| |
| /* |
| * 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; |
| } |
