svgo/plugins/_transforms.js

'use strict';

var regTransformTypes = /matrix|translate|scale|rotate|skewX|skewY/,
  regTransformSplit =
    /\s*(matrix|translate|scale|rotate|skewX|skewY)\s*\(\s*(.+?)\s*\)[\s,]*/,
  regNumericValues = /[-+]?(?:\d*\.\d+|\d+\.?)(?:[eE][-+]?\d+)?/g;

/**
 * Convert transform string to JS representation.
 *
 * @param {String} transformString input string
 * @param {Object} params plugin params
 * @return {Array} output array
 */
exports.transform2js = function (transformString) {
  // JS representation of the transform data
  var transforms = [],
    // current transform context
    current;

  // split value into ['', 'translate', '10 50', '', 'scale', '2', '', 'rotate', '-45', '']
  transformString.split(regTransformSplit).forEach(function (item) {
    var num;

    if (item) {
      // if item is a translate function
      if (regTransformTypes.test(item)) {
        // then collect it and change current context
        transforms.push((current = { name: item }));
        // else if item is data
      } else {
        // then split it into [10, 50] and collect as context.data
        // eslint-disable-next-line no-cond-assign
        while ((num = regNumericValues.exec(item))) {
          num = Number(num);
          if (current.data) current.data.push(num);
          else current.data = [num];
        }
      }
    }
  });

  // return empty array if broken transform (no data)
  return current && current.data ? transforms : [];
};

/**
 * Multiply transforms into one.
 *
 * @param {Array} input transforms array
 * @return {Array} output matrix array
 */
exports.transformsMultiply = function (transforms) {
  // convert transforms objects to the matrices
  transforms = transforms.map(function (transform) {
    if (transform.name === 'matrix') {
      return transform.data;
    }
    return transformToMatrix(transform);
  });

  // multiply all matrices into one
  transforms = {
    name: 'matrix',
    data:
      transforms.length > 0 ? transforms.reduce(multiplyTransformMatrices) : [],
  };

  return transforms;
};

/**
 * Do math like a schoolgirl.
 *
 * @type {Object}
 */
var mth = (exports.mth = {
  rad: function (deg) {
    return (deg * Math.PI) / 180;
  },

  deg: function (rad) {
    return (rad * 180) / Math.PI;
  },

  cos: function (deg) {
    return Math.cos(this.rad(deg));
  },

  acos: function (val, floatPrecision) {
    return +this.deg(Math.acos(val)).toFixed(floatPrecision);
  },

  sin: function (deg) {
    return Math.sin(this.rad(deg));
  },

  asin: function (val, floatPrecision) {
    return +this.deg(Math.asin(val)).toFixed(floatPrecision);
  },

  tan: function (deg) {
    return Math.tan(this.rad(deg));
  },

  atan: function (val, floatPrecision) {
    return +this.deg(Math.atan(val)).toFixed(floatPrecision);
  },
});

/**
 * Decompose matrix into simple transforms. See
 * https://frederic-wang.fr/decomposition-of-2d-transform-matrices.html
 *
 * @param {Object} data matrix transform object
 * @return {Object|Array} transforms array or original transform object
 */
exports.matrixToTransform = function (transform, params) {
  var floatPrecision = params.floatPrecision,
    data = transform.data,
    transforms = [],
    sx = +Math.hypot(data[0], data[1]).toFixed(params.transformPrecision),
    sy = +((data[0] * data[3] - data[1] * data[2]) / sx).toFixed(
      params.transformPrecision
    ),
    colsSum = data[0] * data[2] + data[1] * data[3],
    rowsSum = data[0] * data[1] + data[2] * data[3],
    scaleBefore = rowsSum != 0 || sx == sy;

  // [..., ..., ..., ..., tx, ty] → translate(tx, ty)
  if (data[4] || data[5]) {
    transforms.push({
      name: 'translate',
      data: data.slice(4, data[5] ? 6 : 5),
    });
  }

