| /* |
| * Copyright 2011 Google Inc. |
| * |
| * Use of this source code is governed by a BSD-style license that can be |
| * found in the LICENSE file. |
| */ |
| |
| #include "include/core/SkMatrix44.h" |
| #include <type_traits> |
| #include <utility> |
| |
| // Copying SkMatrix44 byte-wise is performance-critical to Blink. This class is |
| // contained in several Transform classes, which are copied multiple times |
| // during the rendering life cycle. See crbug.com/938563 for reference. |
| #if defined(SK_BUILD_FOR_WIN) || defined(SK_BUILD_FOR_MAC) |
| // std::is_trivially_copyable is not supported for some older clang versions, |
| // which (at least as of this patch) are in use for Chromecast. |
| static_assert(std::is_trivially_copyable<SkMatrix44>::value, |
| "SkMatrix44 must be trivially copyable"); |
| #endif |
| |
| static inline bool eq4(const SkScalar* SK_RESTRICT a, |
| const SkScalar* SK_RESTRICT b) { |
| return (a[0] == b[0]) & (a[1] == b[1]) & (a[2] == b[2]) & (a[3] == b[3]); |
| } |
| |
| bool SkMatrix44::operator==(const SkMatrix44& other) const { |
| if (this == &other) { |
| return true; |
| } |
| |
| if (this->isIdentity() && other.isIdentity()) { |
| return true; |
| } |
| |
| const SkScalar* SK_RESTRICT a = &fMat[0][0]; |
| const SkScalar* SK_RESTRICT b = &other.fMat[0][0]; |
| |
| #if 0 |
| for (int i = 0; i < 16; ++i) { |
| if (a[i] != b[i]) { |
| return false; |
| } |
| } |
| return true; |
| #else |
| // to reduce branch instructions, we compare 4 at a time. |
| // see bench/Matrix44Bench.cpp for test. |
| if (!eq4(&a[0], &b[0])) { |
| return false; |
| } |
| if (!eq4(&a[4], &b[4])) { |
| return false; |
| } |
| if (!eq4(&a[8], &b[8])) { |
| return false; |
| } |
| return eq4(&a[12], &b[12]); |
| #endif |
| } |
| |
| /////////////////////////////////////////////////////////////////////////////// |
| void SkMatrix44::recomputeTypeMask() { |
| if (0 != perspX() || 0 != perspY() || 0 != perspZ() || 1 != fMat[3][3]) { |
| fTypeMask = kTranslate_Mask | kScale_Mask | kAffine_Mask | kPerspective_Mask; |
| return; |
| } |
| |
| TypeMask mask = kIdentity_Mask; |
| if (0 != transX() || 0 != transY() || 0 != transZ()) { |
| mask |= kTranslate_Mask; |
| } |
| |
| if (1 != scaleX() || 1 != scaleY() || 1 != scaleZ()) { |
| mask |= kScale_Mask; |
| } |
| |
| if (0 != fMat[1][0] || 0 != fMat[0][1] || 0 != fMat[0][2] || |
| 0 != fMat[2][0] || 0 != fMat[1][2] || 0 != fMat[2][1]) { |
| mask |= kAffine_Mask; |
| } |
| fTypeMask = mask; |
| } |
| |
| /////////////////////////////////////////////////////////////////////////////// |
| |
| void SkMatrix44::asColMajorf(float dst[]) const { |
| const SkScalar* src = &fMat[0][0]; |
| for (int i = 0; i < 16; ++i) { |
| dst[i] = src[i]; |
| } |
| } |
| |
| void SkMatrix44::as3x4RowMajorf(float dst[]) const { |
| dst[0] = fMat[0][0]; dst[1] = fMat[1][0]; dst[2] = fMat[2][0]; dst[3] = fMat[3][0]; |
| dst[4] = fMat[0][1]; dst[5] = fMat[1][1]; dst[6] = fMat[2][1]; dst[7] = fMat[3][1]; |
| dst[8] = fMat[0][2]; dst[9] = fMat[1][2]; dst[10] = fMat[2][2]; dst[11] = fMat[3][2]; |
| } |
| |
| void SkMatrix44::asColMajord(double dst[]) const { |
| const SkScalar* src = &fMat[0][0]; |
| for (int i = 0; i < 16; ++i) { |
| dst[i] = src[i]; |
| } |
| } |
| |
| void SkMatrix44::asRowMajorf(float dst[]) const { |
| const SkScalar* src = &fMat[0][0]; |
| for (int i = 0; i < 4; ++i) { |
| dst[0] = float(src[0]); |
| dst[4] = float(src[1]); |
| dst[8] = float(src[2]); |
| dst[12] = float(src[3]); |
| src += 4; |
| dst += 1; |
| } |
| } |
| |
| void SkMatrix44::asRowMajord(double dst[]) const { |
| const SkScalar* src = &fMat[0][0]; |
| for (int i = 0; i < 4; ++i) { |
| dst[0] = src[0]; |
