michael@0: /*
michael@0:  * Copyright 2011 Google Inc.
michael@0:  *
michael@0:  * Use of this source code is governed by a BSD-style license that can be
michael@0:  * found in the LICENSE file.
michael@0:  */
michael@0: 
michael@0: #include "SkMatrix44.h"
michael@0: 
michael@0: static inline bool eq4(const SkMScalar* SK_RESTRICT a,
michael@0:                       const SkMScalar* SK_RESTRICT b) {
michael@0:     return (a[0] == b[0]) & (a[1] == b[1]) & (a[2] == b[2]) & (a[3] == b[3]);
michael@0: }
michael@0: 
michael@0: bool SkMatrix44::operator==(const SkMatrix44& other) const {
michael@0:     if (this == &other) {
michael@0:         return true;
michael@0:     }
michael@0: 
michael@0:     if (this->isTriviallyIdentity() && other.isTriviallyIdentity()) {
michael@0:         return true;
michael@0:     }
michael@0: 
michael@0:     const SkMScalar* SK_RESTRICT a = &fMat[0][0];
michael@0:     const SkMScalar* SK_RESTRICT b = &other.fMat[0][0];
michael@0: 
michael@0: #if 0
michael@0:     for (int i = 0; i < 16; ++i) {
michael@0:         if (a[i] != b[i]) {
michael@0:             return false;
michael@0:         }
michael@0:     }
michael@0:     return true;
michael@0: #else
michael@0:     // to reduce branch instructions, we compare 4 at a time.
michael@0:     // see bench/Matrix44Bench.cpp for test.
michael@0:     if (!eq4(&a[0], &b[0])) {
michael@0:         return false;
michael@0:     }
michael@0:     if (!eq4(&a[4], &b[4])) {
michael@0:         return false;
michael@0:     }
michael@0:     if (!eq4(&a[8], &b[8])) {
michael@0:         return false;
michael@0:     }
michael@0:     return eq4(&a[12], &b[12]);
michael@0: #endif
michael@0: }
michael@0: 
michael@0: ///////////////////////////////////////////////////////////////////////////////
michael@0: 
michael@0: int SkMatrix44::computeTypeMask() const {
michael@0:     unsigned mask = 0;
michael@0: 
michael@0:     if (0 != perspX() || 0 != perspY() || 0 != perspZ() || 1 != fMat[3][3]) {
michael@0:         return kTranslate_Mask | kScale_Mask | kAffine_Mask | kPerspective_Mask;
michael@0:     }
michael@0: 
michael@0:     if (0 != transX() || 0 != transY() || 0 != transZ()) {
michael@0:         mask |= kTranslate_Mask;
michael@0:     }
michael@0: 
michael@0:     if (1 != scaleX() || 1 != scaleY() || 1 != scaleZ()) {
michael@0:         mask |= kScale_Mask;
michael@0:     }
michael@0: 
michael@0:     if (0 != fMat[1][0] || 0 != fMat[0][1] || 0 != fMat[0][2] ||
michael@0:         0 != fMat[2][0] || 0 != fMat[1][2] || 0 != fMat[2][1]) {
michael@0:             mask |= kAffine_Mask;
michael@0:     }
michael@0: 
michael@0:     return mask;
michael@0: }
michael@0: 
michael@0: ///////////////////////////////////////////////////////////////////////////////
michael@0: 
michael@0: void SkMatrix44::asColMajorf(float dst[]) const {
michael@0:     const SkMScalar* src = &fMat[0][0];
michael@0: #ifdef SK_MSCALAR_IS_DOUBLE
michael@0:     for (int i = 0; i < 16; ++i) {
michael@0:         dst[i] = SkMScalarToFloat(src[i]);
michael@0:     }
michael@0: #elif defined SK_MSCALAR_IS_FLOAT
michael@0:     memcpy(dst, src, 16 * sizeof(float));
michael@0: #endif
michael@0: }
michael@0: 
michael@0: void SkMatrix44::asColMajord(double dst[]) const {
michael@0:     const SkMScalar* src = &fMat[0][0];
michael@0: #ifdef SK_MSCALAR_IS_DOUBLE
michael@0:     memcpy(dst, src, 16 * sizeof(double));
michael@0: #elif defined SK_MSCALAR_IS_FLOAT
michael@0:     for (int i = 0; i < 16; ++i) {
michael@0:         dst[i] = SkMScalarToDouble(src[i]);
michael@0:     }
michael@0: #endif
michael@0: }
michael@0: 
michael@0: void SkMatrix44::asRowMajorf(float dst[]) const {
michael@0:     const SkMScalar* src = &fMat[0][0];
michael@0:     for (int i = 0; i < 4; ++i) {
michael@0:         dst[0] = SkMScalarToFloat(src[0]);
michael@0:         dst[4] = SkMScalarToFloat(src[1]);
michael@0:         dst[8] = SkMScalarToFloat(src[2]);
michael@0:         dst[12] = SkMScalarToFloat(src[3]);
michael@0:         src += 4;
michael@0:         dst += 1;
michael@0:     }
michael@0: }
michael@0: 
michael@0: void SkMatrix44::asRowMajord(double dst[]) const {
michael@0:     const SkMScalar* src = &fMat[0][0];
michael@0:     for (int i = 0; i < 4; ++i) {
michael@0:         dst[0] = SkMScalarToDouble(src[0]);
michael@0:         dst[4] = SkMScalarToDouble(src[1]);
michael@0:         dst[8] = SkMScalarToDouble(src[2]);
michael@0:         dst[12] = SkMScalarToDouble(src[3]);
michael@0:         src += 4;
michael@0:         dst += 1;
michael@0:     }
michael@0: }
michael@0: 
michael@0: void SkMatrix44::setColMajorf(const float src[]) {
michael@0:     SkMScalar* dst = &fMat[0][0];
michael@0: #ifdef SK_MSCALAR_IS_DOUBLE
michael@0:     for (int i = 0; i < 16; ++i) {
michael@0:         dst[i] = SkMScalarToFloat(src[i]);
michael@0:     }
michael@0: #elif defined SK_MSCALAR_IS_FLOAT
michael@0:     memcpy(dst, src, 16 * sizeof(float));
michael@0: #endif
michael@0: 
michael@0:     this->dirtyTypeMask();
michael@0: }
michael@0: 
michael@0: void SkMatrix44::setColMajord(const double src[]) {
michael@0:     SkMScalar* dst = &fMat[0][0];
michael@0: #ifdef SK_MSCALAR_IS_DOUBLE
michael@0:     memcpy(dst, src, 16 * sizeof(double));
michael@0: #elif defined SK_MSCALAR_IS_FLOAT
