/*
* 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 "SkMatrix44.h"
SkMatrix44::SkMatrix44() {
this->setIdentity();
}
SkMatrix44::SkMatrix44(const SkMatrix44& src) {
memcpy(this, &src, sizeof(src));
}
SkMatrix44::SkMatrix44(const SkMatrix44& a, const SkMatrix44& b) {
this->setConcat(a, b);
}
SkMScalar SkMatrix44::get(int row, int col) const {
SkASSERT(row <= 3 && row >= 0);
SkASSERT(col <= 3 && col >= 0);
return fMat[col][row];
}
void SkMatrix44::set(int row, int col, const SkMScalar& value) {
SkASSERT(row <= 3 && row >= 0);
SkASSERT(col <= 3 && col >= 0);
fMat[col][row] = value;
}
///////////////////////////////////////////////////////////////////////////////
void SkMatrix44::asColMajorf(float dst[]) const {
const SkMScalar* src = &fMat[0][0];
#ifdef SK_MSCALAR_IS_DOUBLE
for (int i = 0; i < 16; ++i) {
dst[i] = SkMScalarToFloat(src[i]);
}
#else
memcpy(dst, src, 16 * sizeof(float));
#endif
}
void SkMatrix44::asColMajord(double dst[]) const {
const SkMScalar* src = &fMat[0][0];
#ifdef SK_MSCALAR_IS_DOUBLE
memcpy(dst, src, 16 * sizeof(double));
#else
for (int i = 0; i < 16; ++i) {
dst[i] = SkMScalarToDouble(src[i]);
}
#endif
}
void SkMatrix44::asRowMajorf(float dst[]) const {
const SkMScalar* src = &fMat[0][0];
for (int i = 0; i < 4; ++i) {
dst[0] = SkMScalarToFloat(src[0]);
dst[4] = SkMScalarToFloat(src[1]);
dst[8] = SkMScalarToFloat(src[2]);
dst[12] = SkMScalarToFloat(src[3]);
src += 4;
dst += 1;
}
}
void SkMatrix44::asRowMajord(double dst[]) const {
const SkMScalar* src = &fMat[0][0];
for (int i = 0; i < 4; ++i) {
dst[0] = SkMScalarToDouble(src[0]);
dst[4] = SkMScalarToDouble(src[1]);
dst[8] = SkMScalarToDouble(src[2]);
dst[12] = SkMScalarToDouble(src[3]);
src += 4;
dst += 1;
}
}
///////////////////////////////////////////////////////////////////////////////
bool SkMatrix44::isIdentity() const {
static const SkMScalar sIdentityMat[4][4] = {
{ 1, 0, 0, 0 },
{ 0, 1, 0, 0 },
{ 0, 0, 1, 0 },
{ 0, 0, 0, 1 },
};
return !memcmp(fMat, sIdentityMat, sizeof(fMat));
}
///////////////////////////////////////////////////////////////////////////////
void SkMatrix44::setIdentity() {
sk_bzero(fMat, sizeof(fMat));
fMat[0][0] = fMat[1][1] = fMat[2][2] = fMat[3][3] = 1;
}
void SkMatrix44::set3x3(SkMScalar m00, SkMScalar m01, SkMScalar m02,
SkMScalar m10, SkMScalar m11, SkMScalar m12,
SkMScalar m20, SkMScalar m21, SkMScalar m22) {
sk_bzero(fMat, sizeof(fMat));
fMat[0][0] = m00; fMat[0][1] = m01; fMat[0][2] = m02; fMat[0][3] = 0;
fMat[1][0] = m10; fMat[1][1] = m11; fMat[1][2] = m12; fMat[1][3] = 0;
fMat[2][0] = m20; fMat[2][1] = m21; fMat[2][2] = m22; fMat[2][3] = 0;
fMat[3][0] = 0; fMat[3][1] = 0; fMat[3][2] = 0; fMat[3][3] = 1;
}
///////////////////////////////////////////////////////////////////////////////
void SkMatrix44::setTranslate(SkMScalar tx, SkMScalar ty, SkMScalar tz) {
this->setIdentity();
fMat[3][0] = tx;
fMat[3][1] = ty;
fMat[3][2] = tz;