| dst[4] = src[1]; |
| dst[8] = src[2]; |
| dst[12] = src[3]; |
| src += 4; |
| dst += 1; |
| } |
| } |
| |
| void SkMatrix44::setColMajorf(const float src[]) { |
| SkScalar* dst = &fMat[0][0]; |
| for (int i = 0; i < 16; ++i) { |
| dst[i] = src[i]; |
| } |
| |
| this->recomputeTypeMask(); |
| } |
| |
| void SkMatrix44::setColMajord(const double src[]) { |
| SkScalar* dst = &fMat[0][0]; |
| for (int i = 0; i < 16; ++i) { |
| dst[i] = SkScalar(src[i]); |
| } |
| |
| this->recomputeTypeMask(); |
| } |
| |
| void SkMatrix44::setRowMajorf(const float src[]) { |
| SkScalar* dst = &fMat[0][0]; |
| for (int i = 0; i < 4; ++i) { |
| dst[0] = src[0]; |
| dst[4] = src[1]; |
| dst[8] = src[2]; |
| dst[12] = src[3]; |
| src += 4; |
| dst += 1; |
| } |
| this->recomputeTypeMask(); |
| } |
| |
| void SkMatrix44::setRowMajord(const double src[]) { |
| SkScalar* dst = &fMat[0][0]; |
| for (int i = 0; i < 4; ++i) { |
| dst[0] = SkScalar(src[0]); |
| dst[4] = SkScalar(src[1]); |
| dst[8] = SkScalar(src[2]); |
| dst[12] = SkScalar(src[3]); |
| src += 4; |
| dst += 1; |
| } |
| this->recomputeTypeMask(); |
| } |
| |
| /////////////////////////////////////////////////////////////////////////////// |
| |
| const SkMatrix44& SkMatrix44::I() { |
| static constexpr SkMatrix44 gIdentity44(kIdentity_Constructor); |
| return gIdentity44; |
| } |
| |
| void SkMatrix44::setIdentity() { |
| fMat[0][0] = 1; |
| fMat[0][1] = 0; |
| fMat[0][2] = 0; |
| fMat[0][3] = 0; |
| fMat[1][0] = 0; |
| fMat[1][1] = 1; |
| fMat[1][2] = 0; |
| fMat[1][3] = 0; |
| fMat[2][0] = 0; |
| fMat[2][1] = 0; |
| fMat[2][2] = 1; |
| fMat[2][3] = 0; |
| fMat[3][0] = 0; |
| fMat[3][1] = 0; |
| fMat[3][2] = 0; |
| fMat[3][3] = 1; |
| this->setTypeMask(kIdentity_Mask); |
| } |
| |
| void SkMatrix44::set3x3(SkScalar m_00, SkScalar m_10, SkScalar m_20, |
| SkScalar m_01, SkScalar m_11, SkScalar m_21, |
| SkScalar m_02, SkScalar m_12, SkScalar m_22) { |
| fMat[0][0] = m_00; fMat[0][1] = m_10; fMat[0][2] = m_20; fMat[0][3] = 0; |
| fMat[1][0] = m_01; fMat[1][1] = m_11; fMat[1][2] = m_21; fMat[1][3] = 0; |
| fMat[2][0] = m_02; fMat[2][1] = m_12; fMat[2][2] = m_22; fMat[2][3] = 0; |
| fMat[3][0] = 0; fMat[3][1] = 0; fMat[3][2] = 0; fMat[3][3] = 1; |
| this->recomputeTypeMask(); |
| } |
| |
| void SkMatrix44::set3x3RowMajorf(const float src[]) { |
| fMat[0][0] = src[0]; fMat[0][1] = src[3]; fMat[0][2] = src[6]; fMat[0][3] = 0; |
| fMat[1][0] = src[1]; fMat[1][1] = src[4]; fMat[1][2] = src[7]; fMat[1][3] = 0; |
| fMat[2][0] = src[2]; fMat[2][1] = src[5]; fMat[2][2] = src[8]; fMat[2][3] = 0; |
| fMat[3][0] = 0; fMat[3][1] = 0; fMat[3][2] = 0; fMat[3][3] = 1; |
| this->recomputeTypeMask(); |
| } |
| |
| void SkMatrix44::set3x4RowMajorf(const float src[]) { |
| fMat[0][0] = src[0]; fMat[1][0] = src[1]; fMat[2][0] = src[2]; fMat[3][0] = src[3]; |
| fMat[0][1] = src[4]; fMat[1][1] = src[5]; fMat[2][1] = src[6]; fMat[3][1] = src[7]; |
| fMat[0][2] = src[8]; fMat[1][2] = src[9]; fMat[2][2] = src[10]; fMat[3][2] = src[11]; |
| fMat[0][3] = 0; fMat[1][3] = 0; fMat[2][3] = 0; fMat[3][3] = 1; |
| this->recomputeTypeMask(); |
| } |
| |
| void SkMatrix44::set4x4(SkScalar m_00, SkScalar m_10, SkScalar m_20, SkScalar m_30, |
| SkScalar m_01, SkScalar m_11, SkScalar m_21, SkScalar m_31, |
| SkScalar m_02, SkScalar m_12, SkScalar m_22, SkScalar m_32, |
| SkScalar m_03, SkScalar m_13, SkScalar m_23, SkScalar m_33) { |
| fMat[0][0] = m_00; fMat[0][1] = m_10; fMat[0][2] = m_20; fMat[0][3] = m_30; |
| fMat[1][0] = m_01; fMat[1][1] = m_11; fMat[1][2] = m_21; fMat[1][3] = m_31; |
| fMat[2][0] = m_02; fMat[2][1] = m_12; fMat[2][2] = m_22; fMat[2][3] = m_32; |
| fMat[3][0] = m_03; fMat[3][1] = m_13; fMat[3][2] = m_23; fMat[3][3] = m_33; |