  // [sx, 0, tan(a)·sy, sy, 0, 0] → skewX(a)·scale(sx, sy)
  if (!data[1] && data[2]) {
    transforms.push({
      name: 'skewX',
      data: [mth.atan(data[2] / sy, floatPrecision)],
    });

    // [sx, sx·tan(a), 0, sy, 0, 0] → skewY(a)·scale(sx, sy)
  } else if (data[1] && !data[2]) {
    transforms.push({
      name: 'skewY',
      data: [mth.atan(data[1] / data[0], floatPrecision)],
    });
    sx = data[0];
    sy = data[3];

    // [sx·cos(a), sx·sin(a), sy·-sin(a), sy·cos(a), x, y] → rotate(a[, cx, cy])·(scale or skewX) or
    // [sx·cos(a), sy·sin(a), sx·-sin(a), sy·cos(a), x, y] → scale(sx, sy)·rotate(a[, cx, cy]) (if !scaleBefore)
  } else if (!colsSum || (sx == 1 && sy == 1) || !scaleBefore) {
    if (!scaleBefore) {
      sx = (data[0] < 0 ? -1 : 1) * Math.hypot(data[0], data[2]);
      sy = (data[3] < 0 ? -1 : 1) * Math.hypot(data[1], data[3]);
      transforms.push({ name: 'scale', data: [sx, sy] });
    }
    var angle = Math.min(Math.max(-1, data[0] / sx), 1),
      rotate = [
        mth.acos(angle, floatPrecision) *
          ((scaleBefore ? 1 : sy) * data[1] < 0 ? -1 : 1),
      ];

    if (rotate[0]) transforms.push({ name: 'rotate', data: rotate });

    if (rowsSum && colsSum)
      transforms.push({
        name: 'skewX',
        data: [mth.atan(colsSum / (sx * sx), floatPrecision)],
      });

    // rotate(a, cx, cy) can consume translate() within optional arguments cx, cy (rotation point)
    if (rotate[0] && (data[4] || data[5])) {
      transforms.shift();
      var cos = data[0] / sx,
        sin = data[1] / (scaleBefore ? sx : sy),
        x = data[4] * (scaleBefore || sy),
        y = data[5] * (scaleBefore || sx),
        denom =
          (Math.pow(1 - cos, 2) + Math.pow(sin, 2)) * (scaleBefore || sx * sy);
      rotate.push(((1 - cos) * x - sin * y) / denom);
      rotate.push(((1 - cos) * y + sin * x) / denom);
    }

    // Too many transformations, return original matrix if it isn't just a scale/translate
  } else if (data[1] || data[2]) {
    return transform;
  }

  if ((scaleBefore && (sx != 1 || sy != 1)) || !transforms.length)
    transforms.push({
      name: 'scale',
      data: sx == sy ? [sx] : [sx, sy],
    });

  return transforms;
};

/**
 * Convert transform to the matrix data.
 *
 * @param {Object} transform transform object
 * @return {Array} matrix data
 */
function transformToMatrix(transform) {
  if (transform.name === 'matrix') return transform.data;

  var matrix;

  switch (transform.name) {
    case 'translate':
      // [1, 0, 0, 1, tx, ty]
      matrix = [1, 0, 0, 1, transform.data[0], transform.data[1] || 0];
      break;
    case 'scale':
      // [sx, 0, 0, sy, 0, 0]
      matrix = [
        transform.data[0],
        0,
        0,
        transform.data[1] || transform.data[0],
        0,
        0,
      ];
      break;
    case 'rotate':
      // [cos(a), sin(a), -sin(a), cos(a), x, y]
      var cos = mth.cos(transform.data[0]),
        sin = mth.sin(transform.data[0]),
        cx = transform.data[1] || 0,
        cy = transform.data[2] || 0;

