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/*
* Copyright 2021 Google LLC
*
* Use of this source code is governed by a BSD-style license that can be
* found in the LICENSE file.
*/
#include "src/core/SkMatrixInvert.h"
#include "include/private/base/SkFloatingPoint.h"
SkScalar SkInvert2x2Matrix(const SkScalar inMatrix[4], SkScalar outMatrix[4]) {
double a00 = inMatrix[0];
double a01 = inMatrix[1];
double a10 = inMatrix[2];
double a11 = inMatrix[3];
// Calculate the determinant
double determinant = a00 * a11 - a01 * a10;
if (outMatrix) {
double invdet = sk_ieee_double_divide(1.0, determinant);
outMatrix[0] = a11 * invdet;
outMatrix[1] = -a01 * invdet;
outMatrix[2] = -a10 * invdet;
outMatrix[3] = a00 * invdet;
// If 1/det overflows to infinity (i.e. det is denormalized) or any of the inverted matrix
// values is non-finite, return zero to indicate a non-invertible matrix.
if (!SkScalarsAreFinite(outMatrix, 4)) {
determinant = 0.0f;
}
}
return determinant;
}
SkScalar SkInvert3x3Matrix(const SkScalar inMatrix[9], SkScalar outMatrix[9]) {
double a00 = inMatrix[0];
double a01 = inMatrix[1];
double a02 = inMatrix[2];
double a10 = inMatrix[3];
double a11 = inMatrix[4];
double a12 = inMatrix[5];
double a20 = inMatrix[6];
double a21 = inMatrix[7];
double a22 = inMatrix[8];
double b01 = a22 * a11 - a12 * a21;
double b11 = -a22 * a10 + a12 * a20;
double b21 = a21 * a10 - a11 * a20;
// Calculate the determinant
double determinant = a00 * b01 + a01 * b11 + a02 * b21;
if (outMatrix) {
double invdet = sk_ieee_double_divide(1.0, determinant);
outMatrix[0] = b01 * invdet;
outMatrix[1] = (-a22 * a01 + a02 * a21) * invdet;
outMatrix[2] = ( a12 * a01 - a02 * a11) * invdet;
outMatrix[3] = b11 * invdet;
outMatrix[4] = ( a22 * a00 - a02 * a20) * invdet;
outMatrix[5] = (-a12 * a00 + a02 * a10) * invdet;
outMatrix[6] = b21 * invdet;
outMatrix[7] = (-a21 * a00 + a01 * a20) * invdet;
outMatrix[8] = ( a11 * a00 - a01 * a10) * invdet;
// If 1/det overflows to infinity (i.e. det is denormalized) or any of the inverted matrix
// values is non-finite, return zero to indicate a non-invertible matrix.
if (!SkScalarsAreFinite(outMatrix, 9)) {
determinant = 0.0f;
}
}
return determinant;
}
SkScalar SkInvert4x4Matrix(const SkScalar inMatrix[16], SkScalar outMatrix[16]) {
double a00 = inMatrix[0];
double a01 = inMatrix[1];
double a02 = inMatrix[2];
double a03 = inMatrix[3];
double a10 = inMatrix[4];
double a11 = inMatrix[5];
double a12 = inMatrix[6];
double a13 = inMatrix[7];
double a20 = inMatrix[8];
double a21 = inMatrix[9];
double a22 = inMatrix[10];
double a23 = inMatrix[11];
double a30 = inMatrix[12];
double a31 = inMatrix[13];
double a32 = inMatrix[14];
double a33 = inMatrix[15];
double b00 = a00 * a11 - a01 * a10;
double b01 = a00 * a12 - a02 * a10;
double b02 = a00 * a13 - a03 * a10;
double b03 = a01 * a12 - a02 * a11;
double b04 = a01 * a13 - a03 * a11;
double b05 = a02 * a13 - a03 * a12;
double b06 = a20 * a31 - a21 * a30;
double b07 = a20 * a32 - a22 * a30;
double b08 = a20 * a33 - a23 * a30;
double b09 = a21 * a32 - a22 * a31;
double b10 = a21 * a33 - a23 * a31;
double b11 = a22 * a33 - a23 * a32;
// Calculate the determinant
double determinant = b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06;
if (outMatrix) {
double invdet = sk_ieee_double_divide(1.0, determinant);
b00 *= invdet;
b01 *= invdet;
b02 *= invdet;
b03 *= invdet;
b04 *= invdet;
b05 *= invdet;
b06 *= invdet;
b07 *= invdet;
b08 *= invdet;
b09 *= invdet;
b10 *= invdet;
b11 *= invdet;
outMatrix[0] = a11 * b11 - a12 * b10 + a13 * b09;
outMatrix[1] = a02 * b10 - a01 * b11 - a03 * b09;
outMatrix[2] = a31 * b05 - a32 * b04 + a33 * b03;
outMatrix[3] = a22 * b04 - a21 * b05 - a23 * b03;
outMatrix[4] = a12 * b08 - a10 * b11 - a13 * b07;
outMatrix[5] = a00 * b11 - a02 * b08 + a03 * b07;
outMatrix[6] = a32 * b02 - a30 * b05 - a33 * b01;
outMatrix[7] = a20 * b05 - a22 * b02 + a23 * b01;
outMatrix[8] = a10 * b10 - a11 * b08 + a13 * b06;
outMatrix[9] = a01 * b08 - a00 * b10 - a03 * b06;
outMatrix[10] = a30 * b04 - a31 * b02 + a33 * b00;
outMatrix[11] = a21 * b02 - a20 * b04 - a23 * b00;
outMatrix[12] = a11 * b07 - a10 * b09 - a12 * b06;
outMatrix[13] = a00 * b09 - a01 * b07 + a02 * b06;
outMatrix[14] = a31 * b01 - a30 * b03 - a32 * b00;
outMatrix[15] = a20 * b03 - a21 * b01 + a22 * b00;
// If 1/det overflows to infinity (i.e. det is denormalized) or any of the inverted matrix
// values is non-finite, return zero to indicate a non-invertible matrix.
if (!SkScalarsAreFinite(outMatrix, 16)) {
determinant = 0.0f;
}
}
return determinant;
}
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