) {
          s4.push(s5);
          s5 = peg$parsewsp();
        }
        s5 = peg$parsenumber();
        if (s5 !== peg$FAILED) {
          s6 = [];
          s7 = peg$parsewsp();
          while (s7 !== peg$FAILED) {
            s6.push(s7);
            s7 = peg$parsewsp();
          }
          if (input.charCodeAt(peg$currPos) === 41) {
            s7 = peg$c2;
            peg$currPos++;
          } else {
            s7 = peg$FAILED;
            if (peg$silentFails === 0) {
              peg$fail(peg$e2);
            }
          }
          if (s7 !== peg$FAILED) {
            peg$savedPos = s0;
            s0 = peg$f6(s5);
          } else {
            peg$currPos = s0;
            s0 = peg$FAILED;
          }
        } else {
          peg$currPos = s0;
          s0 = peg$FAILED;
        }
      } else {
        peg$currPos = s0;
        s0 = peg$FAILED;
      }
    } else {
      peg$currPos = s0;
      s0 = peg$FAILED;
    }
    return s0;
  }
  function peg$parseskewY() {
    var s0, s1, s2, s3, s4, s5, s6, s7;
    s0 = peg$currPos;
    if (input.substr(peg$currPos, 5) === peg$c7) {
      s1 = peg$c7;
      peg$currPos += 5;
    } else {
      s1 = peg$FAILED;
      if (peg$silentFails === 0) {
        peg$fail(peg$e7);
      }
    }
    if (s1 !== peg$FAILED) {
      s2 = [];
      s3 = peg$parsewsp();
      while (s3 !== peg$FAILED) {
        s2.push(s3);
        s3 = peg$parsewsp();
      }
      if (input.charCodeAt(peg$currPos) === 40) {
        s3 = peg$c1;
        peg$currPos++;
      } else {
        s3 = peg$FAILED;
        if (peg$silentFails === 0) {
          peg$fail(peg$e1);
        }
      }
      if (s3 !== peg$FAILED) {
        s4 = [];
        s5 = peg$parsewsp();
        while (s5 !== peg$FAILED) {
          s4.push(s5);
          s5 = peg$parsewsp();
        }
        s5 = peg$parsenumber();
        if (s5 !== peg$FAILED) {
          s6 = [];
          s7 = peg$parsewsp();
          while (s7 !== peg$FAILED) {
            s6.push(s7);
            s7 = peg$parsewsp();
          }
          if (input.charCodeAt(peg$currPos) === 41) {
            s7 = peg$c2;
            peg$currPos++;
          } else {
            s7 = peg$FAILED;
            if (peg$silentFails === 0) {
              peg$fail(peg$e2);
            }
          }
          if (s7 !== peg$FAILED) {
            peg$savedPos = s0;
            s0 = peg$f7(s5);
          } else {
            peg$currPos = s0;
            s0 = peg$FAILED;
          }
        } else {
          peg$currPos = s0;
          s0 = peg$FAILED;
        }
      } else {
        peg$currPos = s0;
        s0 = peg$FAILED;
      }
    } else {
      peg$currPos = s0;
      s0 = peg$FAILED;
    }
    return s0;
  }
  function peg$parsenumber() {
    var s0, s1, s2, s3;
    s0 = peg$currPos;
    s1 = peg$currPos;
    s2 = peg$parsesign();
    if (s2 === peg$FAILED) {
      s2 = null;
    }
    s3 = peg$parsefloatingPointConstant();
    if (s3 !== peg$FAILED) {
      s2 = [s2, s3];
      s1 = s2;
    } else {
      peg$currPos = s1;
      s1 = peg$FAILED;
    }
    if (s1 !== peg$FAILED) {
      peg$savedPos = s0;
      s1 = peg$f8(s1);
    }
    s0 = s1;
    if (s0 === peg$FAILED) {
      s0 = peg$currPos;
      s1 = peg$currPos;
      s2 = peg$parsesign();
      if (s2 === peg$FAILED) {
        s2 = null;
      }
      s3 = peg$parseintegerConstant();
      if (s3 !== peg$FAILED) {
        s2 = [s2, s3];
        s1 = s2;
      } else {
        peg$currPos = s1;
        s1 = peg$FAILED;
      }
      if (s1 !== peg$FAILED) {
        peg$savedPos = s0;
        s1 = peg$f9(s1);
      }
      s0 = s1;
    }
    return s0;
  }
  function peg$parsecommaWspNumber() {
    var s0, s1, s2;
    s0 = peg$currPos;
