public/en/builder/src/zrender/core/fourPointsTransform.js

/**
 * The algoritm is learnt from
 * https://franklinta.com/2014/09/08/computing-css-matrix3d-transforms/
 * And we made some optimization for matrix inversion.
 * Other similar approaches:
 * "cv::getPerspectiveTransform", "Direct Linear Transformation".
 */
var LN2 = Math.log(2);

function determinant(rows, rank, rowStart, rowMask, colMask, detCache) {
  var cacheKey = rowMask + '-' + colMask;
  var fullRank = rows.length;

  if (detCache.hasOwnProperty(cacheKey)) {
    return detCache[cacheKey];
  }

  if (rank === 1) {
    // In this case the colMask must be like: `11101111`. We can find the place of `0`.
    var colStart = Math.round(Math.log((1 << fullRank) - 1 & ~colMask) / LN2);
    return rows[rowStart][colStart];
  }

  var subRowMask = rowMask | 1 << rowStart;
  var subRowStart = rowStart + 1;

  while (rowMask & 1 << subRowStart) {
    subRowStart++;
  }

  var sum = 0;

  for (var j = 0, colLocalIdx = 0; j < fullRank; j++) {
    var colTag = 1 << j;

    if (!(colTag & colMask)) {
      sum += (colLocalIdx % 2 ? -1 : 1) * rows[rowStart][j] // det(subMatrix(0, j))
      * determinant(rows, rank - 1, subRowStart, subRowMask, colMask | colTag, detCache);
      colLocalIdx++;
    }
  }

  detCache[cacheKey] = sum;
  return sum;
}
/**
 * Usage:
 * ```js
 * var transformer = buildTransformer(
 *     [10, 44, 100, 44, 100, 300, 10, 300],
 *     [50, 54, 130, 14, 140, 330, 14, 220]
 * );
 * var out = [];
 * transformer && transformer([11, 33], out);
 * ```
 *
 * Notice: `buildTransformer` may take more than 10ms in some Android device.
 *
 * @param {Array.<number>} src source four points, [x0, y0, x1, y1, x2, y2, x3, y3]
 * @param {Array.<number>} dest destination four points, [x0, y0, x1, y1, x2, y2, x3, y3]
 * @return {Function} transformer If fail, return null/undefined.
 */


export function buildTransformer(src, dest) {
  var mA = [[src[0], src[1], 1, 0, 0, 0, -dest[0] * src[0], -dest[0] * src[1]], [0, 0, 0, src[0], src[1], 1, -dest[1] * src[0], -dest[1] * src[1]], [src[2], src[3], 1, 0, 0, 0, -dest[2] * src[2], -dest[2] * src[3]], [0, 0, 0, src[2], src[3], 1, -dest[3] * src[2], -dest[3] * src[3]], [src[4], src[5], 1, 0, 0, 0, -dest[4] * src[4], -dest[4] * src[5]], [0, 0, 0, src[4], src[5], 1, -dest[5] * src[4], -dest[5] * src[5]], [src[6], src[7], 1, 0, 0, 0, -dest[6] * src[6], -dest[6] * src[7]], [0, 0, 0, src[6], src[7], 1, -dest[7] * src[6], -dest[7] * src[7]]];
  var detCache = {};
  var det = determinant(mA, 8, 0, 0, 0, detCache);

  if (det === 0) {
    return;
  } // `invert(mA) * dest`, that is, `adj(mA) / det * dest`.


  var vh = [];

  for (var i = 0; i < 8; i++) {
    for (var j = 0; j < 8; j++) {
      vh[j] == null && (vh[j] = 0);
      vh[j] += ((i + j) % 2 ? -1 : 1) * // det(subMatrix(i, j))
      determinant(mA, 7, i === 0 ? 1 : 0, 1 << i, 1 << j, detCache) / det * dest[i];
    }
  }

  return function (out, srcPointX, srcPointY) {
    var pk = srcPointX * vh[6] + srcPointY * vh[7] + 1;
    out[0] = (srcPointX * vh[0] + srcPointY * vh[1] + vh[2]) / pk;
    out[1] = (srcPointX * vh[3] + srcPointY * vh[4] + vh[5]) / pk;
  };
}