| /* | |
| * Copyright 2006 The Android Open Source Project | |
| * | |
| * Use of this source code is governed by a BSD-style license that can be | |
| * found in the LICENSE file. | |
| */ | |
| #include "SkMatrix.h" | |
| #include "SkFloatBits.h" | |
| #include "SkMathPriv.h" | |
| #include "SkMatrixPriv.h" | |
| #include "SkNx.h" | |
| #include "SkPaint.h" | |
| #include "SkPoint3.h" | |
| #include "SkRSXform.h" | |
| #include "SkString.h" | |
| #include "SkTo.h" | |
| #include <cstddef> | |
| #include <utility> | |
| static void normalize_perspective(SkScalar mat[9]) { | |
| // If it was interesting to never store the last element, we could divide all 8 other | |
| // elements here by the 9th, making it 1.0... | |
| // | |
| // When SkScalar was SkFixed, we would sometimes rescale the entire matrix to keep its | |
| // component values from getting too large. This is not a concern when using floats/doubles, | |
| // so we do nothing now. | |
| // Disable this for now, but it could be enabled. | |
| #if 0 | |
| if (0 == mat[SkMatrix::kMPersp0] && 0 == mat[SkMatrix::kMPersp1]) { | |
| SkScalar p2 = mat[SkMatrix::kMPersp2]; | |
| if (p2 != 0 && p2 != 1) { | |
| double inv = 1.0 / p2; | |
| for (int i = 0; i < 6; ++i) { | |
| mat[i] = SkDoubleToScalar(mat[i] * inv); | |
| } | |
| mat[SkMatrix::kMPersp2] = 1; | |
| } | |
| } | |
| #endif | |
| } | |
| // In a few places, we performed the following | |
| // a * b + c * d + e | |
| // as | |
| // a * b + (c * d + e) | |
| // | |
| // sdot and scross are indended to capture these compound operations into a | |
| // function, with an eye toward considering upscaling the intermediates to | |
| // doubles for more precision (as we do in concat and invert). | |
| // | |
| // However, these few lines that performed the last add before the "dot", cause | |
| // tiny image differences, so we guard that change until we see the impact on | |
| // chrome's layouttests. | |
| // | |
| #define SK_LEGACY_MATRIX_MATH_ORDER | |
| /* [scale-x skew-x trans-x] [X] [X'] | |
| [skew-y scale-y trans-y] * [Y] = [Y'] | |
| [persp-0 persp-1 persp-2] [1] [1 ] | |
| */ | |
| void SkMatrix::reset() { | |
| fMat[kMScaleX] = fMat[kMScaleY] = fMat[kMPersp2] = 1; | |
| fMat[kMSkewX] = fMat[kMSkewY] = | |
| fMat[kMTransX] = fMat[kMTransY] = | |
| fMat[kMPersp0] = fMat[kMPersp1] = 0; | |
| this->setTypeMask(kIdentity_Mask | kRectStaysRect_Mask); | |
| } | |
| void SkMatrix::set9(const SkScalar buffer[]) { | |
| memcpy(fMat, buffer, 9 * sizeof(SkScalar)); | |
| normalize_perspective(fMat); | |
| this->setTypeMask(kUnknown_Mask); | |
| } | |
| void SkMatrix::setAffine(const SkScalar buffer[]) { | |
| fMat[kMScaleX] = buffer[kAScaleX]; | |
| fMat[kMSkewX] = buffer[kASkewX]; | |
| fMat[kMTransX] = buffer[kATransX]; | |
| fMat[kMSkewY] = buffer[kASkewY]; | |
| fMat[kMScaleY] = buffer[kAScaleY]; | |
| fMat[kMTransY] = buffer[kATransY]; | |
| fMat[kMPersp0] = 0; | |
| fMat[kMPersp1] = 0; | |
| fMat[kMPersp2] = 1; | |
| this->setTypeMask(kUnknown_Mask); | |
| } | |
| // this guy aligns with the masks, so we can compute a mask from a varaible 0/1 | |
| enum { | |
| kTranslate_Shift, | |
| kScale_Shift, | |
| kAffine_Shift, | |
| kPerspective_Shift, | |
| kRectStaysRect_Shift | |
| }; | |
| static const int32_t kScalar1Int = 0x3f800000; | |
| uint8_t SkMatrix::computePerspectiveTypeMask() const { | |
| // Benchmarking suggests that replacing this set of SkScalarAs2sCompliment | |
| // is a win, but replacing those below is not. We don't yet understand | |
| // that result. | |
| if (fMat[kMPersp0] != 0 || fMat[kMPersp1] != 0 || fMat[kMPersp2] != 1) { | |
| // If this is a perspective transform, we return true for all other | |
| // transform flags - this does not disable any optimizations, respects | |
| // the rule that the type mask must be conservative, and speeds up | |
| // type mask computation. | |
| return SkToU8(kORableMasks); | |
| } | |
| return SkToU8(kOnlyPerspectiveValid_Mask | kUnknown_Mask); | |
| } | |
| uint8_t SkMatrix::computeTypeMask() const { | |
| unsigned mask = 0; | |
| if (fMat[kMPersp0] != 0 || fMat[kMPersp1] != 0 || fMat[kMPersp2] != 1) { | |
| // Once it is determined that that this is a perspective transform, | |
| // all other flags are moot as far as optimizations are concerned. | |
| return SkToU8(kORableMasks); | |
| } | |
| if (fMat[kMTransX] != 0 || fMat[kMTransY] != 0) { | |
| mask |= kTranslate_Mask; | |
| } | |
| int m00 = SkScalarAs2sCompliment(fMat[SkMatrix::kMScaleX]); | |
| int m01 = SkScalarAs2sCompliment(fMat[SkMatrix::kMSkewX]); | |
| int m10 = SkScalarAs2sCompliment(fMat[SkMatrix::kMSkewY]); | |
| int m11 = SkScalarAs2sCompliment(fMat[SkMatrix::kMScaleY]); | |
| if (m01 | m10) { | |
| // The skew components may be scale-inducing, unless we are dealing | |
| // with a pure rotation. Testing for a pure rotation is expensive, | |
| // so we opt for being conservative by always setting the scale bit. | |
| // along with affine. | |
| // By doing this, we are also ensuring that matrices have the same | |
| // type masks as their inverses. | |
| mask |= kAffine_Mask | kScale_Mask; | |
| // For rectStaysRect, in the affine case, we only need check that | |
| // the primary diagonal is all zeros and that the secondary diagonal | |
| // is all non-zero. | |
| // map non-zero to 1 | |
| m01 = m01 != 0; | |
| m10 = m10 != 0; | |
| int dp0 = 0 == (m00 | m11) ; // true if both are 0 | |
| int ds1 = m01 & m10; // true if both are 1 | |
| mask |= (dp0 & ds1) << kRectStaysRect_Shift; | |
| } else { | |
| // Only test for scale explicitly if not affine, since affine sets the | |
| // scale bit. | |
| if ((m00 ^ kScalar1Int) | (m11 ^ kScalar1Int)) { | |
| mask |= kScale_Mask; | |
| } | |
| // Not affine, therefore we already know secondary diagonal is | |
| // all zeros, so we just need to check that primary diagonal is | |
| // all non-zero. | |
| // map non-zero to 1 | |
| m00 = m00 != 0; | |
| m11 = m11 != 0; | |
| // record if the (p)rimary diagonal is all non-zero | |
| mask |= (m00 & m11) << kRectStaysRect_Shift; | |
| } | |
| return SkToU8(mask); | |
| } | |
| /////////////////////////////////////////////////////////////////////////////// | |
| bool operator==(const SkMatrix& a, const SkMatrix& b) { | |
| const SkScalar* SK_RESTRICT ma = a.fMat; | |
| const SkScalar* SK_RESTRICT mb = b.fMat; | |
| return ma[0] == mb[0] && ma[1] == mb[1] && ma[2] == mb[2] && | |
| ma[3] == mb[3] && ma[4] == mb[4] && ma[5] == mb[5] && | |
| ma[6] == mb[6] && ma[7] == mb[7] && ma[8] == mb[8]; | |
| } | |
| /////////////////////////////////////////////////////////////////////////////// | |
| // helper function to determine if upper-left 2x2 of matrix is degenerate | |
| static inline bool is_degenerate_2x2(SkScalar scaleX, SkScalar skewX, | |
| SkScalar skewY, SkScalar scaleY) { | |
| SkScalar perp_dot = scaleX*scaleY - skewX*skewY; | |
| return SkScalarNearlyZero(perp_dot, SK_ScalarNearlyZero*SK_ScalarNearlyZero); | |
| } | |
| /////////////////////////////////////////////////////////////////////////////// | |
| bool SkMatrix::isSimilarity(SkScalar tol) const { | |
| // if identity or translate matrix | |
| TypeMask mask = this->getType(); | |
| if (mask <= kTranslate_Mask) { | |
| return true; | |
| } | |
| if (mask & kPerspective_Mask) { | |
| return false; | |
| } | |
| SkScalar mx = fMat[kMScaleX]; | |
| SkScalar my = fMat[kMScaleY]; | |
