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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/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; }