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/*
* 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 "skia/ext/skia_matrix_44.h"
#include <type_traits>
#include <utility>
namespace skia {
// Copying Matrix44 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<Matrix44>::value,
"Matrix44 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 Matrix44::operator==(const Matrix44& 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 Matrix44::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 Matrix44::asColMajorf(float dst[]) const {
const SkScalar* src = &fMat[0][0];
for (int i = 0; i < 16; ++i) {
dst[i] = src[i];
}
}
void Matrix44::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 Matrix44::asColMajord(double dst[]) const {
const SkScalar* src = &fMat[0][0];
for (int i = 0; i < 16; ++i) {
dst[i] = src[i];
}
}
void Matrix44::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 Matrix44::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 Matrix44::setColMajorf(const float src[]) {
SkScalar* dst = &fMat[0][0];
for (int i = 0; i < 16; ++i) {
dst[i] = src[i];
}
this->recomputeTypeMask();
}
void Matrix44::setColMajord(const double src[]) {
SkScalar* dst = &fMat[0][0];
for (int i = 0; i < 16; ++i) {
dst[i] = SkScalar(src[i]);
}
this->recomputeTypeMask();
}
void Matrix44::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 Matrix44::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 Matrix44& Matrix44::I() {
static constexpr Matrix44 gIdentity44(kIdentity_Constructor);
return gIdentity44;
}
void Matrix44::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 Matrix44::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 Matrix44::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 Matrix44::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 Matrix44::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();
}
///////////////////////////////////////////////////////////////////////////////
Matrix44& Matrix44::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;
}
Matrix44& Matrix44::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;
}
Matrix44& Matrix44::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;
}
///////////////////////////////////////////////////////////////////////////////
Matrix44& Matrix44::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;
}
Matrix44& Matrix44::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;
}
Matrix44& Matrix44::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 Matrix44::setRotateAbout(SkScalar x,
SkScalar y,
SkScalar z,
SkScalar radians) {
double len2 = static_cast<double>(x) * x + static_cast<double>(y) * y +
static_cast<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 Matrix44::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 Matrix44::setConcat(const Matrix44& a, const Matrix44& b) {
const Matrix44::TypeMask a_mask = a.getType();
const Matrix44::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 Matrix44::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 Matrix44& 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 Matrix44::invert(Matrix44* 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;
}
Matrix44 tmp;
// Use storage if it's available and distinct from this matrix.
Matrix44* 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 Matrix44::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 Matrix44::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 Matrix44::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 Matrix44::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 Matrix44::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 Matrix44::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];
}
Matrix44::Matrix44(const SkMatrix& src) {
this->operator=(src);
}
Matrix44& Matrix44::operator=(const SkMatrix& src) {
initFromMatrix(fMat, src);
if (src.isIdentity()) {
this->setTypeMask(kIdentity_Mask);
} else {
this->recomputeTypeMask();
}
return *this;
}
Matrix44::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;
}
} // namespace skia