michael@0:     for (int i = 0; i < 16; ++i) {
michael@0:         dst[i] = SkDoubleToMScalar(src[i]);
michael@0:     }
michael@0: #endif
michael@0: 
michael@0:     this->dirtyTypeMask();
michael@0: }
michael@0: 
michael@0: void SkMatrix44::setRowMajorf(const float src[]) {
michael@0:     SkMScalar* dst = &fMat[0][0];
michael@0:     for (int i = 0; i < 4; ++i) {
michael@0:         dst[0] = SkMScalarToFloat(src[0]);
michael@0:         dst[4] = SkMScalarToFloat(src[1]);
michael@0:         dst[8] = SkMScalarToFloat(src[2]);
michael@0:         dst[12] = SkMScalarToFloat(src[3]);
michael@0:         src += 4;
michael@0:         dst += 1;
michael@0:     }
michael@0:     this->dirtyTypeMask();
michael@0: }
michael@0: 
michael@0: void SkMatrix44::setRowMajord(const double src[]) {
michael@0:     SkMScalar* dst = &fMat[0][0];
michael@0:     for (int i = 0; i < 4; ++i) {
michael@0:         dst[0] = SkDoubleToMScalar(src[0]);
michael@0:         dst[4] = SkDoubleToMScalar(src[1]);
michael@0:         dst[8] = SkDoubleToMScalar(src[2]);
michael@0:         dst[12] = SkDoubleToMScalar(src[3]);
michael@0:         src += 4;
michael@0:         dst += 1;
michael@0:     }
michael@0:     this->dirtyTypeMask();
michael@0: }
michael@0: 
michael@0: ///////////////////////////////////////////////////////////////////////////////
michael@0: 
michael@0: const SkMatrix44& SkMatrix44::I() {
michael@0:     static const SkMatrix44 gIdentity44(kIdentity_Constructor);
michael@0:     return gIdentity44;
michael@0: }
michael@0: 
michael@0: void SkMatrix44::setIdentity() {
michael@0:     fMat[0][0] = 1;
michael@0:     fMat[0][1] = 0;
michael@0:     fMat[0][2] = 0;
michael@0:     fMat[0][3] = 0;
michael@0:     fMat[1][0] = 0;
michael@0:     fMat[1][1] = 1;
michael@0:     fMat[1][2] = 0;
michael@0:     fMat[1][3] = 0;
michael@0:     fMat[2][0] = 0;
michael@0:     fMat[2][1] = 0;
michael@0:     fMat[2][2] = 1;
michael@0:     fMat[2][3] = 0;
michael@0:     fMat[3][0] = 0;
michael@0:     fMat[3][1] = 0;
michael@0:     fMat[3][2] = 0;
michael@0:     fMat[3][3] = 1;
michael@0:     this->setTypeMask(kIdentity_Mask);
michael@0: }
michael@0: 
michael@0: void SkMatrix44::set3x3(SkMScalar m00, SkMScalar m01, SkMScalar m02,
michael@0:                         SkMScalar m10, SkMScalar m11, SkMScalar m12,
michael@0:                         SkMScalar m20, SkMScalar m21, SkMScalar m22) {
michael@0:     fMat[0][0] = m00; fMat[0][1] = m01; fMat[0][2] = m02; fMat[0][3] = 0;
michael@0:     fMat[1][0] = m10; fMat[1][1] = m11; fMat[1][2] = m12; fMat[1][3] = 0;
michael@0:     fMat[2][0] = m20; fMat[2][1] = m21; fMat[2][2] = m22; fMat[2][3] = 0;
michael@0:     fMat[3][0] = 0;   fMat[3][1] = 0;   fMat[3][2] = 0;   fMat[3][3] = 1;
michael@0:     this->dirtyTypeMask();
michael@0: }
michael@0: 
michael@0: ///////////////////////////////////////////////////////////////////////////////
michael@0: 
michael@0: void SkMatrix44::setTranslate(SkMScalar dx, SkMScalar dy, SkMScalar dz) {
michael@0:     this->setIdentity();
michael@0: 
michael@0:     if (!dx && !dy && !dz) {
michael@0:         return;
michael@0:     }
michael@0: 
michael@0:     fMat[3][0] = dx;
michael@0:     fMat[3][1] = dy;
michael@0:     fMat[3][2] = dz;
michael@0:     this->setTypeMask(kTranslate_Mask);
michael@0: }
michael@0: 
michael@0: void SkMatrix44::preTranslate(SkMScalar dx, SkMScalar dy, SkMScalar dz) {
michael@0:     if (!dx && !dy && !dz) {
michael@0:         return;
michael@0:     }
michael@0: 
michael@0:     for (int i = 0; i < 4; ++i) {
michael@0:         fMat[3][i] = fMat[0][i] * dx + fMat[1][i] * dy + fMat[2][i] * dz + fMat[3][i];
michael@0:     }
michael@0:     this->dirtyTypeMask();
michael@0: }
michael@0: 
michael@0: void SkMatrix44::postTranslate(SkMScalar dx, SkMScalar dy, SkMScalar dz) {
michael@0:     if (!dx && !dy && !dz) {
michael@0:         return;
michael@0:     }
michael@0: 
michael@0:     if (this->getType() & kPerspective_Mask) {
michael@0:         for (int i = 0; i < 4; ++i) {
michael@0:             fMat[i][0] += fMat[i][3] * dx;
michael@0:             fMat[i][1] += fMat[i][3] * dy;
michael@0:             fMat[i][2] += fMat[i][3] * dz;
michael@0:         }
michael@0:     } else {
michael@0:         fMat[3][0] += dx;
michael@0:         fMat[3][1] += dy;
michael@0:         fMat[3][2] += dz;
michael@0:         this->dirtyTypeMask();
michael@0:     }
michael@0: }
michael@0: 
michael@0: ///////////////////////////////////////////////////////////////////////////////
michael@0: 
michael@0: void SkMatrix44::setScale(SkMScalar sx, SkMScalar sy, SkMScalar sz) {
michael@0:     this->setIdentity();
michael@0: 
michael@0:     if (1 == sx && 1 == sy && 1 == sz) {
michael@0:         return;
michael@0:     }
michael@0: 
michael@0:     fMat[0][0] = sx;
michael@0:     fMat[1][1] = sy;
michael@0:     fMat[2][2] = sz;
michael@0:     this->setTypeMask(kScale_Mask);
michael@0: }
michael@0: 
michael@0: void SkMatrix44::preScale(SkMScalar sx, SkMScalar sy, SkMScalar sz) {
michael@0:     if (1 == sx && 1 == sy && 1 == sz) {
michael@0:         return;
michael@0:     }
michael@0: 
michael@0:     // The implementation matrix * pureScale can be shortcut
michael@0:     // by knowing that pureScale components effectively scale
michael@0:     // the columns of the original matrix.