| // if no skew, can just compare scale factors | |
| if (!(mask & kAffine_Mask)) { | |
| return !SkScalarNearlyZero(mx) && SkScalarNearlyEqual(SkScalarAbs(mx), SkScalarAbs(my)); | |
| } | |
| SkScalar sx = fMat[kMSkewX]; | |
| SkScalar sy = fMat[kMSkewY]; | |
| if (is_degenerate_2x2(mx, sx, sy, my)) { | |
| return false; | |
| } | |
| // upper 2x2 is rotation/reflection + uniform scale if basis vectors | |
| // are 90 degree rotations of each other | |
| return (SkScalarNearlyEqual(mx, my, tol) && SkScalarNearlyEqual(sx, -sy, tol)) | |
| || (SkScalarNearlyEqual(mx, -my, tol) && SkScalarNearlyEqual(sx, sy, tol)); | |
| } | |
| bool SkMatrix::preservesRightAngles(SkScalar tol) const { | |
| TypeMask mask = this->getType(); | |
| if (mask <= kTranslate_Mask) { | |
| // identity, translate and/or scale | |
| return true; | |
| } | |
| if (mask & kPerspective_Mask) { | |
| return false; | |
| } | |
| SkASSERT(mask & (kAffine_Mask | kScale_Mask)); | |
| SkScalar mx = fMat[kMScaleX]; | |
| SkScalar my = fMat[kMScaleY]; | |
| SkScalar sx = fMat[kMSkewX]; | |
| SkScalar sy = fMat[kMSkewY]; | |
| if (is_degenerate_2x2(mx, sx, sy, my)) { | |
| return false; | |
| } | |
| // upper 2x2 is scale + rotation/reflection if basis vectors are orthogonal | |
| SkVector vec[2]; | |
| vec[0].set(mx, sy); | |
| vec[1].set(sx, my); | |
| return SkScalarNearlyZero(vec[0].dot(vec[1]), SkScalarSquare(tol)); | |
| } | |
| /////////////////////////////////////////////////////////////////////////////// | |
| static inline SkScalar sdot(SkScalar a, SkScalar b, SkScalar c, SkScalar d) { | |
| return a * b + c * d; | |
| } | |
| static inline SkScalar sdot(SkScalar a, SkScalar b, SkScalar c, SkScalar d, | |
| SkScalar e, SkScalar f) { | |
| return a * b + c * d + e * f; | |
| } | |
| static inline SkScalar scross(SkScalar a, SkScalar b, SkScalar c, SkScalar d) { | |
| return a * b - c * d; | |
| } | |
| void SkMatrix::setTranslate(SkScalar dx, SkScalar dy) { | |
| if ((dx != 0) | (dy != 0)) { | |
| fMat[kMTransX] = dx; | |
| fMat[kMTransY] = dy; | |
| fMat[kMScaleX] = fMat[kMScaleY] = fMat[kMPersp2] = 1; | |
| fMat[kMSkewX] = fMat[kMSkewY] = | |
| fMat[kMPersp0] = fMat[kMPersp1] = 0; | |
| this->setTypeMask(kTranslate_Mask | kRectStaysRect_Mask); | |
| } else { | |
| this->reset(); | |
| } | |
| } | |
| void SkMatrix::preTranslate(SkScalar dx, SkScalar dy) { | |
| const unsigned mask = this->getType(); | |
| if (mask <= kTranslate_Mask) { | |
| fMat[kMTransX] += dx; | |
| fMat[kMTransY] += dy; | |
| } else if (mask & kPerspective_Mask) { | |
| SkMatrix m; | |
| m.setTranslate(dx, dy); | |
| this->preConcat(m); | |
| return; | |
| } else { | |
| fMat[kMTransX] += sdot(fMat[kMScaleX], dx, fMat[kMSkewX], dy); | |
| fMat[kMTransY] += sdot(fMat[kMSkewY], dx, fMat[kMScaleY], dy); | |
| } | |
| this->updateTranslateMask(); | |
| } | |
| void SkMatrix::postTranslate(SkScalar dx, SkScalar dy) { | |
| if (this->hasPerspective()) { | |
| SkMatrix m; | |
| m.setTranslate(dx, dy); | |
| this->postConcat(m); | |
| } else { | |
| fMat[kMTransX] += dx; | |
| fMat[kMTransY] += dy; | |
| this->updateTranslateMask(); | |
| } | |
| } | |
| /////////////////////////////////////////////////////////////////////////////// | |
| void SkMatrix::setScale(SkScalar sx, SkScalar sy, SkScalar px, SkScalar py) { | |
| if (1 == sx && 1 == sy) { | |
| this->reset(); | |
| } else { | |
| this->setScaleTranslate(sx, sy, px - sx * px, py - sy * py); | |
| } | |
| } | |
| void SkMatrix::setScale(SkScalar sx, SkScalar sy) { | |
| if (1 == sx && 1 == sy) { | |
| this->reset(); | |
| } else { | |
| fMat[kMScaleX] = sx; | |
| fMat[kMScaleY] = sy; | |
| fMat[kMPersp2] = 1; | |
| fMat[kMTransX] = fMat[kMTransY] = | |
| fMat[kMSkewX] = fMat[kMSkewY] = | |
| fMat[kMPersp0] = fMat[kMPersp1] = 0; | |
| this->setTypeMask(kScale_Mask | kRectStaysRect_Mask); | |
| } | |
| } | |
| void SkMatrix::preScale(SkScalar sx, SkScalar sy, SkScalar px, SkScalar py) { | |
| if (1 == sx && 1 == sy) { | |
| return; | |
| } | |
| SkMatrix m; | |
| m.setScale(sx, sy, px, py); | |
| this->preConcat(m); | |
| } | |
| void SkMatrix::preScale(SkScalar sx, SkScalar sy) { | |
| if (1 == sx && 1 == sy) { | |
| return; | |
| } | |
| // the assumption is that these multiplies are very cheap, and that | |
| // a full concat and/or just computing the matrix type is more expensive. | |
| // Also, the fixed-point case checks for overflow, but the float doesn't, | |
| // so we can get away with these blind multiplies. | |
| fMat[kMScaleX] *= sx; | |
| fMat[kMSkewY] *= sx; | |
| fMat[kMPersp0] *= sx; | |
| fMat[kMSkewX] *= sy; | |
| fMat[kMScaleY] *= sy; | |
| fMat[kMPersp1] *= sy; | |
| // Attempt to simplify our type when applying an inverse scale. | |
| // TODO: The persp/affine preconditions are in place to keep the mask consistent with | |
| // what computeTypeMask() would produce (persp/skew always implies kScale). | |
| // We should investigate whether these flag dependencies are truly needed. | |
| if (fMat[kMScaleX] == 1 && fMat[kMScaleY] == 1 | |
| && !(fTypeMask & (kPerspective_Mask | kAffine_Mask))) { | |
| this->clearTypeMask(kScale_Mask); | |
| } else { | |
| this->orTypeMask(kScale_Mask); | |
| } | |
| } | |
| void SkMatrix::postScale(SkScalar sx, SkScalar sy, SkScalar px, SkScalar py) { | |
| if (1 == sx && 1 == sy) { | |
| return; | |
| } | |
| SkMatrix m; | |
| m.setScale(sx, sy, px, py); | |
| this->postConcat(m); | |
| } | |
| void SkMatrix::postScale(SkScalar sx, SkScalar sy) { | |
| if (1 == sx && 1 == sy) { | |
| return; | |
| } | |
| SkMatrix m; | |
| m.setScale(sx, sy); | |
| this->postConcat(m); | |
| } | |
| // this guy perhaps can go away, if we have a fract/high-precision way to | |
| // scale matrices | |
| bool SkMatrix::postIDiv(int divx, int divy) { | |
| if (divx == 0 || divy == 0) { | |
| return false; | |
| } | |
| const float invX = 1.f / divx; | |
| const float invY = 1.f / divy; | |
| fMat[kMScaleX] *= invX; | |
| fMat[kMSkewX] *= invX; | |
| fMat[kMTransX] *= invX; | |
| fMat[kMScaleY] *= invY; | |
| fMat[kMSkewY] *= invY; | |
| fMat[kMTransY] *= invY; | |
| this->setTypeMask(kUnknown_Mask); | |
| return true; | |
| } | |
| //////////////////////////////////////////////////////////////////////////////////// | |
| void SkMatrix::setSinCos(SkScalar sinV, SkScalar cosV, SkScalar px, SkScalar py) { | |
| const SkScalar oneMinusCosV = 1 - cosV; | |
| fMat[kMScaleX] = cosV; | |
| fMat[kMSkewX] = -sinV; | |
| fMat[kMTransX] = sdot(sinV, py, oneMinusCosV, px); | |
| fMat[kMSkewY] = sinV; | |
| fMat[kMScaleY] = cosV; | |
| fMat[kMTransY] = sdot(-sinV, px, oneMinusCosV, py); | |
| fMat[kMPersp0] = fMat[kMPersp1] = 0; | |
| fMat[kMPersp2] = 1; | |
| this->setTypeMask(kUnknown_Mask | kOnlyPerspectiveValid_Mask); | |
| } | |
| SkMatrix& SkMatrix::setRSXform(const SkRSXform& xform) { | |
| fMat[kMScaleX] = xform.fSCos; | |
| fMat[kMSkewX] = -xform.fSSin; | |
| fMat[kMTransX] = xform.fTx; | |
| fMat[kMSkewY] = xform.fSSin; | |
| fMat[kMScaleY] = xform.fSCos; | |
| fMat[kMTransY] = xform.fTy; | |
| fMat[kMPersp0] = fMat[kMPersp1] = 0; | |
| fMat[kMPersp2] = 1; | |
| this->setTypeMask(kUnknown_Mask | kOnlyPerspectiveValid_Mask); | |
| return *this; | |
| } | |
| void SkMatrix::setSinCos(SkScalar sinV, SkScalar cosV) { | |
| fMat[kMScaleX] = cosV; | |
| fMat[kMSkewX] = -sinV; | |
| fMat[kMTransX] = 0; | |
| fMat[kMSkewY] = sinV; | |
| fMat[kMScaleY] = cosV; | |
| fMat[kMTransY] = 0; | |
