bd028579
 易尊强
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/**
* 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".
*/
const LN2 = Math.log(2);
function determinant(
rows: number[][],
rank: number,
rowStart: number,
rowMask: number,
colMask: number,
detCache: {[key: string]: number}
) {
const cacheKey = rowMask + '-' + colMask;
const 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`.
const colStart = Math.round(Math.log(((1 << fullRank) - 1) & ~colMask) / LN2);
return rows[rowStart][colStart];
}
const subRowMask = rowMask | (1 << rowStart);
let subRowStart = rowStart + 1;
while (rowMask & (1 << subRowStart)) {
subRowStart++;
}
let sum = 0;
for (let j = 0, colLocalIdx = 0; j < fullRank; j++) {
const 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
* const transformer = buildTransformer(
* [10, 44, 100, 44, 100, 300, 10, 300],
* [50, 54, 130, 14, 140, 330, 14, 220]
* );
* const out = [];
* transformer && transformer([11, 33], out);
* ```
*
* Notice: `buildTransformer` may take more than 10ms in some Android device.
*
* @param src source four points, [x0, y0, x1, y1, x2, y2, x3, y3]
* @param dest destination four points, [x0, y0, x1, y1, x2, y2, x3, y3]
* @return transformer If fail, return null/undefined.
*/
export function buildTransformer(src: number[], dest: number[]) {
const 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]]
];
const detCache = {};
const 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`.
const vh: number[] = [];
for (let i = 0; i < 8; i++) {
for (let 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: number[], srcPointX: number, srcPointY: number) {
const 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;
};
}
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