      matrix = [
        cos,
        sin,
        -sin,
        cos,
        (1 - cos) * cx + sin * cy,
        (1 - cos) * cy - sin * cx,
      ];
      break;
    case 'skewX':
      // [1, 0, tan(a), 1, 0, 0]
      matrix = [1, 0, mth.tan(transform.data[0]), 1, 0, 0];
      break;
    case 'skewY':
      // [1, tan(a), 0, 1, 0, 0]
      matrix = [1, mth.tan(transform.data[0]), 0, 1, 0, 0];
      break;
  }

  return matrix;
}

/**
 * Applies transformation to an arc. To do so, we represent ellipse as a matrix, multiply it
 * by the transformation matrix and use a singular value decomposition to represent in a form
 * rotate(θ)·scale(a b)·rotate(φ). This gives us new ellipse params a, b and θ.
 * SVD is being done with the formulae provided by Wolffram|Alpha (svd {{m0, m2}, {m1, m3}})
 *
 * @param {Array} cursor [x, y]
 * @param {Array} arc [a, b, rotation in deg]
 * @param {Array} transform transformation matrix
 * @return {Array} arc transformed input arc
 */
exports.transformArc = function (cursor, arc, transform) {
  const x = arc[5] - cursor[0];
  const y = arc[6] - cursor[1];
  var a = arc[0],
    b = arc[1],
    rot = (arc[2] * Math.PI) / 180,
    cos = Math.cos(rot),
    sin = Math.sin(rot),
    h =
      Math.pow(x * cos + y * sin, 2) / (4 * a * a) +
      Math.pow(y * cos - x * sin, 2) / (4 * b * b);
  if (h > 1) {
    h = Math.sqrt(h);
    a *= h;
    b *= h;
  }
  var ellipse = [a * cos, a * sin, -b * sin, b * cos, 0, 0],
    m = multiplyTransformMatrices(transform, ellipse),
    // Decompose the new ellipse matrix
    lastCol = m[2] * m[2] + m[3] * m[3],
    squareSum = m[0] * m[0] + m[1] * m[1] + lastCol,
    root =
      Math.hypot(m[0] - m[3], m[1] + m[2]) *
      Math.hypot(m[0] + m[3], m[1] - m[2]);

  if (!root) {
    // circle
    arc[0] = arc[1] = Math.sqrt(squareSum / 2);
    arc[2] = 0;
  } else {
    var majorAxisSqr = (squareSum + root) / 2,
      minorAxisSqr = (squareSum - root) / 2,
      major = Math.abs(majorAxisSqr - lastCol) > 1e-6,
      sub = (major ? majorAxisSqr : minorAxisSqr) - lastCol,
      rowsSum = m[0] * m[2] + m[1] * m[3],
      term1 = m[0] * sub + m[2] * rowsSum,
      term2 = m[1] * sub + m[3] * rowsSum;
    arc[0] = Math.sqrt(majorAxisSqr);
    arc[1] = Math.sqrt(minorAxisSqr);
    arc[2] =
      (((major ? term2 < 0 : term1 > 0) ? -1 : 1) *
        Math.acos((major ? term1 : term2) / Math.hypot(term1, term2)) *
        180) /
      Math.PI;
  }

  if (transform[0] < 0 !== transform[3] < 0) {
    // Flip the sweep flag if coordinates are being flipped horizontally XOR vertically
    arc[4] = 1 - arc[4];
  }

  return arc;
};

/**
 * Multiply transformation matrices.
 *
 * @param {Array} a matrix A data
 * @param {Array} b matrix B data
 * @return {Array} result
 */
function multiplyTransformMatrices(a, b) {
  return [
    a[0] * b[0] + a[2] * b[1],
    a[1] * b[0] + a[3] * b[1],
    a[0] * b[2] + a[2] * b[3],
    a[1] * b[2] + a[3] * b[3],
    a[0] * b[4] + a[2] * b[5] + a[4],
    a[1] * b[4] + a[3] * b[5] + a[5],
  ];
}