| fMat[kMPersp0] = fMat[kMPersp1] = 0; | |
| fMat[kMPersp2] = 1; | |
| this->setTypeMask(kUnknown_Mask | kOnlyPerspectiveValid_Mask); | |
| } | |
| void SkMatrix::setRotate(SkScalar degrees, SkScalar px, SkScalar py) { | |
| SkScalar sinV, cosV; | |
| sinV = SkScalarSinCos(SkDegreesToRadians(degrees), &cosV); | |
| this->setSinCos(sinV, cosV, px, py); | |
| } | |
| void SkMatrix::setRotate(SkScalar degrees) { | |
| SkScalar sinV, cosV; | |
| sinV = SkScalarSinCos(SkDegreesToRadians(degrees), &cosV); | |
| this->setSinCos(sinV, cosV); | |
| } | |
| void SkMatrix::preRotate(SkScalar degrees, SkScalar px, SkScalar py) { | |
| SkMatrix m; | |
| m.setRotate(degrees, px, py); | |
| this->preConcat(m); | |
| } | |
| void SkMatrix::preRotate(SkScalar degrees) { | |
| SkMatrix m; | |
| m.setRotate(degrees); | |
| this->preConcat(m); | |
| } | |
| void SkMatrix::postRotate(SkScalar degrees, SkScalar px, SkScalar py) { | |
| SkMatrix m; | |
| m.setRotate(degrees, px, py); | |
| this->postConcat(m); | |
| } | |
| void SkMatrix::postRotate(SkScalar degrees) { | |
| SkMatrix m; | |
| m.setRotate(degrees); | |
| this->postConcat(m); | |
| } | |
| //////////////////////////////////////////////////////////////////////////////////// | |
| void SkMatrix::setSkew(SkScalar sx, SkScalar sy, SkScalar px, SkScalar py) { | |
| fMat[kMScaleX] = 1; | |
| fMat[kMSkewX] = sx; | |
| fMat[kMTransX] = -sx * py; | |
| fMat[kMSkewY] = sy; | |
| fMat[kMScaleY] = 1; | |
| fMat[kMTransY] = -sy * px; | |
| fMat[kMPersp0] = fMat[kMPersp1] = 0; | |
| fMat[kMPersp2] = 1; | |
| this->setTypeMask(kUnknown_Mask | kOnlyPerspectiveValid_Mask); | |
| } | |
| void SkMatrix::setSkew(SkScalar sx, SkScalar sy) { | |
| fMat[kMScaleX] = 1; | |
| fMat[kMSkewX] = sx; | |
| fMat[kMTransX] = 0; | |
| fMat[kMSkewY] = sy; | |
| fMat[kMScaleY] = 1; | |
| fMat[kMTransY] = 0; | |
| fMat[kMPersp0] = fMat[kMPersp1] = 0; | |
| fMat[kMPersp2] = 1; | |
| this->setTypeMask(kUnknown_Mask | kOnlyPerspectiveValid_Mask); | |
| } | |
| void SkMatrix::preSkew(SkScalar sx, SkScalar sy, SkScalar px, SkScalar py) { | |
| SkMatrix m; | |
| m.setSkew(sx, sy, px, py); | |
| this->preConcat(m); | |
| } | |
| void SkMatrix::preSkew(SkScalar sx, SkScalar sy) { | |
| SkMatrix m; | |
| m.setSkew(sx, sy); | |
| this->preConcat(m); | |
| } | |
| void SkMatrix::postSkew(SkScalar sx, SkScalar sy, SkScalar px, SkScalar py) { | |
| SkMatrix m; | |
| m.setSkew(sx, sy, px, py); | |
| this->postConcat(m); | |
| } | |
| void SkMatrix::postSkew(SkScalar sx, SkScalar sy) { | |
| SkMatrix m; | |
| m.setSkew(sx, sy); | |
| this->postConcat(m); | |
| } | |
| /////////////////////////////////////////////////////////////////////////////// | |
| bool SkMatrix::setRectToRect(const SkRect& src, const SkRect& dst, ScaleToFit align) { | |
| if (src.isEmpty()) { | |
| this->reset(); | |
| return false; | |
| } | |
| if (dst.isEmpty()) { | |
| sk_bzero(fMat, 8 * sizeof(SkScalar)); | |
| fMat[kMPersp2] = 1; | |
| this->setTypeMask(kScale_Mask | kRectStaysRect_Mask); | |
| } else { | |
| SkScalar tx, sx = dst.width() / src.width(); | |
| SkScalar ty, sy = dst.height() / src.height(); | |
| bool xLarger = false; | |
| if (align != kFill_ScaleToFit) { | |
| if (sx > sy) { | |
| xLarger = true; | |
| sx = sy; | |
| } else { | |
| sy = sx; | |
| } | |
| } | |
| tx = dst.fLeft - src.fLeft * sx; | |
| ty = dst.fTop - src.fTop * sy; | |
| if (align == kCenter_ScaleToFit || align == kEnd_ScaleToFit) { | |
| SkScalar diff; | |
| if (xLarger) { | |
| diff = dst.width() - src.width() * sy; | |
| } else { | |
| diff = dst.height() - src.height() * sy; | |
| } | |
| if (align == kCenter_ScaleToFit) { | |
| diff = SkScalarHalf(diff); | |
| } | |
| if (xLarger) { | |
| tx += diff; | |
| } else { | |
| ty += diff; | |
| } | |
| } | |
| this->setScaleTranslate(sx, sy, tx, ty); | |
| } | |
| return true; | |
| } | |
| /////////////////////////////////////////////////////////////////////////////// | |
| static inline float muladdmul(float a, float b, float c, float d) { | |
| return sk_double_to_float((double)a * b + (double)c * d); | |
| } | |
| static inline float rowcol3(const float row[], const float col[]) { | |
| return row[0] * col[0] + row[1] * col[3] + row[2] * col[6]; | |
| } | |
| static bool only_scale_and_translate(unsigned mask) { | |
| return 0 == (mask & (SkMatrix::kAffine_Mask | SkMatrix::kPerspective_Mask)); | |
| } | |
| void SkMatrix::setConcat(const SkMatrix& a, const SkMatrix& b) { | |
| TypeMask aType = a.getType(); | |
| TypeMask bType = b.getType(); | |
| if (a.isTriviallyIdentity()) { | |
| *this = b; | |
| } else if (b.isTriviallyIdentity()) { | |
| *this = a; | |
| } else if (only_scale_and_translate(aType | bType)) { | |
| this->setScaleTranslate(a.fMat[kMScaleX] * b.fMat[kMScaleX], | |
| a.fMat[kMScaleY] * b.fMat[kMScaleY], | |
| a.fMat[kMScaleX] * b.fMat[kMTransX] + a.fMat[kMTransX], | |
| a.fMat[kMScaleY] * b.fMat[kMTransY] + a.fMat[kMTransY]); | |
| } else { | |
| SkMatrix tmp; | |
| if ((aType | bType) & kPerspective_Mask) { | |
| tmp.fMat[kMScaleX] = rowcol3(&a.fMat[0], &b.fMat[0]); | |
| tmp.fMat[kMSkewX] = rowcol3(&a.fMat[0], &b.fMat[1]); | |
| tmp.fMat[kMTransX] = rowcol3(&a.fMat[0], &b.fMat[2]); | |
| tmp.fMat[kMSkewY] = rowcol3(&a.fMat[3], &b.fMat[0]); | |
| tmp.fMat[kMScaleY] = rowcol3(&a.fMat[3], &b.fMat[1]); | |
| tmp.fMat[kMTransY] = rowcol3(&a.fMat[3], &b.fMat[2]); | |
| tmp.fMat[kMPersp0] = rowcol3(&a.fMat[6], &b.fMat[0]); | |
| tmp.fMat[kMPersp1] = rowcol3(&a.fMat[6], &b.fMat[1]); | |
| tmp.fMat[kMPersp2] = rowcol3(&a.fMat[6], &b.fMat[2]); | |
| normalize_perspective(tmp.fMat); | |
| tmp.setTypeMask(kUnknown_Mask); | |
| } else { | |
| tmp.fMat[kMScaleX] = muladdmul(a.fMat[kMScaleX], | |
| b.fMat[kMScaleX], | |
| a.fMat[kMSkewX], | |
| b.fMat[kMSkewY]); | |
| tmp.fMat[kMSkewX] = muladdmul(a.fMat[kMScaleX], | |
| b.fMat[kMSkewX], | |
| a.fMat[kMSkewX], | |
| b.fMat[kMScaleY]); | |
| tmp.fMat[kMTransX] = muladdmul(a.fMat[kMScaleX], | |
| b.fMat[kMTransX], | |
| a.fMat[kMSkewX], | |
| b.fMat[kMTransY]) + a.fMat[kMTransX]; | |
| tmp.fMat[kMSkewY] = muladdmul(a.fMat[kMSkewY], | |
| b.fMat[kMScaleX], | |
| a.fMat[kMScaleY], | |
| b.fMat[kMSkewY]); | |
| tmp.fMat[kMScaleY] = muladdmul(a.fMat[kMSkewY], | |
| b.fMat[kMSkewX], | |
| a.fMat[kMScaleY], | |
| b.fMat[kMScaleY]); | |
| tmp.fMat[kMTransY] = muladdmul(a.fMat[kMSkewY], | |
| b.fMat[kMTransX], | |
| a.fMat[kMScaleY], | |
| b.fMat[kMTransY]) + a.fMat[kMTransY]; | |
| tmp.fMat[kMPersp0] = 0; | |
| tmp.fMat[kMPersp1] = 0; | |
| tmp.fMat[kMPersp2] = 1; | |
| //SkDebugf("Concat mat non-persp type: %d\n", tmp.getType()); | |
| //SkASSERT(!(tmp.getType() & kPerspective_Mask)); | |
| tmp.setTypeMask(kUnknown_Mask | kOnlyPerspectiveValid_Mask); | |
| } | |
| *this = tmp; | |
| } | |
| } | |
| void SkMatrix::preConcat(const SkMatrix& mat) { | |
| // check for identity first, so we don't do a needless copy of ourselves | |
| // to ourselves inside setConcat() | |
| if(!mat.isIdentity()) { | |
| this->setConcat(*this, mat); | |
| } | |
| } | |
| void SkMatrix::postConcat(const SkMatrix& mat) { | |
| // check for identity first, so we don't do a needless copy of ourselves | |
| // to ourselves inside setConcat() | |
| if (!mat.isIdentity()) { | |
| this->setConcat(mat, *this); | |
| } | |
| } | |
| /////////////////////////////////////////////////////////////////////////////// | |