    s1 = peg$parsecommaWsp();
    if (s1 !== peg$FAILED) {
      s2 = peg$parsenumber();
      if (s2 !== peg$FAILED) {
        peg$savedPos = s0;
        s0 = peg$f10(s2);
      } else {
        peg$currPos = s0;
        s0 = peg$FAILED;
      }
    } else {
      peg$currPos = s0;
      s0 = peg$FAILED;
    }
    return s0;
  }
  function peg$parsecommaWspTwoNumbers() {
    var s0, s1, s2, s3, s4;
    s0 = peg$currPos;
    s1 = peg$parsecommaWsp();
    if (s1 !== peg$FAILED) {
      s2 = peg$parsenumber();
      if (s2 !== peg$FAILED) {
        s3 = peg$parsecommaWsp();
        if (s3 !== peg$FAILED) {
          s4 = peg$parsenumber();
          if (s4 !== peg$FAILED) {
            peg$savedPos = s0;
            s0 = peg$f11(s2, s4);
          } else {
            peg$currPos = s0;
            s0 = peg$FAILED;
          }
        } else {
          peg$currPos = s0;
          s0 = peg$FAILED;
        }
      } else {
        peg$currPos = s0;
        s0 = peg$FAILED;
      }
    } else {
      peg$currPos = s0;
      s0 = peg$FAILED;
    }
    return s0;
  }
  function peg$parsecommaWsp() {
    var s0, s1, s2, s3, s4;
    s0 = peg$currPos;
    s1 = [];
    s2 = peg$parsewsp();
    if (s2 !== peg$FAILED) {
      while (s2 !== peg$FAILED) {
        s1.push(s2);
        s2 = peg$parsewsp();
      }
    } else {
      s1 = peg$FAILED;
    }
    if (s1 !== peg$FAILED) {
      s2 = peg$parsecomma();
      if (s2 === peg$FAILED) {
        s2 = null;
      }
      s3 = [];
      s4 = peg$parsewsp();
      while (s4 !== peg$FAILED) {
        s3.push(s4);
        s4 = peg$parsewsp();
      }
      s1 = [s1, s2, s3];
      s0 = s1;
    } else {
      peg$currPos = s0;
      s0 = peg$FAILED;
    }
    if (s0 === peg$FAILED) {
      s0 = peg$currPos;
      s1 = peg$parsecomma();
      if (s1 !== peg$FAILED) {
        s2 = [];
        s3 = peg$parsewsp();
        while (s3 !== peg$FAILED) {
          s2.push(s3);
          s3 = peg$parsewsp();
        }
        s1 = [s1, s2];
        s0 = s1;
      } else {
        peg$currPos = s0;
        s0 = peg$FAILED;
      }
    }
    return s0;
  }
  function peg$parsecomma() {
    var s0;
    if (input.charCodeAt(peg$currPos) === 44) {
      s0 = peg$c8;
      peg$currPos++;
    } else {
      s0 = peg$FAILED;
      if (peg$silentFails === 0) {
        peg$fail(peg$e8);
      }
    }
    return s0;
  }
  function peg$parseintegerConstant() {
    var s0, s1;
    s0 = peg$currPos;
    s1 = peg$parsedigitSequence();
    if (s1 !== peg$FAILED) {
      peg$savedPos = s0;
      s1 = peg$f12(s1);
    }
    s0 = s1;
    return s0;
  }
  function peg$parsefloatingPointConstant() {
    var s0, s1, s2;
    s0 = peg$currPos;
    s1 = peg$parsefractionalConstant();
    if (s1 !== peg$FAILED) {
      s2 = peg$parseexponent();
      if (s2 === peg$FAILED) {
        s2 = null;
      }
      peg$savedPos = s0;
      s0 = peg$f13(s1, s2);
    } else {
      peg$currPos = s0;
      s0 = peg$FAILED;
    }
    if (s0 === peg$FAILED) {
      s0 = peg$currPos;
      s1 = peg$parsedigitSequence();
      if (s1 !== peg$FAILED) {
        s2 = peg$parseexponent();
        if (s2 !== peg$FAILED) {
          peg$savedPos = s0;
          s0 = peg$f14(s1, s2);
        } else {
          peg$currPos = s0;
          s0 = peg$FAILED;
        }
      } else {
        peg$currPos = s0;
        s0 = peg$FAILED;
      }
    }
    return s0;
  }
  function peg$parsefractionalConstant() {
    var s0, s1, s2, s3;
    peg$silentFails++;
    s0 = peg$currPos;
    s1 = peg$parsedigitSequence();
    if (s1 === peg$FAILED) {
      s1 = null;
    }
    if (input.charCodeAt(peg$currPos) === 46) {
      s2 = peg$c9;
      peg$currPos++;
    } else {
      s2 = peg$FAILED;