| this->recomputeTypeMask(); |
| } |
| |
| |
| /////////////////////////////////////////////////////////////////////////////// |
| |
| SkMatrix44& SkMatrix44::setTranslate(SkScalar dx, SkScalar dy, SkScalar dz) { |
| this->setIdentity(); |
| |
| if (!dx && !dy && !dz) { |
| return *this; |
| } |
| |
| fMat[3][0] = dx; |
| fMat[3][1] = dy; |
| fMat[3][2] = dz; |
| this->setTypeMask(kTranslate_Mask); |
| return *this; |
| } |
| |
| SkMatrix44& SkMatrix44::preTranslate(SkScalar dx, SkScalar dy, SkScalar dz) { |
| if (!dx && !dy && !dz) { |
| return *this; |
| } |
| |
| for (int i = 0; i < 4; ++i) { |
| fMat[3][i] = fMat[0][i] * dx + fMat[1][i] * dy + fMat[2][i] * dz + fMat[3][i]; |
| } |
| this->recomputeTypeMask(); |
| return *this; |
| } |
| |
| SkMatrix44& SkMatrix44::postTranslate(SkScalar dx, SkScalar dy, SkScalar dz) { |
| if (!dx && !dy && !dz) { |
| return *this; |
| } |
| |
| if (this->getType() & kPerspective_Mask) { |
| for (int i = 0; i < 4; ++i) { |
| fMat[i][0] += fMat[i][3] * dx; |
| fMat[i][1] += fMat[i][3] * dy; |
| fMat[i][2] += fMat[i][3] * dz; |
| } |
| } else { |
| fMat[3][0] += dx; |
| fMat[3][1] += dy; |
| fMat[3][2] += dz; |
| this->recomputeTypeMask(); |
| } |
| return *this; |
| } |
| |
| /////////////////////////////////////////////////////////////////////////////// |
| |
| SkMatrix44& SkMatrix44::setScale(SkScalar sx, SkScalar sy, SkScalar sz) { |
| this->setIdentity(); |
| |
| if (1 == sx && 1 == sy && 1 == sz) { |
| return *this; |
| } |
| |
| fMat[0][0] = sx; |
| fMat[1][1] = sy; |
| fMat[2][2] = sz; |
| this->setTypeMask(kScale_Mask); |
| return *this; |
| } |
| |
| SkMatrix44& SkMatrix44::preScale(SkScalar sx, SkScalar sy, SkScalar sz) { |
| if (1 == sx && 1 == sy && 1 == sz) { |
| return *this; |
| } |
| |
| // The implementation matrix * pureScale can be shortcut |
| // by knowing that pureScale components effectively scale |
| // the columns of the original matrix. |
| for (int i = 0; i < 4; i++) { |
| fMat[0][i] *= sx; |
| fMat[1][i] *= sy; |
| fMat[2][i] *= sz; |
| } |
| this->recomputeTypeMask(); |
| return *this; |
| } |
| |
| SkMatrix44& SkMatrix44::postScale(SkScalar sx, SkScalar sy, SkScalar sz) { |
| if (1 == sx && 1 == sy && 1 == sz) { |
| return *this; |
| } |
| |
| for (int i = 0; i < 4; i++) { |
| fMat[i][0] *= sx; |
| fMat[i][1] *= sy; |
| fMat[i][2] *= sz; |
| } |
| this->recomputeTypeMask(); |
| return *this; |
| } |
| |
| /////////////////////////////////////////////////////////////////////////////// |
| |
| void SkMatrix44::setRotateAbout(SkScalar x, SkScalar y, SkScalar z, SkScalar radians) { |
| double len2 = (double)x * x + (double)y * y + (double)z * z; |
| if (1 != len2) { |
| if (0 == len2) { |
| this->setIdentity(); |
| return; |
| } |
| double scale = 1 / sqrt(len2); |
| x = SkScalar(x * scale); |
| y = SkScalar(y * scale); |
| z = SkScalar(z * scale); |
| } |
| this->setRotateAboutUnit(x, y, z, radians); |
| } |
| |
| void SkMatrix44::setRotateAboutUnit(SkScalar x, SkScalar y, SkScalar z, SkScalar radians) { |
| double c = cos(radians); |
| double s = sin(radians); |
| double C = 1 - c; |
| double xs = x * s; |
| double ys = y * s; |
| double zs = z * s; |
| double xC = x * C; |
| double yC = y * C; |
| double zC = z * C; |
| double xyC = x * yC; |
| double yzC = y * zC; |
| double zxC = z * xC; |
| |
| // if you're looking at wikipedia, remember that we're column major. |
| this->set3x3(SkScalar(x * xC + c), // scale x |
| SkScalar(xyC + zs), // skew x |
| SkScalar(zxC - ys), // trans x |
| |
| SkScalar(xyC - zs), // skew y |
| SkScalar(y * yC + c), // scale y |
| SkScalar(yzC + xs), // trans y |
| |
| SkScalar(zxC + ys), // persp x |
| SkScalar(yzC - xs), // persp y |