| /* Matrix inversion is very expensive, but also the place where keeping | |
| precision may be most important (here and matrix concat). Hence to avoid | |
| bitmap blitting artifacts when walking the inverse, we use doubles for | |
| the intermediate math, even though we know that is more expensive. | |
| */ | |
| static inline SkScalar scross_dscale(SkScalar a, SkScalar b, | |
| SkScalar c, SkScalar d, double scale) { | |
| return SkDoubleToScalar(scross(a, b, c, d) * scale); | |
| } | |
| static inline double dcross(double a, double b, double c, double d) { | |
| return a * b - c * d; | |
| } | |
| static inline SkScalar dcross_dscale(double a, double b, | |
| double c, double d, double scale) { | |
| return SkDoubleToScalar(dcross(a, b, c, d) * scale); | |
| } | |
| static double sk_inv_determinant(const float mat[9], int isPerspective) { | |
| double det; | |
| if (isPerspective) { | |
| det = mat[SkMatrix::kMScaleX] * | |
| dcross(mat[SkMatrix::kMScaleY], mat[SkMatrix::kMPersp2], | |
| mat[SkMatrix::kMTransY], mat[SkMatrix::kMPersp1]) | |
| + | |
| mat[SkMatrix::kMSkewX] * | |
| dcross(mat[SkMatrix::kMTransY], mat[SkMatrix::kMPersp0], | |
| mat[SkMatrix::kMSkewY], mat[SkMatrix::kMPersp2]) | |
| + | |
| mat[SkMatrix::kMTransX] * | |
| dcross(mat[SkMatrix::kMSkewY], mat[SkMatrix::kMPersp1], | |
| mat[SkMatrix::kMScaleY], mat[SkMatrix::kMPersp0]); | |
| } else { | |
| det = dcross(mat[SkMatrix::kMScaleX], mat[SkMatrix::kMScaleY], | |
| mat[SkMatrix::kMSkewX], mat[SkMatrix::kMSkewY]); | |
| } | |
| // Since the determinant is on the order of the cube of the matrix members, | |
| // compare to the cube of the default nearly-zero constant (although an | |
| // estimate of the condition number would be better if it wasn't so expensive). | |
| if (SkScalarNearlyZero(sk_double_to_float(det), | |
| SK_ScalarNearlyZero * SK_ScalarNearlyZero * SK_ScalarNearlyZero)) { | |
| return 0; | |
| } | |
| return 1.0 / det; | |
| } | |
| void SkMatrix::SetAffineIdentity(SkScalar affine[6]) { | |
| affine[kAScaleX] = 1; | |
| affine[kASkewY] = 0; | |
| affine[kASkewX] = 0; | |
| affine[kAScaleY] = 1; | |
| affine[kATransX] = 0; | |
| affine[kATransY] = 0; | |
| } | |
| bool SkMatrix::asAffine(SkScalar affine[6]) const { | |
| if (this->hasPerspective()) { | |
| return false; | |
| } | |
| if (affine) { | |
| affine[kAScaleX] = this->fMat[kMScaleX]; | |
| affine[kASkewY] = this->fMat[kMSkewY]; | |
| affine[kASkewX] = this->fMat[kMSkewX]; | |
| affine[kAScaleY] = this->fMat[kMScaleY]; | |
| affine[kATransX] = this->fMat[kMTransX]; | |
| affine[kATransY] = this->fMat[kMTransY]; | |
| } | |
| return true; | |
| } | |
| void SkMatrix::ComputeInv(SkScalar dst[9], const SkScalar src[9], double invDet, bool isPersp) { | |
| SkASSERT(src != dst); | |
| SkASSERT(src && dst); | |
| if (isPersp) { | |
| dst[kMScaleX] = scross_dscale(src[kMScaleY], src[kMPersp2], src[kMTransY], src[kMPersp1], invDet); | |
| dst[kMSkewX] = scross_dscale(src[kMTransX], src[kMPersp1], src[kMSkewX], src[kMPersp2], invDet); | |
| dst[kMTransX] = scross_dscale(src[kMSkewX], src[kMTransY], src[kMTransX], src[kMScaleY], invDet); | |
| dst[kMSkewY] = scross_dscale(src[kMTransY], src[kMPersp0], src[kMSkewY], src[kMPersp2], invDet); | |
| dst[kMScaleY] = scross_dscale(src[kMScaleX], src[kMPersp2], src[kMTransX], src[kMPersp0], invDet); | |
| dst[kMTransY] = scross_dscale(src[kMTransX], src[kMSkewY], src[kMScaleX], src[kMTransY], invDet); | |
| dst[kMPersp0] = scross_dscale(src[kMSkewY], src[kMPersp1], src[kMScaleY], src[kMPersp0], invDet); | |
| dst[kMPersp1] = scross_dscale(src[kMSkewX], src[kMPersp0], src[kMScaleX], src[kMPersp1], invDet); | |
| dst[kMPersp2] = scross_dscale(src[kMScaleX], src[kMScaleY], src[kMSkewX], src[kMSkewY], invDet); | |
| } else { // not perspective | |
| dst[kMScaleX] = SkDoubleToScalar(src[kMScaleY] * invDet); | |
| dst[kMSkewX] = SkDoubleToScalar(-src[kMSkewX] * invDet); | |
| dst[kMTransX] = dcross_dscale(src[kMSkewX], src[kMTransY], src[kMScaleY], src[kMTransX], invDet); | |
| dst[kMSkewY] = SkDoubleToScalar(-src[kMSkewY] * invDet); | |
| dst[kMScaleY] = SkDoubleToScalar(src[kMScaleX] * invDet); | |
| dst[kMTransY] = dcross_dscale(src[kMSkewY], src[kMTransX], src[kMScaleX], src[kMTransY], invDet); | |
| dst[kMPersp0] = 0; | |
| dst[kMPersp1] = 0; | |
| dst[kMPersp2] = 1; | |
| } | |
| } | |
| bool SkMatrix::invertNonIdentity(SkMatrix* inv) const { | |
| SkASSERT(!this->isIdentity()); | |
| TypeMask mask = this->getType(); | |
| if (0 == (mask & ~(kScale_Mask | kTranslate_Mask))) { | |
| bool invertible = true; | |
| if (inv) { | |
| if (mask & kScale_Mask) { | |
| SkScalar invX = fMat[kMScaleX]; | |
| SkScalar invY = fMat[kMScaleY]; | |
| if (0 == invX || 0 == invY) { | |
| return false; | |
| } | |
| invX = SkScalarInvert(invX); | |
| invY = SkScalarInvert(invY); | |
| // Must be careful when writing to inv, since it may be the | |
| // same memory as this. | |
| inv->fMat[kMSkewX] = inv->fMat[kMSkewY] = | |
| inv->fMat[kMPersp0] = inv->fMat[kMPersp1] = 0; | |
| inv->fMat[kMScaleX] = invX; | |
| inv->fMat[kMScaleY] = invY; | |
| inv->fMat[kMPersp2] = 1; | |
| inv->fMat[kMTransX] = -fMat[kMTransX] * invX; | |
| inv->fMat[kMTransY] = -fMat[kMTransY] * invY; | |
| inv->setTypeMask(mask | kRectStaysRect_Mask); | |
| } else { | |
| // translate only | |
| inv->setTranslate(-fMat[kMTransX], -fMat[kMTransY]); | |
| } | |
| } else { // inv is nullptr, just check if we're invertible | |
| if (!fMat[kMScaleX] || !fMat[kMScaleY]) { | |
| invertible = false; | |
| } | |
| } | |
| return invertible; | |
| } | |
| int isPersp = mask & kPerspective_Mask; | |
| double invDet = sk_inv_determinant(fMat, isPersp); | |
| if (invDet == 0) { // underflow | |
| return false; | |
| } | |
| bool applyingInPlace = (inv == this); | |
| SkMatrix* tmp = inv; | |
| SkMatrix storage; | |
| if (applyingInPlace || nullptr == tmp) { | |
| tmp = &storage; // we either need to avoid trampling memory or have no memory | |
| } | |
| ComputeInv(tmp->fMat, fMat, invDet, isPersp); | |
| if (!tmp->isFinite()) { | |
| return false; | |
| } | |
| tmp->setTypeMask(fTypeMask); | |
| if (applyingInPlace) { | |
| *inv = storage; // need to copy answer back | |
| } | |
| return true; | |
| } | |
| /////////////////////////////////////////////////////////////////////////////// | |
| void SkMatrix::Identity_pts(const SkMatrix& m, SkPoint dst[], const SkPoint src[], int count) { | |
| SkASSERT(m.getType() == 0); | |
| if (dst != src && count > 0) { | |
| memcpy(dst, src, count * sizeof(SkPoint)); | |
| } | |
| } | |
| void SkMatrix::Trans_pts(const SkMatrix& m, SkPoint dst[], const SkPoint src[], int count) { | |
| SkASSERT(m.getType() <= SkMatrix::kTranslate_Mask); | |
| if (count > 0) { | |
| SkScalar tx = m.getTranslateX(); | |
| SkScalar ty = m.getTranslateY(); | |
| if (count & 1) { | |
| dst->fX = src->fX + tx; | |
| dst->fY = src->fY + ty; | |
| src += 1; | |
| dst += 1; | |
| } | |
| Sk4s trans4(tx, ty, tx, ty); | |
| count >>= 1; | |
| if (count & 1) { | |
| (Sk4s::Load(src) + trans4).store(dst); | |
| src += 2; | |
| dst += 2; | |
| } | |
| count >>= 1; | |
| for (int i = 0; i < count; ++i) { | |
| (Sk4s::Load(src+0) + trans4).store(dst+0); | |
| (Sk4s::Load(src+2) + trans4).store(dst+2); | |
| src += 4; | |
| dst += 4; | |
| } | |
| } | |
| } | |
| void SkMatrix::Scale_pts(const SkMatrix& m, SkPoint dst[], const SkPoint src[], int count) { | |