fMat[3][3] = 1;
}
void SkMatrix44::preTranslate(SkMScalar dx, SkMScalar dy, SkMScalar dz) {
SkMatrix44 mat;
mat.setTranslate(dx, dy, dz);
this->preConcat(mat);
}
void SkMatrix44::postTranslate(SkMScalar dx, SkMScalar dy, SkMScalar dz) {
fMat[3][0] += dx;
fMat[3][1] += dy;
fMat[3][2] += dz;
}
///////////////////////////////////////////////////////////////////////////////
void SkMatrix44::setScale(SkMScalar sx, SkMScalar sy, SkMScalar sz) {
sk_bzero(fMat, sizeof(fMat));
fMat[0][0] = sx;
fMat[1][1] = sy;
fMat[2][2] = sz;
fMat[3][3] = 1;
}
void SkMatrix44::preScale(SkMScalar sx, SkMScalar sy, SkMScalar sz) {
SkMatrix44 tmp;
tmp.setScale(sx, sy, sz);
this->preConcat(tmp);
}
void SkMatrix44::postScale(SkMScalar sx, SkMScalar sy, SkMScalar sz) {
for (int i = 0; i < 4; i++) {
fMat[i][0] *= sx;
fMat[i][1] *= sy;
fMat[i][2] *= sz;
}
}
///////////////////////////////////////////////////////////////////////////////
void SkMatrix44::setRotateAbout(SkMScalar x, SkMScalar y, SkMScalar z,
SkMScalar radians) {
double len2 = x * x + y * y + z * z;
if (len2 != 1) {
if (len2 == 0) {
this->setIdentity();
return;
}
double scale = 1 / sqrt(len2);
x = SkDoubleToMScalar(x * scale);
y = SkDoubleToMScalar(y * scale);
z = SkDoubleToMScalar(z * scale);
}
this->setRotateAboutUnit(x, y, z, radians);
}
void SkMatrix44::setRotateAboutUnit(SkMScalar x, SkMScalar y, SkMScalar z,
SkMScalar 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(SkDoubleToMScalar(x * xC + c), // scale x
SkDoubleToMScalar(xyC + zs), // skew x
SkDoubleToMScalar(zxC - ys), // trans x
SkDoubleToMScalar(xyC - zs), // skew y
SkDoubleToMScalar(y * yC + c), // scale y
SkDoubleToMScalar(yzC + xs), // trans y
SkDoubleToMScalar(zxC + ys), // persp x
SkDoubleToMScalar(yzC - xs), // persp y
SkDoubleToMScalar(z * zC + c)); // persp 2
}
///////////////////////////////////////////////////////////////////////////////
void SkMatrix44::setConcat(const SkMatrix44& a, const SkMatrix44& b) {
SkMScalar result[4][4];
for (int i = 0; i < 4; i++) {
for (int j = 0; j < 4; j++) {
double value = 0;
for (int k = 0; k < 4; k++) {
value += SkMScalarToDouble(a.fMat[k][i]) * b.fMat[j][k];
}
result[j][i] = SkDoubleToMScalar(value);
}
}
memcpy(fMat, result, sizeof(result));
}
///////////////////////////////////////////////////////////////////////////////
static inline SkMScalar det2x2(double m00, double m01, double m10, double m11) {
return SkDoubleToMScalar(m00 * m11 - m10 * m01);
}
static inline double det3x3(double m00, double m01, double m02,
double m10, double m11, double m12,
double m20, double m21, double m22) {
return m00 * det2x2(m11, m12, m21, m22) -
m10 * det2x2(m01, m02, m21, m22) +
m20 * det2x2(m01, m02, m11, m12);
}
/** We always perform the calculation in doubles, to avoid prematurely losing
precision along the way. This relies on the compiler automatically
promoting our SkMScalar values to double (if needed).