      if (peg$silentFails === 0) {
        peg$fail(peg$e10);
      }
    }
    if (s2 !== peg$FAILED) {
      s3 = peg$parsedigitSequence();
      if (s3 !== peg$FAILED) {
        peg$savedPos = s0;
        s0 = peg$f15(s1, s3);
      } else {
        peg$currPos = s0;
        s0 = peg$FAILED;
      }
    } else {
      peg$currPos = s0;
      s0 = peg$FAILED;
    }
    if (s0 === peg$FAILED) {
      s0 = peg$currPos;
      s1 = peg$parsedigitSequence();
      if (s1 !== peg$FAILED) {
        if (input.charCodeAt(peg$currPos) === 46) {
          s2 = peg$c9;
          peg$currPos++;
        } else {
          s2 = peg$FAILED;
          if (peg$silentFails === 0) {
            peg$fail(peg$e10);
          }
        }
        if (s2 !== peg$FAILED) {
          peg$savedPos = s0;
          s0 = peg$f16(s1);
        } else {
          peg$currPos = s0;
          s0 = peg$FAILED;
        }
      } else {
        peg$currPos = s0;
        s0 = peg$FAILED;
      }
    }
    peg$silentFails--;
    if (s0 === peg$FAILED) {
      s1 = peg$FAILED;
      if (peg$silentFails === 0) {
        peg$fail(peg$e9);
      }
    }
    return s0;
  }
  function peg$parseexponent() {
    var s0, s1, s2, s3;
    s0 = peg$currPos;
    s1 = input.charAt(peg$currPos);
    if (peg$r0.test(s1)) {
      peg$currPos++;
    } else {
      s1 = peg$FAILED;
      if (peg$silentFails === 0) {
        peg$fail(peg$e11);
      }
    }
    if (s1 !== peg$FAILED) {
      s2 = peg$parsesign();
      if (s2 === peg$FAILED) {
        s2 = null;
      }
      s3 = peg$parsedigitSequence();
      if (s3 !== peg$FAILED) {
        peg$savedPos = s0;
        s0 = peg$f17(s2, s3);
      } else {
        peg$currPos = s0;
        s0 = peg$FAILED;
      }
    } else {
      peg$currPos = s0;
      s0 = peg$FAILED;
    }
    return s0;
  }
  function peg$parsesign() {
    var s0;
    s0 = input.charAt(peg$currPos);
    if (peg$r1.test(s0)) {
      peg$currPos++;
    } else {
      s0 = peg$FAILED;
      if (peg$silentFails === 0) {
        peg$fail(peg$e12);
      }
    }
    return s0;
  }
  function peg$parsedigitSequence() {
    var s0, s1;
    s0 = [];
    s1 = peg$parsedigit();
    if (s1 !== peg$FAILED) {
      while (s1 !== peg$FAILED) {
        s0.push(s1);
        s1 = peg$parsedigit();
      }
    } else {
      s0 = peg$FAILED;
    }
    return s0;
  }
  function peg$parsedigit() {
    var s0;
    s0 = input.charAt(peg$currPos);
    if (peg$r2.test(s0)) {
      peg$currPos++;
    } else {
      s0 = peg$FAILED;
      if (peg$silentFails === 0) {
        peg$fail(peg$e13);
      }
    }
    return s0;
  }
  function peg$parsewsp() {
    var s0;
    s0 = input.charAt(peg$currPos);
    if (peg$r3.test(s0)) {
      peg$currPos++;
    } else {
      s0 = peg$FAILED;
      if (peg$silentFails === 0) {
        peg$fail(peg$e14);
      }
    }
    return s0;
  }
  peg$result = peg$startRuleFunction();
  if (options.peg$library) {
    return /** @type {any} */{
      peg$result: peg$result,
      peg$currPos: peg$currPos,
      peg$FAILED: peg$FAILED,
      peg$maxFailExpected: peg$maxFailExpected,
      peg$maxFailPos: peg$maxFailPos
    };
  }
  if (peg$result !== peg$FAILED && peg$currPos === input.length) {
    return peg$result;
  } else {
    if (peg$result !== peg$FAILED && peg$currPos < input.length) {
      peg$fail(peg$endExpectation());
    }
    throw peg$buildStructuredError(peg$maxFailExpected, peg$maxFailPos < input.length ? input.charAt(peg$maxFailPos) : null, peg$maxFailPos < input.length ? peg$computeLocation(peg$maxFailPos, peg$maxFailPos + 1) : peg$computeLocation(peg$maxFailPos, peg$maxFailPos));
  }
}
var peg$allowedStartRules = (/* unused pure expression or super */ null && (["transformList"]));