| SkScalar(z * zC + c)); // persp 2 |
| } |
| |
| /////////////////////////////////////////////////////////////////////////////// |
| |
| static bool bits_isonly(int value, int mask) { |
| return 0 == (value & ~mask); |
| } |
| |
| void SkMatrix44::setConcat(const SkMatrix44& a, const SkMatrix44& b) { |
| const SkMatrix44::TypeMask a_mask = a.getType(); |
| const SkMatrix44::TypeMask b_mask = b.getType(); |
| |
| if (kIdentity_Mask == a_mask) { |
| *this = b; |
| return; |
| } |
| if (kIdentity_Mask == b_mask) { |
| *this = a; |
| return; |
| } |
| |
| bool useStorage = (this == &a || this == &b); |
| SkScalar storage[16]; |
| SkScalar* result = useStorage ? storage : &fMat[0][0]; |
| |
| // Both matrices are at most scale+translate |
| if (bits_isonly(a_mask | b_mask, kScale_Mask | kTranslate_Mask)) { |
| result[0] = a.fMat[0][0] * b.fMat[0][0]; |
| result[1] = result[2] = result[3] = result[4] = 0; |
| result[5] = a.fMat[1][1] * b.fMat[1][1]; |
| result[6] = result[7] = result[8] = result[9] = 0; |
| result[10] = a.fMat[2][2] * b.fMat[2][2]; |
| result[11] = 0; |
| result[12] = a.fMat[0][0] * b.fMat[3][0] + a.fMat[3][0]; |
| result[13] = a.fMat[1][1] * b.fMat[3][1] + a.fMat[3][1]; |
| result[14] = a.fMat[2][2] * b.fMat[3][2] + a.fMat[3][2]; |
| result[15] = 1; |
| } else { |
| for (int j = 0; j < 4; j++) { |
| for (int i = 0; i < 4; i++) { |
| double value = 0; |
| for (int k = 0; k < 4; k++) { |
| value += double(a.fMat[k][i]) * b.fMat[j][k]; |
| } |
| *result++ = SkScalar(value); |
| } |
| } |
| } |
| |
| if (useStorage) { |
| memcpy(fMat, storage, sizeof(storage)); |
| } |
| this->recomputeTypeMask(); |
| } |
| |
| /////////////////////////////////////////////////////////////////////////////// |
| |
| /** We always perform the calculation in doubles, to avoid prematurely losing |
| precision along the way. This relies on the compiler automatically |
| promoting our SkScalar values to double (if needed). |
| */ |
| double SkMatrix44::determinant() const { |
| if (this->isIdentity()) { |
| return 1; |
| } |
| if (this->isScaleTranslate()) { |
| return fMat[0][0] * fMat[1][1] * fMat[2][2] * fMat[3][3]; |
| } |
| |
| double a00 = fMat[0][0]; |
| double a01 = fMat[0][1]; |
| double a02 = fMat[0][2]; |
| double a03 = fMat[0][3]; |
| double a10 = fMat[1][0]; |
| double a11 = fMat[1][1]; |
| double a12 = fMat[1][2]; |
| double a13 = fMat[1][3]; |
| double a20 = fMat[2][0]; |
| double a21 = fMat[2][1]; |
| double a22 = fMat[2][2]; |
| double a23 = fMat[2][3]; |
| double a30 = fMat[3][0]; |
| double a31 = fMat[3][1]; |
| double a32 = fMat[3][2]; |
| double a33 = fMat[3][3]; |
| |
| 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 |
| return b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06; |
| } |
| |
| /////////////////////////////////////////////////////////////////////////////// |
| |
| static bool is_matrix_finite(const SkMatrix44& matrix) { |
| SkScalar accumulator = 0; |
| for (int row = 0; row < 4; ++row) { |
| for (int col = 0; col < 4; ++col) { |
| accumulator *= matrix.get(row, col); |
| } |
| } |
| return accumulator == 0; |
| } |
| |
| bool SkMatrix44::invert(SkMatrix44* storage) const { |
| if (this->isIdentity()) { |
| if (storage) { |
| storage->setIdentity(); |
| } |
| return true; |
| } |
| |
| if (this->isTranslate()) { |
| if (storage) { |
| storage->setTranslate(-fMat[3][0], -fMat[3][1], -fMat[3][2]); |
| } |
| return true; |
| } |
| |
| SkMatrix44 tmp; |
| // Use storage if it's available and distinct from this matrix. |
| SkMatrix44* inverse = (storage && storage != this) ? storage : &tmp; |
| if (this->isScaleTranslate()) { |
| if (0 == fMat[0][0] * fMat[1][1] * fMat[2][2]) { |