michael@0:     for (int i = 0; i < 4; i++) {
michael@0:         fMat[0][i] *= sx;
michael@0:         fMat[1][i] *= sy;
michael@0:         fMat[2][i] *= sz;
michael@0:     }
michael@0:     this->dirtyTypeMask();
michael@0: }
michael@0: 
michael@0: void SkMatrix44::postScale(SkMScalar sx, SkMScalar sy, SkMScalar sz) {
michael@0:     if (1 == sx && 1 == sy && 1 == sz) {
michael@0:         return;
michael@0:     }
michael@0: 
michael@0:     for (int i = 0; i < 4; i++) {
michael@0:         fMat[i][0] *= sx;
michael@0:         fMat[i][1] *= sy;
michael@0:         fMat[i][2] *= sz;
michael@0:     }
michael@0:     this->dirtyTypeMask();
michael@0: }
michael@0: 
michael@0: ///////////////////////////////////////////////////////////////////////////////
michael@0: 
michael@0: void SkMatrix44::setRotateAbout(SkMScalar x, SkMScalar y, SkMScalar z,
michael@0:                                 SkMScalar radians) {
michael@0:     double len2 = (double)x * x + (double)y * y + (double)z * z;
michael@0:     if (1 != len2) {
michael@0:         if (0 == len2) {
michael@0:             this->setIdentity();
michael@0:             return;
michael@0:         }
michael@0:         double scale = 1 / sqrt(len2);
michael@0:         x = SkDoubleToMScalar(x * scale);
michael@0:         y = SkDoubleToMScalar(y * scale);
michael@0:         z = SkDoubleToMScalar(z * scale);
michael@0:     }
michael@0:     this->setRotateAboutUnit(x, y, z, radians);
michael@0: }
michael@0: 
michael@0: void SkMatrix44::setRotateAboutUnit(SkMScalar x, SkMScalar y, SkMScalar z,
michael@0:                                     SkMScalar radians) {
michael@0:     double c = cos(radians);
michael@0:     double s = sin(radians);
michael@0:     double C = 1 - c;
michael@0:     double xs = x * s;
michael@0:     double ys = y * s;
michael@0:     double zs = z * s;
michael@0:     double xC = x * C;
michael@0:     double yC = y * C;
michael@0:     double zC = z * C;
michael@0:     double xyC = x * yC;
michael@0:     double yzC = y * zC;
michael@0:     double zxC = z * xC;
michael@0: 
michael@0:     // if you're looking at wikipedia, remember that we're column major.
michael@0:     this->set3x3(SkDoubleToMScalar(x * xC + c),     // scale x
michael@0:                  SkDoubleToMScalar(xyC + zs),       // skew x
michael@0:                  SkDoubleToMScalar(zxC - ys),       // trans x
michael@0: 
michael@0:                  SkDoubleToMScalar(xyC - zs),       // skew y
michael@0:                  SkDoubleToMScalar(y * yC + c),     // scale y
michael@0:                  SkDoubleToMScalar(yzC + xs),       // trans y
michael@0: 
michael@0:                  SkDoubleToMScalar(zxC + ys),       // persp x
michael@0:                  SkDoubleToMScalar(yzC - xs),       // persp y
michael@0:                  SkDoubleToMScalar(z * zC + c));    // persp 2
michael@0: }
michael@0: 
michael@0: ///////////////////////////////////////////////////////////////////////////////
michael@0: 
michael@0: static bool bits_isonly(int value, int mask) {
michael@0:     return 0 == (value & ~mask);
michael@0: }
michael@0: 
michael@0: void SkMatrix44::setConcat(const SkMatrix44& a, const SkMatrix44& b) {
michael@0:     const SkMatrix44::TypeMask a_mask = a.getType();
michael@0:     const SkMatrix44::TypeMask b_mask = b.getType();
michael@0: 
michael@0:     if (kIdentity_Mask == a_mask) {
michael@0:         *this = b;
michael@0:         return;
michael@0:     }
michael@0:     if (kIdentity_Mask == b_mask) {
michael@0:         *this = a;
michael@0:         return;
michael@0:     }
michael@0: 
michael@0:     bool useStorage = (this == &a || this == &b);
michael@0:     SkMScalar storage[16];
michael@0:     SkMScalar* result = useStorage ? storage : &fMat[0][0];
michael@0: 
michael@0:     // Both matrices are at most scale+translate
michael@0:     if (bits_isonly(a_mask | b_mask, kScale_Mask | kTranslate_Mask)) {
michael@0:         result[0] = a.fMat[0][0] * b.fMat[0][0];
michael@0:         result[1] = result[2] = result[3] = result[4] = 0;
michael@0:         result[5] = a.fMat[1][1] * b.fMat[1][1];
michael@0:         result[6] = result[7] = result[8] = result[9] = 0;
michael@0:         result[10] = a.fMat[2][2] * b.fMat[2][2];
michael@0:         result[11] = 0;
michael@0:         result[12] = a.fMat[0][0] * b.fMat[3][0] + a.fMat[3][0];
michael@0:         result[13] = a.fMat[1][1] * b.fMat[3][1] + a.fMat[3][1];
michael@0:         result[14] = a.fMat[2][2] * b.fMat[3][2] + a.fMat[3][2];
michael@0:         result[15] = 1;
michael@0:     } else {
michael@0:         for (int j = 0; j < 4; j++) {
michael@0:             for (int i = 0; i < 4; i++) {
michael@0:                 double value = 0;
michael@0:                 for (int k = 0; k < 4; k++) {
michael@0:                     value += SkMScalarToDouble(a.fMat[k][i]) * b.fMat[j][k];
michael@0:                 }
michael@0:                 *result++ = SkDoubleToMScalar(value);
michael@0:             }
michael@0:         }
michael@0:     }
michael@0: 
michael@0:     if (useStorage) {
michael@0:         memcpy(fMat, storage, sizeof(storage));
michael@0:     }
michael@0:     this->dirtyTypeMask();
michael@0: }
michael@0: 
michael@0: ///////////////////////////////////////////////////////////////////////////////
michael@0: 
michael@0: /** We always perform the calculation in doubles, to avoid prematurely losing
michael@0:     precision along the way. This relies on the compiler automatically
michael@0:     promoting our SkMScalar values to double (if needed).