*/
double SkMatrix44::determinant() const {
return fMat[0][0] * det3x3(fMat[1][1], fMat[1][2], fMat[1][3],
fMat[2][1], fMat[2][2], fMat[2][3],
fMat[3][1], fMat[3][2], fMat[3][3]) -
fMat[1][0] * det3x3(fMat[0][1], fMat[0][2], fMat[0][3],
fMat[2][1], fMat[2][2], fMat[2][3],
fMat[3][1], fMat[3][2], fMat[3][3]) +
fMat[2][0] * det3x3(fMat[0][1], fMat[0][2], fMat[0][3],
fMat[1][1], fMat[1][2], fMat[1][3],
fMat[3][1], fMat[3][2], fMat[3][3]) -
fMat[3][0] * det3x3(fMat[0][1], fMat[0][2], fMat[0][3],
fMat[1][1], fMat[1][2], fMat[1][3],
fMat[2][1], fMat[2][2], fMat[2][3]);
}
///////////////////////////////////////////////////////////////////////////////
// just picked a small value. not sure how to pick the "right" one
#define TOO_SMALL_FOR_DETERMINANT (1.e-8)
static inline double dabs(double x) {
if (x < 0) {
x = -x;
}
return x;
}
bool SkMatrix44::invert(SkMatrix44* inverse) const {
double det = this->determinant();
if (dabs(det) < TOO_SMALL_FOR_DETERMINANT) {
return false;
}
if (NULL == inverse) {
return true;
}
// we explicitly promote to doubles to keep the intermediate values in
// higher precision (assuming SkMScalar isn't already a double)
double m00 = fMat[0][0];
double m01 = fMat[0][1];
double m02 = fMat[0][2];
double m03 = fMat[0][3];
double m10 = fMat[1][0];
double m11 = fMat[1][1];
double m12 = fMat[1][2];
double m13 = fMat[1][3];
double m20 = fMat[2][0];
double m21 = fMat[2][1];
double m22 = fMat[2][2];
double m23 = fMat[2][3];
double m30 = fMat[3][0];
double m31 = fMat[3][1];
double m32 = fMat[3][2];
double m33 = fMat[3][3];
double tmp[4][4];
tmp[0][0] = m12*m23*m31 - m13*m22*m31 + m13*m21*m32 - m11*m23*m32 - m12*m21*m33 + m11*m22*m33;
tmp[0][1] = m03*m22*m31 - m02*m23*m31 - m03*m21*m32 + m01*m23*m32 + m02*m21*m33 - m01*m22*m33;
tmp[0][2] = m02*m13*m31 - m03*m12*m31 + m03*m11*m32 - m01*m13*m32 - m02*m11*m33 + m01*m12*m33;
tmp[0][3] = m03*m12*m21 - m02*m13*m21 - m03*m11*m22 + m01*m13*m22 + m02*m11*m23 - m01*m12*m23;
tmp[1][0] = m13*m22*m30 - m12*m23*m30 - m13*m20*m32 + m10*m23*m32 + m12*m20*m33 - m10*m22*m33;
tmp[1][1] = m02*m23*m30 - m03*m22*m30 + m03*m20*m32 - m00*m23*m32 - m02*m20*m33 + m00*m22*m33;
tmp[1][2] = m03*m12*m30 - m02*m13*m30 - m03*m10*m32 + m00*m13*m32 + m02*m10*m33 - m00*m12*m33;
tmp[1][3] = m02*m13*m20 - m03*m12*m20 + m03*m10*m22 - m00*m13*m22 - m02*m10*m23 + m00*m12*m23;
tmp[2][0] = m11*m23*m30 - m13*m21*m30 + m13*m20*m31 - m10*m23*m31 - m11*m20*m33 + m10*m21*m33;
tmp[2][1] = m03*m21*m30 - m01*m23*m30 - m03*m20*m31 + m00*m23*m31 + m01*m20*m33 - m00*m21*m33;
tmp[2][2] = m01*m13*m30 - m03*m11*m30 + m03*m10*m31 - m00*m13*m31 - m01*m10*m33 + m00*m11*m33;