| return false; |
| } |
| |
| double invXScale = 1 / fMat[0][0]; |
| double invYScale = 1 / fMat[1][1]; |
| double invZScale = 1 / fMat[2][2]; |
| |
| inverse->fMat[0][0] = SkDoubleToScalar(invXScale); |
| inverse->fMat[0][1] = 0; |
| inverse->fMat[0][2] = 0; |
| inverse->fMat[0][3] = 0; |
| |
| inverse->fMat[1][0] = 0; |
| inverse->fMat[1][1] = SkDoubleToScalar(invYScale); |
| inverse->fMat[1][2] = 0; |
| inverse->fMat[1][3] = 0; |
| |
| inverse->fMat[2][0] = 0; |
| inverse->fMat[2][1] = 0; |
| inverse->fMat[2][2] = SkDoubleToScalar(invZScale); |
| inverse->fMat[2][3] = 0; |
| |
| inverse->fMat[3][0] = SkDoubleToScalar(-fMat[3][0] * invXScale); |
| inverse->fMat[3][1] = SkDoubleToScalar(-fMat[3][1] * invYScale); |
| inverse->fMat[3][2] = SkDoubleToScalar(-fMat[3][2] * invZScale); |
| inverse->fMat[3][3] = 1; |
| |
| inverse->setTypeMask(this->getType()); |
| |
| if (!is_matrix_finite(*inverse)) { |
| return false; |
| } |
| if (storage && inverse != storage) { |
| *storage = *inverse; |
| } |
| return true; |
| } |
| |
| double a00 = fMat[0][0]; |
| double a01 = fMat[0][1]; |
| double a02 = fMat[0][2]; |
| double a03 = fMat[0][3]; |
| double a10 = fMat[1][0]; |
| double a11 = fMat[1][1]; |
| double a12 = fMat[1][2]; |
| double a13 = fMat[1][3]; |
| double a20 = fMat[2][0]; |
| double a21 = fMat[2][1]; |
| double a22 = fMat[2][2]; |
| double a23 = fMat[2][3]; |
| double a30 = fMat[3][0]; |
| double a31 = fMat[3][1]; |
| double a32 = fMat[3][2]; |
| double a33 = fMat[3][3]; |
| |
| if (!(this->getType() & kPerspective_Mask)) { |
| // If we know the matrix has no perspective, then the perspective |
| // component is (0, 0, 0, 1). We can use this information to save a lot |
| // of arithmetic that would otherwise be spent to compute the inverse |
| // of a general matrix. |
| |
| SkASSERT(a03 == 0); |
| SkASSERT(a13 == 0); |
| SkASSERT(a23 == 0); |
| SkASSERT(a33 == 1); |
| |
| double b00 = a00 * a11 - a01 * a10; |
| double b01 = a00 * a12 - a02 * a10; |
| double b03 = a01 * a12 - a02 * a11; |
| double b06 = a20 * a31 - a21 * a30; |
| double b07 = a20 * a32 - a22 * a30; |
| double b08 = a20; |
| double b09 = a21 * a32 - a22 * a31; |
| double b10 = a21; |
| double b11 = a22; |
| |
| // Calculate the determinant |
| double det = b00 * b11 - b01 * b10 + b03 * b08; |
| |
| double invdet = sk_ieee_double_divide(1.0, det); |
| // If det is zero, we want to return false. However, we also want to return false |
| // if 1/det overflows to infinity (i.e. det is denormalized). Both of these are |
| // handled by checking that 1/det is finite. |
| if (!sk_float_isfinite(sk_double_to_float(invdet))) { |
| return false; |
| } |
| |
| b00 *= invdet; |
| b01 *= invdet; |
| b03 *= invdet; |
| b06 *= invdet; |
| b07 *= invdet; |
| b08 *= invdet; |
| b09 *= invdet; |
| b10 *= invdet; |
| b11 *= invdet; |
| |
| inverse->fMat[0][0] = SkDoubleToScalar(a11 * b11 - a12 * b10); |
| inverse->fMat[0][1] = SkDoubleToScalar(a02 * b10 - a01 * b11); |
| inverse->fMat[0][2] = SkDoubleToScalar(b03); |
| inverse->fMat[0][3] = 0; |
| inverse->fMat[1][0] = SkDoubleToScalar(a12 * b08 - a10 * b11); |
| inverse->fMat[1][1] = SkDoubleToScalar(a00 * b11 - a02 * b08); |
| inverse->fMat[1][2] = SkDoubleToScalar(-b01); |
| inverse->fMat[1][3] = 0; |
| inverse->fMat[2][0] = SkDoubleToScalar(a10 * b10 - a11 * b08); |
| inverse->fMat[2][1] = SkDoubleToScalar(a01 * b08 - a00 * b10); |
| inverse->fMat[2][2] = SkDoubleToScalar(b00); |
| inverse->fMat[2][3] = 0; |
| inverse->fMat[3][0] = SkDoubleToScalar(a11 * b07 - a10 * b09 - a12 * b06); |
| inverse->fMat[3][1] = SkDoubleToScalar(a00 * b09 - a01 * b07 + a02 * b06); |
| inverse->fMat[3][2] = SkDoubleToScalar(a31 * b01 - a30 * b03 - a32 * b00); |