;// ./src/fromTransformAttribute.js


/**
 * Parser for SVG Trasform Attribute http://www.w3.org/TR/SVG/coords.html#TransformAttribute
 * @param transformString {string} Transform string as defined by w3 Consortium
 * @returns {MatrixDescriptor[]} Array of MatrixDescriptor
 *
 * @example
 * > fromTransformAttribute('translate(-10,-10) scale(2,2) translate(10,10)')
 * [
 *  { type: 'translate', tx: -10, ty: -10},
 *  { type: 'scale', sx: 2, sy: 2 },
 *  { type: 'translate', tx: 10, ty: 10}
 * ]
 *
 * > compose(fromDefinition(fromTransformAttribute('translate(-10, -10) scale(10, 10)')))
 * { a: 10, c: 0, e: -10, b: 0, d: 10, f: -10 }
 */
function fromTransformAttribute(transformString) {
  return peg$parse(transformString);
}
;// ./src/decompose.js


/**
 * Decompose a matrix into translation, scaling and rotation components, optionally
 * take horizontal and vertical flip in to consideration.
 * Note this function decomposes a matrix in rotation -> scaling -> translation order. I.e. for
 * certain translation T {tx, ty}, rotation R and scaling S { sx, sy }, it's only true for:
 *  decomposeTSR(compose(T, S, R)) === { translate: T, rotation: R, scale: S }
 * composing in a different order may yield a different decomposition result.
 * @param matrix {Matrix} Affine Matrix
 * @param  flipX {boolean} Whether the matrix contains vertical flip, i.e. mirrors on x-axis
 * @param  flipY {boolean} Whether the matrix contains horizontal flip, i.e. mirrors on y-axis
 * @returns {Transform} A transform object consisted by its translation, scaling
 * and rotation components.
 */
function decomposeTSR(matrix) {
  var flipX = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : false;
  var flipY = arguments.length > 2 && arguments[2] !== undefined ? arguments[2] : false;
  // Remove flip from the matrix first - flip could be incorrectly interpreted as
  // rotations (e.g. flipX + flipY = rotate by 180 degrees).
  // Note flipX is a vertical flip, and flipY is a horizontal flip.
  if (flipX) {
    if (flipY) {
      matrix = compose(matrix, scale(-1, -1));
    } else {
      matrix = compose(matrix, scale(1, -1));
    }
  } else if (flipY) {
    matrix = compose(matrix, scale(-1, 1));
  }
  var a = matrix.a;
  var b = matrix.b;
  var c = matrix.c;
  var d = matrix.d;
  var scaleX, scaleY, rotation;
  if (a !== 0 || c !== 0) {
    var hypotAc = Math.hypot(a, c);
    scaleX = hypotAc;
    scaleY = (a * d - b * c) / hypotAc;
    var acos = Math.acos(a / hypotAc);
    rotation = c > 0 ? -acos : acos;
  } else if (b !== 0 || d !== 0) {
    var hypotBd = Math.hypot(b, d);
    scaleX = (a * d - b * c) / hypotBd;
    scaleY = hypotBd;
    var _acos = Math.acos(b / hypotBd);
    rotation = Math.PI / 2 + (d > 0 ? -_acos : _acos);
  } else {
    scaleX = 0;
    scaleY = 0;
    rotation = 0;
  }