michael@0:  */
michael@0: double SkMatrix44::determinant() const {
michael@0:     if (this->isIdentity()) {
michael@0:         return 1;
michael@0:     }
michael@0:     if (this->isScaleTranslate()) {
michael@0:         return fMat[0][0] * fMat[1][1] * fMat[2][2] * fMat[3][3];
michael@0:     }
michael@0: 
michael@0:     double a00 = fMat[0][0];
michael@0:     double a01 = fMat[0][1];
michael@0:     double a02 = fMat[0][2];
michael@0:     double a03 = fMat[0][3];
michael@0:     double a10 = fMat[1][0];
michael@0:     double a11 = fMat[1][1];
michael@0:     double a12 = fMat[1][2];
michael@0:     double a13 = fMat[1][3];
michael@0:     double a20 = fMat[2][0];
michael@0:     double a21 = fMat[2][1];
michael@0:     double a22 = fMat[2][2];
michael@0:     double a23 = fMat[2][3];
michael@0:     double a30 = fMat[3][0];
michael@0:     double a31 = fMat[3][1];
michael@0:     double a32 = fMat[3][2];
michael@0:     double a33 = fMat[3][3];
michael@0: 
michael@0:     double b00 = a00 * a11 - a01 * a10;
michael@0:     double b01 = a00 * a12 - a02 * a10;
michael@0:     double b02 = a00 * a13 - a03 * a10;
michael@0:     double b03 = a01 * a12 - a02 * a11;
michael@0:     double b04 = a01 * a13 - a03 * a11;
michael@0:     double b05 = a02 * a13 - a03 * a12;
michael@0:     double b06 = a20 * a31 - a21 * a30;
michael@0:     double b07 = a20 * a32 - a22 * a30;
michael@0:     double b08 = a20 * a33 - a23 * a30;
michael@0:     double b09 = a21 * a32 - a22 * a31;
michael@0:     double b10 = a21 * a33 - a23 * a31;
michael@0:     double b11 = a22 * a33 - a23 * a32;
michael@0: 
michael@0:     // Calculate the determinant
michael@0:     return b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06;
michael@0: }
michael@0: 
michael@0: ///////////////////////////////////////////////////////////////////////////////
michael@0: 
michael@0: bool SkMatrix44::invert(SkMatrix44* inverse) const {
michael@0:     if (this->isIdentity()) {
michael@0:         if (inverse) {
michael@0:             inverse->setIdentity();
michael@0:         }
michael@0:         return true;
michael@0:     }
michael@0: 
michael@0:     if (this->isTranslate()) {
michael@0:         if (inverse) {
michael@0:             inverse->setTranslate(-fMat[3][0], -fMat[3][1], -fMat[3][2]);
michael@0:         }
michael@0:         return true;
michael@0:     }
michael@0: 
michael@0:     if (this->isScaleTranslate()) {
michael@0:         if (0 == fMat[0][0] * fMat[1][1] * fMat[2][2]) {
michael@0:             return false;
michael@0:         }
michael@0: 
michael@0:         if (inverse) {
michael@0:             double invXScale = 1 / fMat[0][0];
michael@0:             double invYScale = 1 / fMat[1][1];
michael@0:             double invZScale = 1 / fMat[2][2];
michael@0: 
michael@0:             inverse->fMat[0][0] = invXScale;
michael@0:             inverse->fMat[0][1] = 0;
michael@0:             inverse->fMat[0][2] = 0;
michael@0:             inverse->fMat[0][3] = 0;
michael@0: 
michael@0:             inverse->fMat[1][0] = 0;
michael@0:             inverse->fMat[1][1] = invYScale;
michael@0:             inverse->fMat[1][2] = 0;
michael@0:             inverse->fMat[1][3] = 0;
michael@0: 
michael@0:             inverse->fMat[2][0] = 0;
michael@0:             inverse->fMat[2][1] = 0;
michael@0:             inverse->fMat[2][2] = invZScale;
michael@0:             inverse->fMat[2][3] = 0;
michael@0: 
michael@0:             inverse->fMat[3][0] = -fMat[3][0] * invXScale;
michael@0:             inverse->fMat[3][1] = -fMat[3][1] * invYScale;
michael@0:             inverse->fMat[3][2] = -fMat[3][2] * invZScale;
michael@0:             inverse->fMat[3][3] = 1;
michael@0: 
michael@0:             inverse->setTypeMask(this->getType());
michael@0:         }
michael@0: 
michael@0:         return true;
michael@0:     }
michael@0: 
michael@0:     double a00 = fMat[0][0];
michael@0:     double a01 = fMat[0][1];
michael@0:     double a02 = fMat[0][2];
michael@0:     double a03 = fMat[0][3];
michael@0:     double a10 = fMat[1][0];
michael@0:     double a11 = fMat[1][1];
michael@0:     double a12 = fMat[1][2];
michael@0:     double a13 = fMat[1][3];
michael@0:     double a20 = fMat[2][0];
michael@0:     double a21 = fMat[2][1];
michael@0:     double a22 = fMat[2][2];
michael@0:     double a23 = fMat[2][3];
michael@0:     double a30 = fMat[3][0];
michael@0:     double a31 = fMat[3][1];
michael@0:     double a32 = fMat[3][2];
michael@0:     double a33 = fMat[3][3];
michael@0: 
michael@0:     if (!(this->getType() & kPerspective_Mask)) {
michael@0:         // If we know the matrix has no perspective, then the perspective
michael@0:         // component is (0, 0, 0, 1). We can use this information to save a lot
michael@0:         // of arithmetic that would otherwise be spent to compute the inverse
michael@0:         // of a general matrix.