| inverse->fMat[3][3] = 1; |
| |
| inverse->setTypeMask(this->getType()); |
| if (!is_matrix_finite(*inverse)) { |
| return false; |
| } |
| if (storage && inverse != storage) { |
| *storage = *inverse; |
| } |
| return true; |
| } |
| |
| 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 det = b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06; |
| |
| double invdet = sk_ieee_double_divide(1.0, det); |
| // If det is zero, we want to return false. However, we also want to return false |
| // if 1/det overflows to infinity (i.e. det is denormalized). Both of these are |
| // handled by checking that 1/det is finite. |
| if (!sk_float_isfinite(sk_double_to_float(invdet))) { |
| return false; |
| } |
| |
| b00 *= invdet; |
| b01 *= invdet; |
| b02 *= invdet; |
| b03 *= invdet; |
| b04 *= invdet; |
| b05 *= invdet; |
| b06 *= invdet; |
| b07 *= invdet; |
| b08 *= invdet; |
| b09 *= invdet; |
| b10 *= invdet; |
| b11 *= invdet; |
| |
| inverse->fMat[0][0] = SkDoubleToScalar(a11 * b11 - a12 * b10 + a13 * b09); |
| inverse->fMat[0][1] = SkDoubleToScalar(a02 * b10 - a01 * b11 - a03 * b09); |
| inverse->fMat[0][2] = SkDoubleToScalar(a31 * b05 - a32 * b04 + a33 * b03); |
| inverse->fMat[0][3] = SkDoubleToScalar(a22 * b04 - a21 * b05 - a23 * b03); |
| inverse->fMat[1][0] = SkDoubleToScalar(a12 * b08 - a10 * b11 - a13 * b07); |
| inverse->fMat[1][1] = SkDoubleToScalar(a00 * b11 - a02 * b08 + a03 * b07); |
| inverse->fMat[1][2] = SkDoubleToScalar(a32 * b02 - a30 * b05 - a33 * b01); |
| inverse->fMat[1][3] = SkDoubleToScalar(a20 * b05 - a22 * b02 + a23 * b01); |
| inverse->fMat[2][0] = SkDoubleToScalar(a10 * b10 - a11 * b08 + a13 * b06); |
| inverse->fMat[2][1] = SkDoubleToScalar(a01 * b08 - a00 * b10 - a03 * b06); |
| inverse->fMat[2][2] = SkDoubleToScalar(a30 * b04 - a31 * b02 + a33 * b00); |
| inverse->fMat[2][3] = SkDoubleToScalar(a21 * b02 - a20 * b04 - a23 * b00); |
| inverse->fMat[3][0] = SkDoubleToScalar(a11 * b07 - a10 * b09 - a12 * b06); |
| inverse->fMat[3][1] = SkDoubleToScalar(a00 * b09 - a01 * b07 + a02 * b06); |
| inverse->fMat[3][2] = SkDoubleToScalar(a31 * b01 - a30 * b03 - a32 * b00); |
| inverse->fMat[3][3] = SkDoubleToScalar(a20 * b03 - a21 * b01 + a22 * b00); |
| inverse->setTypeMask(this->getType()); |
| if (!is_matrix_finite(*inverse)) { |
| return false; |
| } |
| if (storage && inverse != storage) { |
| *storage = *inverse; |
| } |
| return true; |
| } |
| |
| /////////////////////////////////////////////////////////////////////////////// |
| |
| void SkMatrix44::transpose() { |
| if (!this->isIdentity()) { |
| using std::swap; |
| swap(fMat[0][1], fMat[1][0]); |
| swap(fMat[0][2], fMat[2][0]); |
| swap(fMat[0][3], fMat[3][0]); |
| swap(fMat[1][2], fMat[2][1]); |
| swap(fMat[1][3], fMat[3][1]); |
| swap(fMat[2][3], fMat[3][2]); |
| this->recomputeTypeMask(); |
| } |
| } |
| |
| /////////////////////////////////////////////////////////////////////////////// |
| |
| void SkMatrix44::mapScalars(const SkScalar src[4], SkScalar dst[4]) const { |
| SkScalar storage[4]; |
| SkScalar* result = (src == dst) ? storage : dst; |
| |
| for (int i = 0; i < 4; i++) { |
| SkScalar value = 0; |
| for (int j = 0; j < 4; j++) { |
| value += fMat[j][i] * src[j]; |
| } |
| result[i] = value; |
| } |
| |
| if (storage == result) { |
| memcpy(dst, storage, sizeof(storage)); |
| } |
| } |
| |
| typedef void (*Map2Procf)(const SkScalar mat[][4], const float src2[], int count, float dst4[]); |
| typedef void (*Map2Procd)(const SkScalar mat[][4], const double src2[], int count, double dst4[]); |
| |
| static void map2_if(const SkScalar mat[][4], const float* SK_RESTRICT src2, |
| int count, float* SK_RESTRICT dst4) { |
