/** * 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.} src source four points, [x0, y0, x1, y1, x2, y2, x3, y3] * @param {Array.} dest destination four points, [x0, y0, x1, y1, x2, y2, x3, y3] * @return {Function} transformer If fail, return null/undefined. */ 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) { // can not make transformer when and only when // any three of the markers are collinear. 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; }; } exports.buildTransformer = buildTransformer;