michael@0: 
michael@0:         SkASSERT(a03 == 0);
michael@0:         SkASSERT(a13 == 0);
michael@0:         SkASSERT(a23 == 0);
michael@0:         SkASSERT(a33 == 1);
michael@0: 
michael@0:         double b00 = a00 * a11 - a01 * a10;
michael@0:         double b01 = a00 * a12 - a02 * a10;
michael@0:         double b03 = a01 * a12 - a02 * a11;
michael@0:         double b06 = a20 * a31 - a21 * a30;
michael@0:         double b07 = a20 * a32 - a22 * a30;
michael@0:         double b08 = a20;
michael@0:         double b09 = a21 * a32 - a22 * a31;
michael@0:         double b10 = a21;
michael@0:         double b11 = a22;
michael@0: 
michael@0:         // Calculate the determinant
michael@0:         double det = b00 * b11 - b01 * b10 + b03 * b08;
michael@0: 
michael@0:         double invdet = 1.0 / det;
michael@0:         // If det is zero, we want to return false. However, we also want to return false
michael@0:         // if 1/det overflows to infinity (i.e. det is denormalized). Both of these are
michael@0:         // handled by checking that 1/det is finite.
michael@0:         if (!sk_float_isfinite(invdet)) {
michael@0:             return false;
michael@0:         }
michael@0:         if (NULL == inverse) {
michael@0:             return true;
michael@0:         }
michael@0: 
michael@0:         b00 *= invdet;
michael@0:         b01 *= invdet;
michael@0:         b03 *= invdet;
michael@0:         b06 *= invdet;
michael@0:         b07 *= invdet;
michael@0:         b08 *= invdet;
michael@0:         b09 *= invdet;
michael@0:         b10 *= invdet;
michael@0:         b11 *= invdet;
michael@0: 
michael@0:         inverse->fMat[0][0] = SkDoubleToMScalar(a11 * b11 - a12 * b10);
michael@0:         inverse->fMat[0][1] = SkDoubleToMScalar(a02 * b10 - a01 * b11);
michael@0:         inverse->fMat[0][2] = SkDoubleToMScalar(b03);
michael@0:         inverse->fMat[0][3] = 0;
michael@0:         inverse->fMat[1][0] = SkDoubleToMScalar(a12 * b08 - a10 * b11);
michael@0:         inverse->fMat[1][1] = SkDoubleToMScalar(a00 * b11 - a02 * b08);
michael@0:         inverse->fMat[1][2] = SkDoubleToMScalar(-b01);
michael@0:         inverse->fMat[1][3] = 0;
michael@0:         inverse->fMat[2][0] = SkDoubleToMScalar(a10 * b10 - a11 * b08);
michael@0:         inverse->fMat[2][1] = SkDoubleToMScalar(a01 * b08 - a00 * b10);
michael@0:         inverse->fMat[2][2] = SkDoubleToMScalar(b00);
michael@0:         inverse->fMat[2][3] = 0;
michael@0:         inverse->fMat[3][0] = SkDoubleToMScalar(a11 * b07 - a10 * b09 - a12 * b06);
michael@0:         inverse->fMat[3][1] = SkDoubleToMScalar(a00 * b09 - a01 * b07 + a02 * b06);
michael@0:         inverse->fMat[3][2] = SkDoubleToMScalar(a31 * b01 - a30 * b03 - a32 * b00);
michael@0:         inverse->fMat[3][3] = 1;
michael@0: 
michael@0:         inverse->setTypeMask(this->getType());
michael@0:         return true;
michael@0:     }
michael@0: 
michael@0:     double b00 = a00 * a11 - a01 * a10;
michael@0:     double b01 = a00 * a12 - a02 * a10;
michael@0:     double b02 = a00 * a13 - a03 * a10;
michael@0:     double b03 = a01 * a12 - a02 * a11;
michael@0:     double b04 = a01 * a13 - a03 * a11;
michael@0:     double b05 = a02 * a13 - a03 * a12;
michael@0:     double b06 = a20 * a31 - a21 * a30;
michael@0:     double b07 = a20 * a32 - a22 * a30;
michael@0:     double b08 = a20 * a33 - a23 * a30;
michael@0:     double b09 = a21 * a32 - a22 * a31;
michael@0:     double b10 = a21 * a33 - a23 * a31;
michael@0:     double b11 = a22 * a33 - a23 * a32;
michael@0: 
michael@0:     // Calculate the determinant
michael@0:     double det = b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06;
michael@0: 
michael@0:     double invdet = 1.0 / det;
michael@0:     // If det is zero, we want to return false. However, we also want to return false
michael@0:     // if 1/det overflows to infinity (i.e. det is denormalized). Both of these are
michael@0:     // handled by checking that 1/det is finite.