| for (int i = 0; i < count; ++i) { |
| dst4[0] = src2[0]; |
| dst4[1] = src2[1]; |
| dst4[2] = 0; |
| dst4[3] = 1; |
| src2 += 2; |
| dst4 += 4; |
| } |
| } |
| |
| static void map2_id(const SkScalar mat[][4], const double* SK_RESTRICT src2, |
| int count, double* SK_RESTRICT dst4) { |
| for (int i = 0; i < count; ++i) { |
| dst4[0] = src2[0]; |
| dst4[1] = src2[1]; |
| dst4[2] = 0; |
| dst4[3] = 1; |
| src2 += 2; |
| dst4 += 4; |
| } |
| } |
| |
| static void map2_tf(const SkScalar mat[][4], const float* SK_RESTRICT src2, |
| int count, float* SK_RESTRICT dst4) { |
| const float mat30 = float(mat[3][0]); |
| const float mat31 = float(mat[3][1]); |
| const float mat32 = float(mat[3][2]); |
| for (int n = 0; n < count; ++n) { |
| dst4[0] = src2[0] + mat30; |
| dst4[1] = src2[1] + mat31; |
| dst4[2] = mat32; |
| dst4[3] = 1; |
| src2 += 2; |
| dst4 += 4; |
| } |
| } |
| |
| static void map2_td(const SkScalar mat[][4], const double* SK_RESTRICT src2, |
| int count, double* SK_RESTRICT dst4) { |
| for (int n = 0; n < count; ++n) { |
| dst4[0] = src2[0] + mat[3][0]; |
| dst4[1] = src2[1] + mat[3][1]; |
| dst4[2] = mat[3][2]; |
| dst4[3] = 1; |
| src2 += 2; |
| dst4 += 4; |
| } |
| } |
| |
| static void map2_sf(const SkScalar mat[][4], const float* SK_RESTRICT src2, |
| int count, float* SK_RESTRICT dst4) { |
| const float mat32 = float(mat[3][2]); |
| for (int n = 0; n < count; ++n) { |
| dst4[0] = float(mat[0][0] * src2[0] + mat[3][0]); |
| dst4[1] = float(mat[1][1] * src2[1] + mat[3][1]); |
| dst4[2] = mat32; |
| dst4[3] = 1; |
| src2 += 2; |
| dst4 += 4; |
| } |
| } |
| |
| static void map2_sd(const SkScalar mat[][4], const double* SK_RESTRICT src2, |
| int count, double* SK_RESTRICT dst4) { |
| for (int n = 0; n < count; ++n) { |
| dst4[0] = mat[0][0] * src2[0] + mat[3][0]; |
| dst4[1] = mat[1][1] * src2[1] + mat[3][1]; |
| dst4[2] = mat[3][2]; |
| dst4[3] = 1; |
| src2 += 2; |
| dst4 += 4; |
| } |
| } |
| |
| static void map2_af(const SkScalar mat[][4], const float* SK_RESTRICT src2, |
| int count, float* SK_RESTRICT dst4) { |
| SkScalar r; |
| for (int n = 0; n < count; ++n) { |
| SkScalar sx = src2[0]; |
| SkScalar sy = src2[1]; |
| r = mat[0][0] * sx + mat[1][0] * sy + mat[3][0]; |
| dst4[0] = float(r); |
| r = mat[0][1] * sx + mat[1][1] * sy + mat[3][1]; |
| dst4[1] = float(r); |
| r = mat[0][2] * sx + mat[1][2] * sy + mat[3][2]; |
| dst4[2] = float(r); |
| dst4[3] = 1; |
| src2 += 2; |
| dst4 += 4; |
| } |
| } |
| |
| static void map2_ad(const SkScalar mat[][4], const double* SK_RESTRICT src2, |
| int count, double* SK_RESTRICT dst4) { |
| for (int n = 0; n < count; ++n) { |
| double sx = src2[0]; |
| double sy = src2[1]; |
| dst4[0] = mat[0][0] * sx + mat[1][0] * sy + mat[3][0]; |
| dst4[1] = mat[0][1] * sx + mat[1][1] * sy + mat[3][1]; |
| dst4[2] = mat[0][2] * sx + mat[1][2] * sy + mat[3][2]; |
| dst4[3] = 1; |
| src2 += 2; |
| dst4 += 4; |
| } |
| } |
| |
| static void map2_pf(const SkScalar mat[][4], const float* SK_RESTRICT src2, |
| int count, float* SK_RESTRICT dst4) { |
| SkScalar r; |
| for (int n = 0; n < count; ++n) { |
| SkScalar sx = src2[0]; |
| SkScalar sy = src2[1]; |
| for (int i = 0; i < 4; i++) { |
| r = mat[0][i] * sx + mat[1][i] * sy + mat[3][i]; |
| dst4[i] = float(r); |
| } |
| src2 += 2; |
| dst4 += 4; |
| } |
| } |
| |
| static void map2_pd(const SkScalar mat[][4], const double* SK_RESTRICT src2, |
| int count, double* SK_RESTRICT dst4) { |
| for (int n = 0; n < count; ++n) { |
| double sx = src2[0]; |
| double sy = src2[1]; |
| for (int i = 0; i < 4; i++) { |
| dst4[i] = mat[0][i] * sx + mat[1][i] * sy + mat[3][i]; |
| } |
| src2 += 2; |
| dst4 += 4; |
| } |
| } |
| |