tmp[2][3] = m03*m11*m20 - m01*m13*m20 - m03*m10*m21 + m00*m13*m21 + m01*m10*m23 - m00*m11*m23;
tmp[3][0] = m12*m21*m30 - m11*m22*m30 - m12*m20*m31 + m10*m22*m31 + m11*m20*m32 - m10*m21*m32;
tmp[3][1] = m01*m22*m30 - m02*m21*m30 + m02*m20*m31 - m00*m22*m31 - m01*m20*m32 + m00*m21*m32;
tmp[3][2] = m02*m11*m30 - m01*m12*m30 - m02*m10*m31 + m00*m12*m31 + m01*m10*m32 - m00*m11*m32;
tmp[3][3] = m01*m12*m20 - m02*m11*m20 + m02*m10*m21 - m00*m12*m21 - m01*m10*m22 + m00*m11*m22;
double invDet = 1.0 / det;
for (int i = 0; i < 4; i++) {
for (int j = 0; j < 4; j++) {
inverse->fMat[i][j] = SkDoubleToMScalar(tmp[i][j] * invDet);
}
}
return true;
}
///////////////////////////////////////////////////////////////////////////////
void SkMatrix44::map(const SkScalar src[4], SkScalar dst[4]) const {
SkScalar result[4];
for (int i = 0; i < 4; i++) {
SkMScalar value = 0;
for (int j = 0; j < 4; j++) {
value += fMat[j][i] * src[j];
}
result[i] = SkMScalarToScalar(value);
}
memcpy(dst, result, sizeof(result));
}
///////////////////////////////////////////////////////////////////////////////
void SkMatrix44::dump() const {
static const char* format =
"[%g %g %g %g][%g %g %g %g][%g %g %g %g][%g %g %g %g]\n";
#if 0
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]);
#else
SkDebugf(format,
fMat[0][0], fMat[0][1], fMat[0][2], fMat[0][3],
fMat[1][0], fMat[1][1], fMat[1][2], fMat[1][3],
fMat[2][0], fMat[2][1], fMat[2][2], fMat[2][3],
fMat[3][0], fMat[3][1], fMat[3][2], fMat[3][3]);
#endif
}
///////////////////////////////////////////////////////////////////////////////
static void initFromMatrix(SkMScalar dst[4][4], const SkMatrix& src) {
sk_bzero(dst, 16 * sizeof(SkMScalar));
dst[0][0] = SkScalarToMScalar(src[SkMatrix::kMScaleX]);
dst[1][0] = SkScalarToMScalar(src[SkMatrix::kMSkewX]);
dst[3][0] = SkScalarToMScalar(src[SkMatrix::kMTransX]);
dst[0][1] = SkScalarToMScalar(src[SkMatrix::kMSkewY]);
dst[1][1] = SkScalarToMScalar(src[SkMatrix::kMScaleY]);
dst[3][1] = SkScalarToMScalar(src[SkMatrix::kMTransY]);
dst[2][2] = dst[3][3] = 1;
}
SkMatrix44::SkMatrix44(const SkMatrix& src) {
initFromMatrix(fMat, src);
}
SkMatrix44& SkMatrix44::operator=(const SkMatrix& src) {
initFromMatrix(fMat, src);
return *this;
}
SkMatrix44::operator SkMatrix() const {
SkMatrix dst;
dst.reset(); // setup our perspective correctly for identity
dst[SkMatrix::kMScaleX] = SkMScalarToScalar(fMat[0][0]);
dst[SkMatrix::kMSkewX] = SkMScalarToScalar(fMat[1][0]);
dst[SkMatrix::kMTransX] = SkMScalarToScalar(fMat[3][0]);
dst[SkMatrix::kMSkewY] = SkMScalarToScalar(fMat[0][1]);
dst[SkMatrix::kMScaleY] = SkMScalarToScalar(fMat[1][1]);
dst[SkMatrix::kMTransY] = SkMScalarToScalar(fMat[3][1]);
return dst;
}