  // put the flip factors back
  if (flipY) {
    scaleX = -scaleX;
  }
  if (flipX) {
    scaleY = -scaleY;
  }
  return {
    translate: {
      tx: matrix.e,
      ty: matrix.f
    },
    scale: {
      sx: scaleX,
      sy: scaleY
    },
    rotation: {
      angle: rotation
    }
  };
}
;// ./src/flip.js
/**
 * Tranformation matrix that mirrors on x-axis
 * @returns {Matrix} Affine Matrix
 */
function flipX() {
  return {
    a: 1,
    c: 0,
    e: 0,
    b: 0,
    d: -1,
    f: 0
  };
}

/**
 * Tranformation matrix that mirrors on y-axis
 * @returns {Matrix} Affine Matrix
 */
function flipY() {
  return {
    a: -1,
    c: 0,
    e: 0,
    b: 0,
    d: 1,
    f: 0
  };
}

/**
 * Tranformation matrix that mirrors on origin
 * @returns {Matrix} Affine Matrix
 */
function flipOrigin() {
  return {
    a: -1,
    c: 0,
    e: 0,
    b: 0,
    d: -1,
    f: 0
  };
}
;// ./src/fromMovingPoints.js






// https://manivannan-ai.medium.com/find-the-angle-between-three-points-from-2d-using-python-348c513e2cd

/**
 * Calculate a transformation matrix from a point that starts from A to A'
 * This approach can be associated to a pointer that moves on a device
 * @param {Point} startingPoint - Starting point (A)
 * @param {Point} endingPoint - Ending point (A')
 */
function fromOneMovingPoint(startingPoint, endingPoint) {
  var tx = endingPoint.x - startingPoint.x;
  var ty = endingPoint.y - startingPoint.y;
  return translate(tx, ty);
}

/**
 * Calculate a transformation matrix about two points that move from positions A and B to A' and B'
 * This approach can be associated to a two finger gesture on a touch device
 * @param {Point} startingPoint1 - Starting Point (A)
 * @param {Point} startingPoint2 - Starting Point (B)
 * @param {Point} endingPoint1 - Ending point (A')
 * @param {Point} endingPoint2 - Ending Point (B')
 */
function fromTwoMovingPoints(startingPoint1, startingPoint2, endingPoint1, endingPoint2) {
  // finds translation
  var translationMatrix = fromOneMovingPoint(startingPoint1, endingPoint1);
  var pointA = applyToPoint(translationMatrix, startingPoint2); // I have to translate this point
  var center = endingPoint1;
  var pointB = endingPoint2;

  // finds rotation matrix
  var angle = Math.atan2(pointB.y - center.y, pointB.x - center.x) - Math.atan2(pointA.y - center.y, pointA.x - center.x);
  var rotationMatrix = rotate(angle, center.x, center.y);

  // finds scale matrix
  var d1 = Math.sqrt(Math.pow(pointA.x - center.x, 2) + Math.pow(pointA.y - center.y, 2));
  var d2 = Math.sqrt(Math.pow(pointB.x - center.x, 2) + Math.pow(pointB.y - center.y, 2));
  var scalingLevel = d2 / d1;
  var scalingMatrix = scale(scalingLevel, scalingLevel, center.x, center.y);
  return compose([translationMatrix, scalingMatrix, rotationMatrix]);
}
;// ./src/index.js




















/******/ 	return __webpack_exports__;
/******/ })()
;
});
//# sourceMappingURL=transformation-matrix.js.map