michael@0:     if (!sk_float_isfinite(invdet)) {
michael@0:         return false;
michael@0:     }
michael@0:     if (NULL == inverse) {
michael@0:         return true;
michael@0:     }
michael@0: 
michael@0:     b00 *= invdet;
michael@0:     b01 *= invdet;
michael@0:     b02 *= invdet;
michael@0:     b03 *= invdet;
michael@0:     b04 *= invdet;
michael@0:     b05 *= invdet;
michael@0:     b06 *= invdet;
michael@0:     b07 *= invdet;
michael@0:     b08 *= invdet;
michael@0:     b09 *= invdet;
michael@0:     b10 *= invdet;
michael@0:     b11 *= invdet;
michael@0: 
michael@0:     inverse->fMat[0][0] = SkDoubleToMScalar(a11 * b11 - a12 * b10 + a13 * b09);
michael@0:     inverse->fMat[0][1] = SkDoubleToMScalar(a02 * b10 - a01 * b11 - a03 * b09);
michael@0:     inverse->fMat[0][2] = SkDoubleToMScalar(a31 * b05 - a32 * b04 + a33 * b03);
michael@0:     inverse->fMat[0][3] = SkDoubleToMScalar(a22 * b04 - a21 * b05 - a23 * b03);
michael@0:     inverse->fMat[1][0] = SkDoubleToMScalar(a12 * b08 - a10 * b11 - a13 * b07);
michael@0:     inverse->fMat[1][1] = SkDoubleToMScalar(a00 * b11 - a02 * b08 + a03 * b07);
michael@0:     inverse->fMat[1][2] = SkDoubleToMScalar(a32 * b02 - a30 * b05 - a33 * b01);
michael@0:     inverse->fMat[1][3] = SkDoubleToMScalar(a20 * b05 - a22 * b02 + a23 * b01);
michael@0:     inverse->fMat[2][0] = SkDoubleToMScalar(a10 * b10 - a11 * b08 + a13 * b06);
michael@0:     inverse->fMat[2][1] = SkDoubleToMScalar(a01 * b08 - a00 * b10 - a03 * b06);
michael@0:     inverse->fMat[2][2] = SkDoubleToMScalar(a30 * b04 - a31 * b02 + a33 * b00);
michael@0:     inverse->fMat[2][3] = SkDoubleToMScalar(a21 * b02 - a20 * b04 - a23 * b00);
michael@0:     inverse->fMat[3][0] = SkDoubleToMScalar(a11 * b07 - a10 * b09 - a12 * b06);
michael@0:     inverse->fMat[3][1] = SkDoubleToMScalar(a00 * b09 - a01 * b07 + a02 * b06);
michael@0:     inverse->fMat[3][2] = SkDoubleToMScalar(a31 * b01 - a30 * b03 - a32 * b00);
michael@0:     inverse->fMat[3][3] = SkDoubleToMScalar(a20 * b03 - a21 * b01 + a22 * b00);
michael@0:     inverse->dirtyTypeMask();
michael@0: 
michael@0:     return true;
michael@0: }
michael@0: 
michael@0: ///////////////////////////////////////////////////////////////////////////////
michael@0: 
michael@0: void SkMatrix44::transpose() {
michael@0:     SkTSwap(fMat[0][1], fMat[1][0]);
michael@0:     SkTSwap(fMat[0][2], fMat[2][0]);
michael@0:     SkTSwap(fMat[0][3], fMat[3][0]);
michael@0:     SkTSwap(fMat[1][2], fMat[2][1]);
michael@0:     SkTSwap(fMat[1][3], fMat[3][1]);
michael@0:     SkTSwap(fMat[2][3], fMat[3][2]);
michael@0: 
michael@0:     if (!this->isTriviallyIdentity()) {
michael@0:         this->dirtyTypeMask();
michael@0:     }
michael@0: }
michael@0: 
michael@0: ///////////////////////////////////////////////////////////////////////////////
michael@0: 
michael@0: void SkMatrix44::mapScalars(const SkScalar src[4], SkScalar dst[4]) const {
michael@0:     SkScalar storage[4];
michael@0:     SkScalar* result = (src == dst) ? storage : dst;
michael@0: 
michael@0:     for (int i = 0; i < 4; i++) {
michael@0:         SkMScalar value = 0;
michael@0:         for (int j = 0; j < 4; j++) {
michael@0:             value += fMat[j][i] * src[j];
michael@0:         }
michael@0:         result[i] = SkMScalarToScalar(value);
michael@0:     }
michael@0: 
michael@0:     if (storage == result) {
michael@0:         memcpy(dst, storage, sizeof(storage));
michael@0:     }
michael@0: }
michael@0: 
michael@0: #ifdef SK_MSCALAR_IS_DOUBLE
michael@0: 
michael@0: void SkMatrix44::mapMScalars(const SkMScalar src[4], SkMScalar dst[4]) const {
michael@0:     SkMScalar storage[4];
michael@0:     SkMScalar* result = (src == dst) ? storage : dst;
michael@0: 
michael@0:     for (int i = 0; i < 4; i++) {
michael@0:         SkMScalar value = 0;
michael@0:         for (int j = 0; j < 4; j++) {
michael@0:             value += fMat[j][i] * src[j];
michael@0:         }
michael@0:         result[i] = value;
michael@0:     }
michael@0: 
michael@0:     if (storage == result) {
michael@0:         memcpy(dst, storage, sizeof(storage));
michael@0:     }
michael@0: }
michael@0: 
michael@0: #endif
michael@0: 
michael@0: typedef void (*Map2Procf)(const SkMScalar mat[][4], const float src2[], int count, float dst4[]);
michael@0: typedef void (*Map2Procd)(const SkMScalar mat[][4], const double src2[], int count, double dst4[]);
michael@0: 
michael@0: static void map2_if(const SkMScalar mat[][4], const float* SK_RESTRICT src2,
michael@0:                     int count, float* SK_RESTRICT dst4) {
michael@0:     for (int i = 0; i < count; ++i) {
michael@0:         dst4[0] = src2[0];
michael@0:         dst4[1] = src2[1];
michael@0:         dst4[2] = 0;
michael@0:         dst4[3] = 1;
michael@0:         src2 += 2;
michael@0:         dst4 += 4;
michael@0:     }
michael@0: }