| void SkMatrix44::map2(const float src2[], int count, float dst4[]) const { |
| static const Map2Procf gProc[] = { |
| map2_if, map2_tf, map2_sf, map2_sf, map2_af, map2_af, map2_af, map2_af |
| }; |
| |
| TypeMask mask = this->getType(); |
| Map2Procf proc = (mask & kPerspective_Mask) ? map2_pf : gProc[mask]; |
| proc(fMat, src2, count, dst4); |
| } |
| |
| void SkMatrix44::map2(const double src2[], int count, double dst4[]) const { |
| static const Map2Procd gProc[] = { |
| map2_id, map2_td, map2_sd, map2_sd, map2_ad, map2_ad, map2_ad, map2_ad |
| }; |
| |
| TypeMask mask = this->getType(); |
| Map2Procd proc = (mask & kPerspective_Mask) ? map2_pd : gProc[mask]; |
| proc(fMat, src2, count, dst4); |
| } |
| |
| bool SkMatrix44::preserves2dAxisAlignment (SkScalar epsilon) const { |
| |
| // Can't check (mask & kPerspective_Mask) because Z isn't relevant here. |
| if (0 != perspX() || 0 != perspY()) return false; |
| |
| // A matrix with two non-zeroish values in any of the upper right |
| // rows or columns will skew. If only one value in each row or |
| // column is non-zeroish, we get a scale plus perhaps a 90-degree |
| // rotation. |
| int col0 = 0; |
| int col1 = 0; |
| int row0 = 0; |
| int row1 = 0; |
| |
| // Must test against epsilon, not 0, because we can get values |
| // around 6e-17 in the matrix that "should" be 0. |
| |
| if (SkScalarAbs(fMat[0][0]) > epsilon) { |
| col0++; |
| row0++; |
| } |
| if (SkScalarAbs(fMat[0][1]) > epsilon) { |
| col1++; |
| row0++; |
| } |
| if (SkScalarAbs(fMat[1][0]) > epsilon) { |
| col0++; |
| row1++; |
| } |
| if (SkScalarAbs(fMat[1][1]) > epsilon) { |
| col1++; |
| row1++; |
| } |
| if (col0 > 1 || col1 > 1 || row0 > 1 || row1 > 1) { |
| return false; |
| } |
| |
| return true; |
| } |
| |
| /////////////////////////////////////////////////////////////////////////////// |
| |
| void SkMatrix44::dump() const { |
| static const char* format = "|%g %g %g %g|\n" |
| "|%g %g %g %g|\n" |
| "|%g %g %g %g|\n" |
| "|%g %g %g %g|\n"; |
| SkDebugf(format, |
| fMat[0][0], fMat[1][0], fMat[2][0], fMat[3][0], |
| fMat[0][1], fMat[1][1], fMat[2][1], fMat[3][1], |
| fMat[0][2], fMat[1][2], fMat[2][2], fMat[3][2], |
| fMat[0][3], fMat[1][3], fMat[2][3], fMat[3][3]); |
| } |
| |
| /////////////////////////////////////////////////////////////////////////////// |
| |
| static void initFromMatrix(SkScalar dst[4][4], const SkMatrix& src) { |
| dst[0][0] = src[SkMatrix::kMScaleX]; |
| dst[1][0] = src[SkMatrix::kMSkewX]; |
| dst[2][0] = 0; |
| dst[3][0] = src[SkMatrix::kMTransX]; |
| dst[0][1] = src[SkMatrix::kMSkewY]; |
| dst[1][1] = src[SkMatrix::kMScaleY]; |
| dst[2][1] = 0; |
| dst[3][1] = src[SkMatrix::kMTransY]; |
| dst[0][2] = 0; |
| dst[1][2] = 0; |
| dst[2][2] = 1; |
| dst[3][2] = 0; |
| dst[0][3] = src[SkMatrix::kMPersp0]; |
| dst[1][3] = src[SkMatrix::kMPersp1]; |
| dst[2][3] = 0; |
| dst[3][3] = src[SkMatrix::kMPersp2]; |
| } |
| |
| SkMatrix44::SkMatrix44(const SkMatrix& src) { |
| this->operator=(src); |
| } |
| |
| SkMatrix44& SkMatrix44::operator=(const SkMatrix& src) { |
| initFromMatrix(fMat, src); |
| |
| if (src.isIdentity()) { |
| this->setTypeMask(kIdentity_Mask); |
| } else { |
| this->recomputeTypeMask(); |
| } |
| return *this; |
| } |
| |
| SkMatrix44::operator SkMatrix() const { |
| SkMatrix dst; |
| |
| dst[SkMatrix::kMScaleX] = fMat[0][0]; |
| dst[SkMatrix::kMSkewX] = fMat[1][0]; |
| dst[SkMatrix::kMTransX] = fMat[3][0]; |
| |
| dst[SkMatrix::kMSkewY] = fMat[0][1]; |
| dst[SkMatrix::kMScaleY] = fMat[1][1]; |
| dst[SkMatrix::kMTransY] = fMat[3][1]; |
| |
| dst[SkMatrix::kMPersp0] = fMat[0][3]; |
| dst[SkMatrix::kMPersp1] = fMat[1][3]; |
| dst[SkMatrix::kMPersp2] = fMat[3][3]; |
| |
| return dst; |
| } |