| SkASSERT(m.getType() <= (SkMatrix::kScale_Mask | SkMatrix::kTranslate_Mask)); | |
| if (count > 0) { | |
| SkScalar tx = m.getTranslateX(); | |
| SkScalar ty = m.getTranslateY(); | |
| SkScalar sx = m.getScaleX(); | |
| SkScalar sy = m.getScaleY(); | |
| if (count & 1) { | |
| dst->fX = src->fX * sx + tx; | |
| dst->fY = src->fY * sy + ty; | |
| src += 1; | |
| dst += 1; | |
| } | |
| Sk4s trans4(tx, ty, tx, ty); | |
| Sk4s scale4(sx, sy, sx, sy); | |
| count >>= 1; | |
| if (count & 1) { | |
| (Sk4s::Load(src) * scale4 + trans4).store(dst); | |
| src += 2; | |
| dst += 2; | |
| } | |
| count >>= 1; | |
| for (int i = 0; i < count; ++i) { | |
| (Sk4s::Load(src+0) * scale4 + trans4).store(dst+0); | |
| (Sk4s::Load(src+2) * scale4 + trans4).store(dst+2); | |
| src += 4; | |
| dst += 4; | |
| } | |
| } | |
| } | |
| void SkMatrix::Persp_pts(const SkMatrix& m, SkPoint dst[], | |
| const SkPoint src[], int count) { | |
| SkASSERT(m.hasPerspective()); | |
| if (count > 0) { | |
| do { | |
| SkScalar sy = src->fY; | |
| SkScalar sx = src->fX; | |
| src += 1; | |
| SkScalar x = sdot(sx, m.fMat[kMScaleX], sy, m.fMat[kMSkewX]) + m.fMat[kMTransX]; | |
| SkScalar y = sdot(sx, m.fMat[kMSkewY], sy, m.fMat[kMScaleY]) + m.fMat[kMTransY]; | |
| #ifdef SK_LEGACY_MATRIX_MATH_ORDER | |
| SkScalar z = sx * m.fMat[kMPersp0] + (sy * m.fMat[kMPersp1] + m.fMat[kMPersp2]); | |
| #else | |
| SkScalar z = sdot(sx, m.fMat[kMPersp0], sy, m.fMat[kMPersp1]) + m.fMat[kMPersp2]; | |
| #endif | |
| if (z) { | |
| z = SkScalarFastInvert(z); | |
| } | |
| dst->fY = y * z; | |
| dst->fX = x * z; | |
| dst += 1; | |
| } while (--count); | |
| } | |
| } | |
| void SkMatrix::Affine_vpts(const SkMatrix& m, SkPoint dst[], const SkPoint src[], int count) { | |
| SkASSERT(m.getType() != SkMatrix::kPerspective_Mask); | |
| if (count > 0) { | |
| SkScalar tx = m.getTranslateX(); | |
| SkScalar ty = m.getTranslateY(); | |
| SkScalar sx = m.getScaleX(); | |
| SkScalar sy = m.getScaleY(); | |
| SkScalar kx = m.getSkewX(); | |
| SkScalar ky = m.getSkewY(); | |
| if (count & 1) { | |
| dst->set(src->fX * sx + src->fY * kx + tx, | |
| src->fX * ky + src->fY * sy + ty); | |
| src += 1; | |
| dst += 1; | |
| } | |
| Sk4s trans4(tx, ty, tx, ty); | |
| Sk4s scale4(sx, sy, sx, sy); | |
| Sk4s skew4(kx, ky, kx, ky); // applied to swizzle of src4 | |
| count >>= 1; | |
| for (int i = 0; i < count; ++i) { | |
| Sk4s src4 = Sk4s::Load(src); | |
| Sk4s swz4 = SkNx_shuffle<1,0,3,2>(src4); // y0 x0, y1 x1 | |
| (src4 * scale4 + swz4 * skew4 + trans4).store(dst); | |
| src += 2; | |
| dst += 2; | |
| } | |
| } | |
| } | |
| const SkMatrix::MapPtsProc SkMatrix::gMapPtsProcs[] = { | |
| SkMatrix::Identity_pts, SkMatrix::Trans_pts, | |
| SkMatrix::Scale_pts, SkMatrix::Scale_pts, | |
| SkMatrix::Affine_vpts, SkMatrix::Affine_vpts, | |
| SkMatrix::Affine_vpts, SkMatrix::Affine_vpts, | |
| // repeat the persp proc 8 times | |
| SkMatrix::Persp_pts, SkMatrix::Persp_pts, | |
| SkMatrix::Persp_pts, SkMatrix::Persp_pts, | |
| SkMatrix::Persp_pts, SkMatrix::Persp_pts, | |
| SkMatrix::Persp_pts, SkMatrix::Persp_pts | |
| }; | |
| /////////////////////////////////////////////////////////////////////////////// | |
| void SkMatrixPriv::MapHomogeneousPointsWithStride(const SkMatrix& mx, SkPoint3 dst[], | |
| size_t dstStride, const SkPoint3 src[], | |
| size_t srcStride, int count) { | |
| SkASSERT((dst && src && count > 0) || 0 == count); | |
| // no partial overlap | |
| SkASSERT(src == dst || &dst[count] <= &src[0] || &src[count] <= &dst[0]); | |
| if (count > 0) { | |
| if (mx.isIdentity()) { | |
| if (src != dst) { | |
| if (srcStride == sizeof(SkPoint3) && dstStride == sizeof(SkPoint3)) { | |
| memcpy(dst, src, count * sizeof(SkPoint3)); | |
| } else { | |
| for (int i = 0; i < count; ++i) { | |
| *dst = *src; | |
| dst = reinterpret_cast<SkPoint3*>(reinterpret_cast<char*>(dst) + dstStride); | |
| src = reinterpret_cast<const SkPoint3*>(reinterpret_cast<const char*>(src) + | |
| srcStride); | |
| } | |
| } | |
| } | |
| return; | |
| } | |
| do { | |
| SkScalar sx = src->fX; | |
| SkScalar sy = src->fY; | |
| SkScalar sw = src->fZ; | |
| src = reinterpret_cast<const SkPoint3*>(reinterpret_cast<const char*>(src) + srcStride); | |
| const SkScalar* mat = mx.fMat; | |
| typedef SkMatrix M; | |
| SkScalar x = sdot(sx, mat[M::kMScaleX], sy, mat[M::kMSkewX], sw, mat[M::kMTransX]); | |
| SkScalar y = sdot(sx, mat[M::kMSkewY], sy, mat[M::kMScaleY], sw, mat[M::kMTransY]); | |
| SkScalar w = sdot(sx, mat[M::kMPersp0], sy, mat[M::kMPersp1], sw, mat[M::kMPersp2]); | |
| dst->set(x, y, w); | |
| dst = reinterpret_cast<SkPoint3*>(reinterpret_cast<char*>(dst) + dstStride); | |
| } while (--count); | |
| } | |
| } | |
| void SkMatrix::mapHomogeneousPoints(SkPoint3 dst[], const SkPoint3 src[], int count) const { | |
| SkMatrixPriv::MapHomogeneousPointsWithStride(*this, dst, sizeof(SkPoint3), src, | |
| sizeof(SkPoint3), count); | |
| } | |
| /////////////////////////////////////////////////////////////////////////////// | |
| void SkMatrix::mapVectors(SkPoint dst[], const SkPoint src[], int count) const { | |
| if (this->hasPerspective()) { | |
| SkPoint origin; | |
| MapXYProc proc = this->getMapXYProc(); | |
| proc(*this, 0, 0, &origin); | |
| for (int i = count - 1; i >= 0; --i) { | |
| SkPoint tmp; | |
| proc(*this, src[i].fX, src[i].fY, &tmp); | |
| dst[i].set(tmp.fX - origin.fX, tmp.fY - origin.fY); | |
| } | |
| } else { | |
| SkMatrix tmp = *this; | |
| tmp.fMat[kMTransX] = tmp.fMat[kMTransY] = 0; | |
| tmp.clearTypeMask(kTranslate_Mask); | |
| tmp.mapPoints(dst, src, count); | |
| } | |
| } | |
| static Sk4f sort_as_rect(const Sk4f& ltrb) { | |
| Sk4f rblt(ltrb[2], ltrb[3], ltrb[0], ltrb[1]); | |
| Sk4f min = Sk4f::Min(ltrb, rblt); | |
| Sk4f max = Sk4f::Max(ltrb, rblt); | |
| // We can extract either pair [0,1] or [2,3] from min and max and be correct, but on | |
| // ARM this sequence generates the fastest (a single instruction). | |
| return Sk4f(min[2], min[3], max[0], max[1]); | |
| } | |
| void SkMatrix::mapRectScaleTranslate(SkRect* dst, const SkRect& src) const { | |
| SkASSERT(dst); | |
| SkASSERT(this->isScaleTranslate()); | |
| SkScalar sx = fMat[kMScaleX]; | |
| SkScalar sy = fMat[kMScaleY]; | |
| SkScalar tx = fMat[kMTransX]; | |
| SkScalar ty = fMat[kMTransY]; | |
| Sk4f scale(sx, sy, sx, sy); | |
| Sk4f trans(tx, ty, tx, ty); | |
| sort_as_rect(Sk4f::Load(&src.fLeft) * scale + trans).store(&dst->fLeft); | |
| } | |
| bool SkMatrix::mapRect(SkRect* dst, const SkRect& src) const { | |
| SkASSERT(dst); | |
| if (this->getType() <= kTranslate_Mask) { | |
| SkScalar tx = fMat[kMTransX]; | |
| SkScalar ty = fMat[kMTransY]; | |
| Sk4f trans(tx, ty, tx, ty); | |
| sort_as_rect(Sk4f::Load(&src.fLeft) + trans).store(&dst->fLeft); | |
| return true; | |
| } | |
| if (this->isScaleTranslate()) { | |
| this->mapRectScaleTranslate(dst, src); | |
| return true; | |
| } else { | |
| SkPoint quad[4]; | |
| src.toQuad(quad); | |
| this->mapPoints(quad, quad, 4); | |
| dst->setBoundsNoCheck(quad, 4); | |
| return this->rectStaysRect(); // might still return true if rotated by 90, etc. | |
| } | |
| } | |
| SkScalar SkMatrix::mapRadius(SkScalar radius) const { | |
| SkVector vec[2]; | |
| vec[0].set(radius, 0); | |
| vec[1].set(0, radius); | |
| this->mapVectors(vec, 2); | |
| SkScalar d0 = vec[0].length(); | |
| SkScalar d1 = vec[1].length(); | |
| // return geometric mean | |