michael@0: 
michael@0: static void map2_id(const SkMScalar mat[][4], const double* SK_RESTRICT src2,
michael@0:                     int count, double* SK_RESTRICT dst4) {
michael@0:     for (int i = 0; i < count; ++i) {
michael@0:         dst4[0] = src2[0];
michael@0:         dst4[1] = src2[1];
michael@0:         dst4[2] = 0;
michael@0:         dst4[3] = 1;
michael@0:         src2 += 2;
michael@0:         dst4 += 4;
michael@0:     }
michael@0: }
michael@0: 
michael@0: static void map2_tf(const SkMScalar mat[][4], const float* SK_RESTRICT src2,
michael@0:                     int count, float* SK_RESTRICT dst4) {
michael@0:     const float mat30 = SkMScalarToFloat(mat[3][0]);
michael@0:     const float mat31 = SkMScalarToFloat(mat[3][1]);
michael@0:     const float mat32 = SkMScalarToFloat(mat[3][2]);
michael@0:     for (int n = 0; n < count; ++n) {
michael@0:         dst4[0] = src2[0] + mat30;
michael@0:         dst4[1] = src2[1] + mat31;
michael@0:         dst4[2] = mat32;
michael@0:         dst4[3] = 1;
michael@0:         src2 += 2;
michael@0:         dst4 += 4;
michael@0:     }
michael@0: }
michael@0: 
michael@0: static void map2_td(const SkMScalar mat[][4], const double* SK_RESTRICT src2,
michael@0:                     int count, double* SK_RESTRICT dst4) {
michael@0:     for (int n = 0; n < count; ++n) {
michael@0:         dst4[0] = src2[0] + mat[3][0];
michael@0:         dst4[1] = src2[1] + mat[3][1];
michael@0:         dst4[2] = mat[3][2];
michael@0:         dst4[3] = 1;
michael@0:         src2 += 2;
michael@0:         dst4 += 4;
michael@0:     }
michael@0: }
michael@0: 
michael@0: static void map2_sf(const SkMScalar mat[][4], const float* SK_RESTRICT src2,
michael@0:                     int count, float* SK_RESTRICT dst4) {
michael@0:     const float mat32 = SkMScalarToFloat(mat[3][2]);
michael@0:     for (int n = 0; n < count; ++n) {
michael@0:         dst4[0] = SkMScalarToFloat(mat[0][0] * src2[0] + mat[3][0]);
michael@0:         dst4[1] = SkMScalarToFloat(mat[1][1] * src2[1] + mat[3][1]);
michael@0:         dst4[2] = mat32;
michael@0:         dst4[3] = 1;
michael@0:         src2 += 2;
michael@0:         dst4 += 4;
michael@0:     }
michael@0: }
michael@0: 
michael@0: static void map2_sd(const SkMScalar mat[][4], const double* SK_RESTRICT src2,
michael@0:                     int count, double* SK_RESTRICT dst4) {
michael@0:     for (int n = 0; n < count; ++n) {
michael@0:         dst4[0] = mat[0][0] * src2[0] + mat[3][0];
michael@0:         dst4[1] = mat[1][1] * src2[1] + mat[3][1];
michael@0:         dst4[2] = mat[3][2];
michael@0:         dst4[3] = 1;
michael@0:         src2 += 2;
michael@0:         dst4 += 4;
michael@0:     }
michael@0: }
michael@0: 
michael@0: static void map2_af(const SkMScalar mat[][4], const float* SK_RESTRICT src2,
michael@0:                     int count, float* SK_RESTRICT dst4) {
michael@0:     SkMScalar r;
michael@0:     for (int n = 0; n < count; ++n) {
michael@0:         SkMScalar sx = SkFloatToMScalar(src2[0]);
michael@0:         SkMScalar sy = SkFloatToMScalar(src2[1]);
michael@0:         r = mat[0][0] * sx + mat[1][0] * sy + mat[3][0];
michael@0:         dst4[0] = SkMScalarToFloat(r);
michael@0:         r = mat[0][1] * sx + mat[1][1] * sy + mat[3][1];
michael@0:         dst4[1] = SkMScalarToFloat(r);
michael@0:         r = mat[0][2] * sx + mat[1][2] * sy + mat[3][2];
michael@0:         dst4[2] = SkMScalarToFloat(r);
michael@0:         dst4[3] = 1;
michael@0:         src2 += 2;
michael@0:         dst4 += 4;
michael@0:     }
michael@0: }
michael@0: 
michael@0: static void map2_ad(const SkMScalar mat[][4], const double* SK_RESTRICT src2,
michael@0:                     int count, double* SK_RESTRICT dst4) {
michael@0:     for (int n = 0; n < count; ++n) {
michael@0:         double sx = src2[0];
michael@0:         double sy = src2[1];
michael@0:         dst4[0] = mat[0][0] * sx + mat[1][0] * sy + mat[3][0];
michael@0:         dst4[1] = mat[0][1] * sx + mat[1][1] * sy + mat[3][1];
michael@0:         dst4[2] = mat[0][2] * sx + mat[1][2] * sy + mat[3][2];
michael@0:         dst4[3] = 1;
michael@0:         src2 += 2;
michael@0:         dst4 += 4;
michael@0:     }
michael@0: }
michael@0: 
michael@0: static void map2_pf(const SkMScalar mat[][4], const float* SK_RESTRICT src2,
michael@0:                     int count, float* SK_RESTRICT dst4) {
michael@0:     SkMScalar r;
michael@0:     for (int n = 0; n < count; ++n) {
michael@0:         SkMScalar sx = SkFloatToMScalar(src2[0]);
michael@0:         SkMScalar sy = SkFloatToMScalar(src2[1]);
michael@0:         for (int i = 0; i < 4; i++) {
michael@0:             r = mat[0][i] * sx + mat[1][i] * sy + mat[3][i];
michael@0:             dst4[i] = SkMScalarToFloat(r);
michael@0:         }
michael@0:         src2 += 2;
michael@0:         dst4 += 4;
michael@0:     }