| return SkScalarSqrt(d0 * d1); | |
| } | |
| /////////////////////////////////////////////////////////////////////////////// | |
| void SkMatrix::Persp_xy(const SkMatrix& m, SkScalar sx, SkScalar sy, | |
| SkPoint* pt) { | |
| SkASSERT(m.hasPerspective()); | |
| SkScalar x = sdot(sx, m.fMat[kMScaleX], sy, m.fMat[kMSkewX]) + m.fMat[kMTransX]; | |
| SkScalar y = sdot(sx, m.fMat[kMSkewY], sy, m.fMat[kMScaleY]) + m.fMat[kMTransY]; | |
| SkScalar z = sdot(sx, m.fMat[kMPersp0], sy, m.fMat[kMPersp1]) + m.fMat[kMPersp2]; | |
| if (z) { | |
| z = SkScalarFastInvert(z); | |
| } | |
| pt->fX = x * z; | |
| pt->fY = y * z; | |
| } | |
| void SkMatrix::RotTrans_xy(const SkMatrix& m, SkScalar sx, SkScalar sy, | |
| SkPoint* pt) { | |
| SkASSERT((m.getType() & (kAffine_Mask | kPerspective_Mask)) == kAffine_Mask); | |
| #ifdef SK_LEGACY_MATRIX_MATH_ORDER | |
| pt->fX = sx * m.fMat[kMScaleX] + (sy * m.fMat[kMSkewX] + m.fMat[kMTransX]); | |
| pt->fY = sx * m.fMat[kMSkewY] + (sy * m.fMat[kMScaleY] + m.fMat[kMTransY]); | |
| #else | |
| pt->fX = sdot(sx, m.fMat[kMScaleX], sy, m.fMat[kMSkewX]) + m.fMat[kMTransX]; | |
| pt->fY = sdot(sx, m.fMat[kMSkewY], sy, m.fMat[kMScaleY]) + m.fMat[kMTransY]; | |
| #endif | |
| } | |
| void SkMatrix::Rot_xy(const SkMatrix& m, SkScalar sx, SkScalar sy, | |
| SkPoint* pt) { | |
| SkASSERT((m.getType() & (kAffine_Mask | kPerspective_Mask))== kAffine_Mask); | |
| SkASSERT(0 == m.fMat[kMTransX]); | |
| SkASSERT(0 == m.fMat[kMTransY]); | |
| #ifdef SK_LEGACY_MATRIX_MATH_ORDER | |
| pt->fX = sx * m.fMat[kMScaleX] + (sy * m.fMat[kMSkewX] + m.fMat[kMTransX]); | |
| pt->fY = sx * m.fMat[kMSkewY] + (sy * m.fMat[kMScaleY] + m.fMat[kMTransY]); | |
| #else | |
| pt->fX = sdot(sx, m.fMat[kMScaleX], sy, m.fMat[kMSkewX]) + m.fMat[kMTransX]; | |
| pt->fY = sdot(sx, m.fMat[kMSkewY], sy, m.fMat[kMScaleY]) + m.fMat[kMTransY]; | |
| #endif | |
| } | |
| void SkMatrix::ScaleTrans_xy(const SkMatrix& m, SkScalar sx, SkScalar sy, | |
| SkPoint* pt) { | |
| SkASSERT((m.getType() & (kScale_Mask | kAffine_Mask | kPerspective_Mask)) | |
| == kScale_Mask); | |
| pt->fX = sx * m.fMat[kMScaleX] + m.fMat[kMTransX]; | |
| pt->fY = sy * m.fMat[kMScaleY] + m.fMat[kMTransY]; | |
| } | |
| void SkMatrix::Scale_xy(const SkMatrix& m, SkScalar sx, SkScalar sy, | |
| SkPoint* pt) { | |
| SkASSERT((m.getType() & (kScale_Mask | kAffine_Mask | kPerspective_Mask)) | |
| == kScale_Mask); | |
| SkASSERT(0 == m.fMat[kMTransX]); | |
| SkASSERT(0 == m.fMat[kMTransY]); | |
| pt->fX = sx * m.fMat[kMScaleX]; | |
| pt->fY = sy * m.fMat[kMScaleY]; | |
| } | |
| void SkMatrix::Trans_xy(const SkMatrix& m, SkScalar sx, SkScalar sy, | |
| SkPoint* pt) { | |
| SkASSERT(m.getType() == kTranslate_Mask); | |
| pt->fX = sx + m.fMat[kMTransX]; | |
| pt->fY = sy + m.fMat[kMTransY]; | |
| } | |
| void SkMatrix::Identity_xy(const SkMatrix& m, SkScalar sx, SkScalar sy, | |
| SkPoint* pt) { | |
| SkASSERT(0 == m.getType()); | |
| pt->fX = sx; | |
| pt->fY = sy; | |
| } | |
| const SkMatrix::MapXYProc SkMatrix::gMapXYProcs[] = { | |
| SkMatrix::Identity_xy, SkMatrix::Trans_xy, | |
| SkMatrix::Scale_xy, SkMatrix::ScaleTrans_xy, | |
| SkMatrix::Rot_xy, SkMatrix::RotTrans_xy, | |
| SkMatrix::Rot_xy, SkMatrix::RotTrans_xy, | |
| // repeat the persp proc 8 times | |
| SkMatrix::Persp_xy, SkMatrix::Persp_xy, | |
| SkMatrix::Persp_xy, SkMatrix::Persp_xy, | |
| SkMatrix::Persp_xy, SkMatrix::Persp_xy, | |
| SkMatrix::Persp_xy, SkMatrix::Persp_xy | |
| }; | |
| /////////////////////////////////////////////////////////////////////////////// | |
| // if its nearly zero (just made up 26, perhaps it should be bigger or smaller) | |
| #define PerspNearlyZero(x) SkScalarNearlyZero(x, (1.0f / (1 << 26))) | |
| bool SkMatrix::isFixedStepInX() const { | |
| return PerspNearlyZero(fMat[kMPersp0]); | |
| } | |
| SkVector SkMatrix::fixedStepInX(SkScalar y) const { | |
| SkASSERT(PerspNearlyZero(fMat[kMPersp0])); | |
| if (PerspNearlyZero(fMat[kMPersp1]) && | |
| PerspNearlyZero(fMat[kMPersp2] - 1)) { | |
| return SkVector::Make(fMat[kMScaleX], fMat[kMSkewY]); | |
| } else { | |
| SkScalar z = y * fMat[kMPersp1] + fMat[kMPersp2]; | |
| return SkVector::Make(fMat[kMScaleX] / z, fMat[kMSkewY] / z); | |
| } | |
| } | |
| /////////////////////////////////////////////////////////////////////////////// | |
| static inline bool checkForZero(float x) { | |
| return x*x == 0; | |
| } | |
| bool SkMatrix::Poly2Proc(const SkPoint srcPt[], SkMatrix* dst) { | |
| dst->fMat[kMScaleX] = srcPt[1].fY - srcPt[0].fY; | |
| dst->fMat[kMSkewY] = srcPt[0].fX - srcPt[1].fX; | |
| dst->fMat[kMPersp0] = 0; | |
| dst->fMat[kMSkewX] = srcPt[1].fX - srcPt[0].fX; | |
| dst->fMat[kMScaleY] = srcPt[1].fY - srcPt[0].fY; | |
| dst->fMat[kMPersp1] = 0; | |
| dst->fMat[kMTransX] = srcPt[0].fX; | |
| dst->fMat[kMTransY] = srcPt[0].fY; | |
| dst->fMat[kMPersp2] = 1; | |
| dst->setTypeMask(kUnknown_Mask); | |
| return true; | |
| } | |
| bool SkMatrix::Poly3Proc(const SkPoint srcPt[], SkMatrix* dst) { | |
| dst->fMat[kMScaleX] = srcPt[2].fX - srcPt[0].fX; | |
| dst->fMat[kMSkewY] = srcPt[2].fY - srcPt[0].fY; | |
| dst->fMat[kMPersp0] = 0; | |
| dst->fMat[kMSkewX] = srcPt[1].fX - srcPt[0].fX; | |
| dst->fMat[kMScaleY] = srcPt[1].fY - srcPt[0].fY; | |
| dst->fMat[kMPersp1] = 0; | |
| dst->fMat[kMTransX] = srcPt[0].fX; | |
| dst->fMat[kMTransY] = srcPt[0].fY; | |
| dst->fMat[kMPersp2] = 1; | |
| dst->setTypeMask(kUnknown_Mask); | |
| return true; | |
| } | |
| bool SkMatrix::Poly4Proc(const SkPoint srcPt[], SkMatrix* dst) { | |
| float a1, a2; | |
| float x0, y0, x1, y1, x2, y2; | |
| x0 = srcPt[2].fX - srcPt[0].fX; | |
| y0 = srcPt[2].fY - srcPt[0].fY; | |
| x1 = srcPt[2].fX - srcPt[1].fX; | |
| y1 = srcPt[2].fY - srcPt[1].fY; | |
| x2 = srcPt[2].fX - srcPt[3].fX; | |
| y2 = srcPt[2].fY - srcPt[3].fY; | |
| /* check if abs(x2) > abs(y2) */ | |
| if ( x2 > 0 ? y2 > 0 ? x2 > y2 : x2 > -y2 : y2 > 0 ? -x2 > y2 : x2 < y2) { | |
| float denom = sk_ieee_float_divide(x1 * y2, x2) - y1; | |
| if (checkForZero(denom)) { | |
| return false; | |
| } | |
| a1 = (((x0 - x1) * y2 / x2) - y0 + y1) / denom; | |
| } else { | |
| float denom = x1 - sk_ieee_float_divide(y1 * x2, y2); | |
| if (checkForZero(denom)) { | |
| return false; | |
| } | |
| a1 = (x0 - x1 - sk_ieee_float_divide((y0 - y1) * x2, y2)) / denom; | |
| } | |
| /* check if abs(x1) > abs(y1) */ | |
| if ( x1 > 0 ? y1 > 0 ? x1 > y1 : x1 > -y1 : y1 > 0 ? -x1 > y1 : x1 < y1) { | |
| float denom = y2 - sk_ieee_float_divide(x2 * y1, x1); | |
| if (checkForZero(denom)) { | |
| return false; | |
| } | |
| a2 = (y0 - y2 - sk_ieee_float_divide((x0 - x2) * y1, x1)) / denom; | |
| } else { | |
| float denom = sk_ieee_float_divide(y2 * x1, y1) - x2; | |
| if (checkForZero(denom)) { | |
| return false; | |
| } | |
| a2 = (sk_ieee_float_divide((y0 - y2) * x1, y1) - x0 + x2) / denom; | |
| } | |
| dst->fMat[kMScaleX] = a2 * srcPt[3].fX + srcPt[3].fX - srcPt[0].fX; | |
| dst->fMat[kMSkewY] = a2 * srcPt[3].fY + srcPt[3].fY - srcPt[0].fY; | |
| dst->fMat[kMPersp0] = a2; | |
| dst->fMat[kMSkewX] = a1 * srcPt[1].fX + srcPt[1].fX - srcPt[0].fX; | |
| dst->fMat[kMScaleY] = a1 * srcPt[1].fY + srcPt[1].fY - srcPt[0].fY; | |
| dst->fMat[kMPersp1] = a1; | |
| dst->fMat[kMTransX] = srcPt[0].fX; | |
| dst->fMat[kMTransY] = srcPt[0].fY; | |
| dst->fMat[kMPersp2] = 1; | |
| dst->setTypeMask(kUnknown_Mask); | |
| return true; | |
| } | |
| typedef bool (*PolyMapProc)(const SkPoint[], SkMatrix*); | |
| /* Adapted from Rob Johnson's original sample code in QuickDraw GX | |
| */ | |
| bool SkMatrix::setPolyToPoly(const SkPoint src[], const SkPoint dst[], int count) { | |
| if ((unsigned)count > 4) { | |
| SkDebugf("--- SkMatrix::setPolyToPoly count out of range %d\n", count); | |
| return false; | |
| } | |
| if (0 == count) { | |
| this->reset(); | |
| return true; | |
| } | |
| if (1 == count) { | |
| this->setTranslate(dst[0].fX - src[0].fX, dst[0].fY - src[0].fY); | |
| return true; | |
| } | |
| const PolyMapProc gPolyMapProcs[] = { | |
| SkMatrix::Poly2Proc, SkMatrix::Poly3Proc, SkMatrix::Poly4Proc | |
| }; | |
| PolyMapProc proc = gPolyMapProcs[count - 2]; | |
| SkMatrix tempMap, result; | |
| if (!proc(src, &tempMap)) { | |
| return false; | |
| } | |
| if (!tempMap.invert(&result)) { | |
| return false; | |
| } | |
| if (!proc(dst, &tempMap)) { | |
| return false; | |
| } | |
| this->setConcat(tempMap, result); | |
| return true; | |
| } | |
| /////////////////////////////////////////////////////////////////////////////// | |
| enum MinMaxOrBoth { | |
| kMin_MinMaxOrBoth, | |
| kMax_MinMaxOrBoth, | |
| kBoth_MinMaxOrBoth | |
| }; | |
| template <MinMaxOrBoth MIN_MAX_OR_BOTH> bool get_scale_factor(SkMatrix::TypeMask typeMask, | |
| const SkScalar m[9], | |
| SkScalar results[/*1 or 2*/]) { | |
| if (typeMask & SkMatrix::kPerspective_Mask) { | |
| return false; | |
| } | |
| if (SkMatrix::kIdentity_Mask == typeMask) { | |
| results[0] = SK_Scalar1; | |
| if (kBoth_MinMaxOrBoth == MIN_MAX_OR_BOTH) { | |
| results[1] = SK_Scalar1; | |
| } | |
| return true; | |
| } | |
| if (!(typeMask & SkMatrix::kAffine_Mask)) { | |
| if (kMin_MinMaxOrBoth == MIN_MAX_OR_BOTH) { | |
| results[0] = SkMinScalar(SkScalarAbs(m[SkMatrix::kMScaleX]), | |
| SkScalarAbs(m[SkMatrix::kMScaleY])); | |
| } else if (kMax_MinMaxOrBoth == MIN_MAX_OR_BOTH) { | |
| results[0] = SkMaxScalar(SkScalarAbs(m[SkMatrix::kMScaleX]), | |
| SkScalarAbs(m[SkMatrix::kMScaleY])); | |
| } else { | |
| results[0] = SkScalarAbs(m[SkMatrix::kMScaleX]); | |
| results[1] = SkScalarAbs(m[SkMatrix::kMScaleY]); | |
| if (results[0] > results[1]) { | |
| using std::swap; | |
| swap(results[0], results[1]); | |
| } | |
| } | |
| return true; | |
| } | |
| // ignore the translation part of the matrix, just look at 2x2 portion. | |
| // compute singular values, take largest or smallest abs value. | |
| // [a b; b c] = A^T*A | |
| SkScalar a = sdot(m[SkMatrix::kMScaleX], m[SkMatrix::kMScaleX], | |
| m[SkMatrix::kMSkewY], m[SkMatrix::kMSkewY]); | |
| SkScalar b = sdot(m[SkMatrix::kMScaleX], m[SkMatrix::kMSkewX], | |
| m[SkMatrix::kMScaleY], m[SkMatrix::kMSkewY]); | |
| SkScalar c = sdot(m[SkMatrix::kMSkewX], m[SkMatrix::kMSkewX], | |
| m[SkMatrix::kMScaleY], m[SkMatrix::kMScaleY]); | |
| // eigenvalues of A^T*A are the squared singular values of A. | |
| // characteristic equation is det((A^T*A) - l*I) = 0 | |
| // l^2 - (a + c)l + (ac-b^2) | |
| // solve using quadratic equation (divisor is non-zero since l^2 has 1 coeff | |
| // and roots are guaranteed to be pos and real). | |
| SkScalar bSqd = b * b; | |
| // if upper left 2x2 is orthogonal save some math | |
| if (bSqd <= SK_ScalarNearlyZero*SK_ScalarNearlyZero) { | |
| if (kMin_MinMaxOrBoth == MIN_MAX_OR_BOTH) { | |
| results[0] = SkMinScalar(a, c); | |
| } else if (kMax_MinMaxOrBoth == MIN_MAX_OR_BOTH) { | |
| results[0] = SkMaxScalar(a, c); | |
| } else { | |
| results[0] = a; | |
| results[1] = c; | |
| if (results[0] > results[1]) { | |
| using std::swap; | |
| swap(results[0], results[1]); | |
| } | |
| } | |
| } else { | |
| SkScalar aminusc = a - c; | |
| SkScalar apluscdiv2 = SkScalarHalf(a + c); | |
| SkScalar x = SkScalarHalf(SkScalarSqrt(aminusc * aminusc + 4 * bSqd)); | |
| if (kMin_MinMaxOrBoth == MIN_MAX_OR_BOTH) { | |
| results[0] = apluscdiv2 - x; | |
| } else if (kMax_MinMaxOrBoth == MIN_MAX_OR_BOTH) { | |
| results[0] = apluscdiv2 + x; | |
| } else { | |
| results[0] = apluscdiv2 - x; | |
| results[1] = apluscdiv2 + x; | |
| } | |
| } | |
| if (!SkScalarIsFinite(results[0])) { | |
| return false; | |
| } | |
| // Due to the floating point inaccuracy, there might be an error in a, b, c | |
| // calculated by sdot, further deepened by subsequent arithmetic operations | |
| // on them. Therefore, we allow and cap the nearly-zero negative values. | |
| SkASSERT(results[0] >= -SK_ScalarNearlyZero); | |
| if (results[0] < 0) { | |
| results[0] = 0; | |
| } | |
| results[0] = SkScalarSqrt(results[0]); | |
| if (kBoth_MinMaxOrBoth == MIN_MAX_OR_BOTH) { | |
| if (!SkScalarIsFinite(results[1])) { | |
| return false; | |
| } | |
| SkASSERT(results[1] >= -SK_ScalarNearlyZero); | |
| if (results[1] < 0) { | |
| results[1] = 0; | |
| } | |
| results[1] = SkScalarSqrt(results[1]); | |
| } | |
| return true; | |
| } | |
| SkScalar SkMatrix::getMinScale() const { | |
| SkScalar factor; | |
| if (get_scale_factor<kMin_MinMaxOrBoth>(this->getType(), fMat, &factor)) { | |
| return factor; | |
| } else { | |
| return -1; | |
| } | |
| } | |
| SkScalar SkMatrix::getMaxScale() const { | |
| SkScalar factor; | |
| if (get_scale_factor<kMax_MinMaxOrBoth>(this->getType(), fMat, &factor)) { | |
| return factor; | |
| } else { | |
| return -1; | |
| } | |
| } | |
| bool SkMatrix::getMinMaxScales(SkScalar scaleFactors[2]) const { | |
| return get_scale_factor<kBoth_MinMaxOrBoth>(this->getType(), fMat, scaleFactors); | |
| } | |
| namespace { | |
| // SkMatrix is C++11 POD (trivial and standard-layout), but not aggregate (it has private fields). | |
| struct AggregateMatrix { | |
| SkScalar matrix[9]; | |
| uint32_t typemask; | |
| const SkMatrix& asSkMatrix() const { return *reinterpret_cast<const SkMatrix*>(this); } | |
| }; | |
| static_assert(sizeof(AggregateMatrix) == sizeof(SkMatrix), "AggregateMatrix size mismatch."); | |
| } // namespace | |
| const SkMatrix& SkMatrix::I() { | |
| static_assert(offsetof(SkMatrix,fMat) == offsetof(AggregateMatrix,matrix), "fMat"); | |
| static_assert(offsetof(SkMatrix,fTypeMask) == offsetof(AggregateMatrix,typemask), "fTypeMask"); | |
| static const AggregateMatrix identity = { {SK_Scalar1, 0, 0, | |
| 0, SK_Scalar1, 0, | |
| 0, 0, SK_Scalar1 }, | |
| kIdentity_Mask | kRectStaysRect_Mask}; | |
| SkASSERT(identity.asSkMatrix().isIdentity()); | |
| return identity.asSkMatrix(); | |
| } | |
| const SkMatrix& SkMatrix::InvalidMatrix() { | |
| static_assert(offsetof(SkMatrix,fMat) == offsetof(AggregateMatrix,matrix), "fMat"); | |
| static_assert(offsetof(SkMatrix,fTypeMask) == offsetof(AggregateMatrix,typemask), "fTypeMask"); | |
| static const AggregateMatrix invalid = | |
| { {SK_ScalarMax, SK_ScalarMax, SK_ScalarMax, | |
| SK_ScalarMax, SK_ScalarMax, SK_ScalarMax, | |
| SK_ScalarMax, SK_ScalarMax, SK_ScalarMax }, | |
| kTranslate_Mask | kScale_Mask | kAffine_Mask | kPerspective_Mask }; | |
| return invalid.asSkMatrix(); | |
| } | |
| bool SkMatrix::decomposeScale(SkSize* scale, SkMatrix* remaining) const { | |
| if (this->hasPerspective()) { | |
| return false; | |
| } | |
| const SkScalar sx = SkVector::Length(this->getScaleX(), this->getSkewY()); | |
| const SkScalar sy = SkVector::Length(this->getSkewX(), this->getScaleY()); | |
| if (!SkScalarIsFinite(sx) || !SkScalarIsFinite(sy) || | |
| SkScalarNearlyZero(sx) || SkScalarNearlyZero(sy)) { | |
| return false; | |
| } | |
| if (scale) { | |
| scale->set(sx, sy); | |
| } | |