michael@0: }
michael@0: 
michael@0: static void map2_pd(const SkMScalar mat[][4], const double* SK_RESTRICT src2,
michael@0:                     int count, double* SK_RESTRICT dst4) {
michael@0:     for (int n = 0; n < count; ++n) {
michael@0:         double sx = src2[0];
michael@0:         double sy = src2[1];
michael@0:         for (int i = 0; i < 4; i++) {
michael@0:             dst4[i] = mat[0][i] * sx + mat[1][i] * sy + mat[3][i];
michael@0:         }
michael@0:         src2 += 2;
michael@0:         dst4 += 4;
michael@0:     }
michael@0: }
michael@0: 
michael@0: void SkMatrix44::map2(const float src2[], int count, float dst4[]) const {
michael@0:     static const Map2Procf gProc[] = {
michael@0:         map2_if, map2_tf, map2_sf, map2_sf, map2_af, map2_af, map2_af, map2_af
michael@0:     };
michael@0: 
michael@0:     TypeMask mask = this->getType();
michael@0:     Map2Procf proc = (mask & kPerspective_Mask) ? map2_pf : gProc[mask];
michael@0:     proc(fMat, src2, count, dst4);
michael@0: }
michael@0: 
michael@0: void SkMatrix44::map2(const double src2[], int count, double dst4[]) const {
michael@0:     static const Map2Procd gProc[] = {
michael@0:         map2_id, map2_td, map2_sd, map2_sd, map2_ad, map2_ad, map2_ad, map2_ad
michael@0:     };
michael@0: 
michael@0:     TypeMask mask = this->getType();
michael@0:     Map2Procd proc = (mask & kPerspective_Mask) ? map2_pd : gProc[mask];
michael@0:     proc(fMat, src2, count, dst4);
michael@0: }
michael@0: 
michael@0: ///////////////////////////////////////////////////////////////////////////////
michael@0: 
michael@0: void SkMatrix44::dump() const {
michael@0:     static const char* format =
michael@0:         "[%g %g %g %g][%g %g %g %g][%g %g %g %g][%g %g %g %g]\n";
michael@0: #if 0
michael@0:     SkDebugf(format,
michael@0:              fMat[0][0], fMat[1][0], fMat[2][0], fMat[3][0],
michael@0:              fMat[0][1], fMat[1][1], fMat[2][1], fMat[3][1],
michael@0:              fMat[0][2], fMat[1][2], fMat[2][2], fMat[3][2],
michael@0:              fMat[0][3], fMat[1][3], fMat[2][3], fMat[3][3]);
michael@0: #else
michael@0:     SkDebugf(format,
michael@0:              fMat[0][0], fMat[0][1], fMat[0][2], fMat[0][3],
michael@0:              fMat[1][0], fMat[1][1], fMat[1][2], fMat[1][3],
michael@0:              fMat[2][0], fMat[2][1], fMat[2][2], fMat[2][3],
michael@0:              fMat[3][0], fMat[3][1], fMat[3][2], fMat[3][3]);
michael@0: #endif
michael@0: }
michael@0: 
michael@0: ///////////////////////////////////////////////////////////////////////////////
michael@0: 
michael@0: static void initFromMatrix(SkMScalar dst[4][4], const SkMatrix& src) {
michael@0:     dst[0][0] = SkScalarToMScalar(src[SkMatrix::kMScaleX]);
michael@0:     dst[1][0] = SkScalarToMScalar(src[SkMatrix::kMSkewX]);
michael@0:     dst[2][0] = 0;
michael@0:     dst[3][0] = SkScalarToMScalar(src[SkMatrix::kMTransX]);
michael@0:     dst[0][1] = SkScalarToMScalar(src[SkMatrix::kMSkewY]);
michael@0:     dst[1][1] = SkScalarToMScalar(src[SkMatrix::kMScaleY]);
michael@0:     dst[2][1] = 0;
michael@0:     dst[3][1] = SkScalarToMScalar(src[SkMatrix::kMTransY]);
michael@0:     dst[0][2] = 0;
michael@0:     dst[1][2] = 0;
michael@0:     dst[2][2] = 1;
michael@0:     dst[3][2] = 0;
michael@0:     dst[0][3] = SkScalarToMScalar(src[SkMatrix::kMPersp0]);
michael@0:     dst[1][3] = SkScalarToMScalar(src[SkMatrix::kMPersp1]);
michael@0:     dst[2][3] = 0;
michael@0:     dst[3][3] = SkScalarToMScalar(src[SkMatrix::kMPersp2]);
michael@0: }
michael@0: 
michael@0: SkMatrix44::SkMatrix44(const SkMatrix& src) {
michael@0:     initFromMatrix(fMat, src);
michael@0: }
michael@0: 
michael@0: SkMatrix44& SkMatrix44::operator=(const SkMatrix& src) {
michael@0:     initFromMatrix(fMat, src);
michael@0: 
michael@0:     if (src.isIdentity()) {
michael@0:         this->setTypeMask(kIdentity_Mask);
michael@0:     } else {
michael@0:         this->dirtyTypeMask();
michael@0:     }
michael@0:     return *this;
michael@0: }
michael@0: 
michael@0: SkMatrix44::operator SkMatrix() const {
michael@0:     SkMatrix dst;
michael@0: 
michael@0:     dst[SkMatrix::kMScaleX]  = SkMScalarToScalar(fMat[0][0]);
michael@0:     dst[SkMatrix::kMSkewX]  = SkMScalarToScalar(fMat[1][0]);
michael@0:     dst[SkMatrix::kMTransX] = SkMScalarToScalar(fMat[3][0]);
michael@0: 
michael@0:     dst[SkMatrix::kMSkewY]  = SkMScalarToScalar(fMat[0][1]);
michael@0:     dst[SkMatrix::kMScaleY] = SkMScalarToScalar(fMat[1][1]);
michael@0:     dst[SkMatrix::kMTransY] = SkMScalarToScalar(fMat[3][1]);
michael@0: 
michael@0:     dst[SkMatrix::kMPersp0] = SkMScalarToScalar(fMat[0][3]);
michael@0:     dst[SkMatrix::kMPersp1] = SkMScalarToScalar(fMat[1][3]);
michael@0:     dst[SkMatrix::kMPersp2] = SkMScalarToScalar(fMat[3][3]);
michael@0: 
michael@0:     return dst;
michael@0: }