| if (remaining) { | |
| *remaining = *this; | |
| // As per skbug.com/7211, this should actually be preScale | |
| remaining->postScale(SkScalarInvert(sx), SkScalarInvert(sy)); | |
| } | |
| return true; | |
| } | |
| /////////////////////////////////////////////////////////////////////////////// | |
| size_t SkMatrix::writeToMemory(void* buffer) const { | |
| // TODO write less for simple matrices | |
| static const size_t sizeInMemory = 9 * sizeof(SkScalar); | |
| if (buffer) { | |
| memcpy(buffer, fMat, sizeInMemory); | |
| } | |
| return sizeInMemory; | |
| } | |
| size_t SkMatrix::readFromMemory(const void* buffer, size_t length) { | |
| static const size_t sizeInMemory = 9 * sizeof(SkScalar); | |
| if (length < sizeInMemory) { | |
| return 0; | |
| } | |
| memcpy(fMat, buffer, sizeInMemory); | |
| this->setTypeMask(kUnknown_Mask); | |
| return sizeInMemory; | |
| } | |
| void SkMatrix::dump() const { | |
| SkString str; | |
| str.appendf("[%8.4f %8.4f %8.4f][%8.4f %8.4f %8.4f][%8.4f %8.4f %8.4f]", | |
| fMat[0], fMat[1], fMat[2], fMat[3], fMat[4], fMat[5], | |
| fMat[6], fMat[7], fMat[8]); | |
| SkDebugf("%s\n", str.c_str()); | |
| } | |
| /////////////////////////////////////////////////////////////////////////////// | |
| #include "SkMatrixUtils.h" | |
| bool SkTreatAsSprite(const SkMatrix& mat, const SkISize& size, const SkPaint& paint) { | |
| // Our path aa is 2-bits, and our rect aa is 8, so we could use 8, | |
| // but in practice 4 seems enough (still looks smooth) and allows | |
| // more slightly fractional cases to fall into the fast (sprite) case. | |
| static const unsigned kAntiAliasSubpixelBits = 4; | |
| const unsigned subpixelBits = paint.isAntiAlias() ? kAntiAliasSubpixelBits : 0; | |
| // quick reject on affine or perspective | |
| if (mat.getType() & ~(SkMatrix::kScale_Mask | SkMatrix::kTranslate_Mask)) { | |
| return false; | |
| } | |
| // quick success check | |
| if (!subpixelBits && !(mat.getType() & ~SkMatrix::kTranslate_Mask)) { | |
| return true; | |
| } | |
| // mapRect supports negative scales, so we eliminate those first | |
| if (mat.getScaleX() < 0 || mat.getScaleY() < 0) { | |
| return false; | |
| } | |
| SkRect dst; | |
| SkIRect isrc = SkIRect::MakeSize(size); | |
| { | |
| SkRect src; | |
| src.set(isrc); | |
| mat.mapRect(&dst, src); | |
| } | |
| // just apply the translate to isrc | |
| isrc.offset(SkScalarRoundToInt(mat.getTranslateX()), | |
| SkScalarRoundToInt(mat.getTranslateY())); | |
| if (subpixelBits) { | |
| isrc.fLeft = SkLeftShift(isrc.fLeft, subpixelBits); | |
| isrc.fTop = SkLeftShift(isrc.fTop, subpixelBits); | |
| isrc.fRight = SkLeftShift(isrc.fRight, subpixelBits); | |
| isrc.fBottom = SkLeftShift(isrc.fBottom, subpixelBits); | |
| const float scale = 1 << subpixelBits; | |
| dst.fLeft *= scale; | |
| dst.fTop *= scale; | |
| dst.fRight *= scale; | |
| dst.fBottom *= scale; | |
| } | |
| SkIRect idst; | |
| dst.round(&idst); | |
| return isrc == idst; | |
| } | |
| // A square matrix M can be decomposed (via polar decomposition) into two matrices -- | |
| // an orthogonal matrix Q and a symmetric matrix S. In turn we can decompose S into U*W*U^T, | |
| // where U is another orthogonal matrix and W is a scale matrix. These can be recombined | |
| // to give M = (Q*U)*W*U^T, i.e., the product of two orthogonal matrices and a scale matrix. | |
| // | |
| // The one wrinkle is that traditionally Q may contain a reflection -- the | |
| // calculation has been rejiggered to put that reflection into W. | |
| bool SkDecomposeUpper2x2(const SkMatrix& matrix, | |
| SkPoint* rotation1, | |
| SkPoint* scale, | |
| SkPoint* rotation2) { | |
| SkScalar A = matrix[SkMatrix::kMScaleX]; | |
| SkScalar B = matrix[SkMatrix::kMSkewX]; | |
| SkScalar C = matrix[SkMatrix::kMSkewY]; | |
| SkScalar D = matrix[SkMatrix::kMScaleY]; | |
| if (is_degenerate_2x2(A, B, C, D)) { | |
| return false; | |
| } | |
| double w1, w2; | |
| SkScalar cos1, sin1; | |
| SkScalar cos2, sin2; | |
| // do polar decomposition (M = Q*S) | |
| SkScalar cosQ, sinQ; | |
| double Sa, Sb, Sd; | |
| // if M is already symmetric (i.e., M = I*S) | |
| if (SkScalarNearlyEqual(B, C)) { | |
| cosQ = 1; | |
| sinQ = 0; | |
| Sa = A; | |
| Sb = B; | |
| Sd = D; | |
| } else { | |
| cosQ = A + D; | |
| sinQ = C - B; | |
| SkScalar reciplen = SkScalarInvert(SkScalarSqrt(cosQ*cosQ + sinQ*sinQ)); | |
| cosQ *= reciplen; | |
| sinQ *= reciplen; | |
| // S = Q^-1*M | |
| // we don't calc Sc since it's symmetric | |
| Sa = A*cosQ + C*sinQ; | |
| Sb = B*cosQ + D*sinQ; | |
| Sd = -B*sinQ + D*cosQ; | |
| } | |
| // Now we need to compute eigenvalues of S (our scale factors) | |
| // and eigenvectors (bases for our rotation) | |
| // From this, should be able to reconstruct S as U*W*U^T | |
| if (SkScalarNearlyZero(SkDoubleToScalar(Sb))) { | |
| // already diagonalized | |
| cos1 = 1; | |
| sin1 = 0; | |
| w1 = Sa; | |
| w2 = Sd; | |
| cos2 = cosQ; | |
| sin2 = sinQ; | |
| } else { | |
| double diff = Sa - Sd; | |
| double discriminant = sqrt(diff*diff + 4.0*Sb*Sb); | |
| double trace = Sa + Sd; | |
| if (diff > 0) { | |
| w1 = 0.5*(trace + discriminant); | |
| w2 = 0.5*(trace - discriminant); | |
| } else { | |
| w1 = 0.5*(trace - discriminant); | |
| w2 = 0.5*(trace + discriminant); | |
| } | |
| cos1 = SkDoubleToScalar(Sb); sin1 = SkDoubleToScalar(w1 - Sa); | |
| SkScalar reciplen = SkScalarInvert(SkScalarSqrt(cos1*cos1 + sin1*sin1)); | |
| cos1 *= reciplen; | |
| sin1 *= reciplen; | |
| // rotation 2 is composition of Q and U | |
| cos2 = cos1*cosQ - sin1*sinQ; | |
| sin2 = sin1*cosQ + cos1*sinQ; | |
| // rotation 1 is U^T | |
| sin1 = -sin1; | |
| } | |
| if (scale) { | |
| scale->fX = SkDoubleToScalar(w1); | |
| scale->fY = SkDoubleToScalar(w2); | |
| } | |
| if (rotation1) { | |
| rotation1->fX = cos1; | |
| rotation1->fY = sin1; | |
| } | |
| if (rotation2) { | |
| rotation2->fX = cos2; | |
| rotation2->fY = sin2; | |
| } | |
| return true; | |
| } | |
| ////////////////////////////////////////////////////////////////////////////////////////////////// | |
| void SkRSXform::toQuad(SkScalar width, SkScalar height, SkPoint quad[4]) const { | |
| #if 0 | |
| // This is the slow way, but it documents what we're doing | |
| quad[0].set(0, 0); | |
| quad[1].set(width, 0); | |
| quad[2].set(width, height); | |
| quad[3].set(0, height); | |
| SkMatrix m; | |
| m.setRSXform(*this).mapPoints(quad, quad, 4); | |
| #else | |
| const SkScalar m00 = fSCos; | |
| const SkScalar m01 = -fSSin; | |
| const SkScalar m02 = fTx; | |
| const SkScalar m10 = -m01; | |
| const SkScalar m11 = m00; | |
| const SkScalar m12 = fTy; | |
| quad[0].set(m02, m12); | |
| quad[1].set(m00 * width + m02, m10 * width + m12); | |
| quad[2].set(m00 * width + m01 * height + m02, m10 * width + m11 * height + m12); | |
| quad[3].set(m01 * height + m02, m11 * height + m12); | |
| #endif | |
| } | |
| void SkRSXform::toTriStrip(SkScalar width, SkScalar height, SkPoint strip[4]) const { | |
| const SkScalar m00 = fSCos; | |
| const SkScalar m01 = -fSSin; | |
| const SkScalar m02 = fTx; | |
| const SkScalar m10 = -m01; | |
| const SkScalar m11 = m00; | |
| const SkScalar m12 = fTy; | |
| strip[0].set(m02, m12); | |
| strip[1].set(m01 * height + m02, m11 * height + m12); | |
| strip[2].set(m00 * width + m02, m10 * width + m12); | |
| strip[3].set(m00 * width + m01 * height + m02, m10 * width + m11 * height + m12); | |
| } |