| /* |
| * 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 "SkString.h" |
| |
| #include <stddef.h> |
| |
| // 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 |
| |
| static inline float SkDoubleToFloat(double x) { |
| return static_cast<float>(x); |
| } |
| |
| /* [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); |
| } |
| |
| // 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; |
| } |
| |
| // it has scales and skews, but it could also be rotation, check it out. |
| SkVector vec[2]; |
| vec[0].set(mx, sx); |
| vec[1].set(sy, my); |
| |
| return SkScalarNearlyZero(vec[0].dot(vec[1]), SkScalarSquare(tol)) && |
| SkScalarNearlyEqual(vec[0].lengthSqd(), vec[1].lengthSqd(), |
| SkScalarSquare(tol)); |
| } |
| |
| bool SkMatrix::preservesRightAngles(SkScalar tol) const { |
| TypeMask mask = this->getType(); |
| |
| if (mask <= (SkMatrix::kTranslate_Mask | SkMatrix::kScale_Mask)) { |
| // identity, translate and/or scale |
| return true; |
| } |
| if (mask & kPerspective_Mask) { |
| return false; |
| } |
| |
| SkASSERT(mask & kAffine_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; |
| } |
| |
| // it has scales and skews, but it could also be rotation, check it out. |
| SkVector vec[2]; |
| vec[0].set(mx, sx); |
| vec[1].set(sy, my); |
| |
| return SkScalarNearlyZero(vec[0].dot(vec[1]), SkScalarSquare(tol)) && |
| SkScalarNearlyEqual(vec[0].lengthSqd(), vec[1].lengthSqd(), |
| 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 || dy) { |
| 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) { |
| if (!dx && !dy) { |
| return; |
| } |
| |
| if (this->hasPerspective()) { |
| SkMatrix m; |
| m.setTranslate(dx, dy); |
| this->preConcat(m); |
| } else { |
| fMat[kMTransX] += sdot(fMat[kMScaleX], dx, fMat[kMSkewX], dy); |
| fMat[kMTransY] += sdot(fMat[kMSkewY], dx, fMat[kMScaleY], dy); |
| this->setTypeMask(kUnknown_Mask | kOnlyPerspectiveValid_Mask); |
| } |
| } |
| |
| void SkMatrix::postTranslate(SkScalar dx, SkScalar dy) { |
| if (!dx && !dy) { |
| return; |
| } |
| |
| if (this->hasPerspective()) { |
| SkMatrix m; |
| m.setTranslate(dx, dy); |
| this->postConcat(m); |
| } else { |
| fMat[kMTransX] += dx; |
| fMat[kMTransY] += dy; |
| this->setTypeMask(kUnknown_Mask | kOnlyPerspectiveValid_Mask); |
| } |
| } |
| |
| /////////////////////////////////////////////////////////////////////////////// |
| |
| void SkMatrix::setScale(SkScalar sx, SkScalar sy, SkScalar px, SkScalar py) { |
| if (1 == sx && 1 == sy) { |
| this->reset(); |
| } else { |
| fMat[kMScaleX] = sx; |
| fMat[kMScaleY] = sy; |
| fMat[kMTransX] = px - sx * px; |
| fMat[kMTransY] = py - sy * py; |
| fMat[kMPersp2] = 1; |
| |
| fMat[kMSkewX] = fMat[kMSkewY] = |
| fMat[kMPersp0] = fMat[kMPersp1] = 0; |
| |
| this->setTypeMask(kScale_Mask | kTranslate_Mask | kRectStaysRect_Mask); |
| } |
| } |
| |
| 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); |
| } |
| } |
| |
| bool SkMatrix::setIDiv(int divx, int divy) { |
| if (!divx || !divy) { |
| return false; |
| } |
| this->setScale(SkScalarInvert(divx), SkScalarInvert(divy)); |
| return true; |
| } |
| |
| 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; |
| |
| 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); |
| } |
| |
| 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)); |
| 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; |
| } |
| } |
| |
| fMat[kMScaleX] = sx; |
| fMat[kMScaleY] = sy; |
| fMat[kMTransX] = tx; |
| fMat[kMTransY] = ty; |
| fMat[kMSkewX] = fMat[kMSkewY] = |
| fMat[kMPersp0] = fMat[kMPersp1] = 0; |
| |
| unsigned mask = kRectStaysRect_Mask; |
| if (sx != 1 || sy != 1) { |
| mask |= kScale_Mask; |
| } |
| if (tx || ty) { |
| mask |= kTranslate_Mask; |
| } |
| this->setTypeMask(mask); |
| } |
| // shared cleanup |
| fMat[kMPersp2] = 1; |
| return true; |
| } |
| |
| /////////////////////////////////////////////////////////////////////////////// |
| |
| static inline float muladdmul(float a, float b, float c, float d) { |
| return SkDoubleToFloat((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 void normalize_perspective(SkScalar mat[9]) { |
| if (SkScalarAbs(mat[SkMatrix::kMPersp2]) > 1) { |
| for (int i = 0; i < 9; i++) |
| mat[i] = SkScalarHalf(mat[i]); |
| } |
| } |
| |
| void SkMatrix::setConcat(const SkMatrix& a, const SkMatrix& b) { |
| TypeMask aType = a.getPerspectiveTypeMaskOnly(); |
| TypeMask bType = b.getPerspectiveTypeMaskOnly(); |
| |
| if (a.isTriviallyIdentity()) { |
| *this = b; |
| } else if (b.isTriviallyIdentity()) { |
| *this = a; |
| } 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 { // not perspective |
| 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]); |
| |
| tmp.fMat[kMTransX] += 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]); |
| |
| tmp.fMat[kMTransY] += a.fMat[kMTransY]; |
| tmp.fMat[kMPersp0] = 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((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; |
| } |
| |
| 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 NULL, just check if we're invertible |
| if (!fMat[kMScaleX] || !fMat[kMScaleY]) { |
| invertible = false; |
| } |
| } |
| return invertible; |
| } |
| |
| int isPersp = mask & kPerspective_Mask; |
| double scale = sk_inv_determinant(fMat, isPersp); |
| |
| if (scale == 0) { // underflow |
| return false; |
| } |
| |
| if (inv) { |
| SkMatrix tmp; |
| if (inv == this) { |
| inv = &tmp; |
| } |
| |
| if (isPersp) { |
| inv->fMat[kMScaleX] = scross_dscale(fMat[kMScaleY], fMat[kMPersp2], fMat[kMTransY], fMat[kMPersp1], scale); |
| inv->fMat[kMSkewX] = scross_dscale(fMat[kMTransX], fMat[kMPersp1], fMat[kMSkewX], fMat[kMPersp2], scale); |
| inv->fMat[kMTransX] = scross_dscale(fMat[kMSkewX], fMat[kMTransY], fMat[kMTransX], fMat[kMScaleY], scale); |
| |
| inv->fMat[kMSkewY] = scross_dscale(fMat[kMTransY], fMat[kMPersp0], fMat[kMSkewY], fMat[kMPersp2], scale); |
| inv->fMat[kMScaleY] = scross_dscale(fMat[kMScaleX], fMat[kMPersp2], fMat[kMTransX], fMat[kMPersp0], scale); |
| inv->fMat[kMTransY] = scross_dscale(fMat[kMTransX], fMat[kMSkewY], fMat[kMScaleX], fMat[kMTransY], scale); |
| |
| inv->fMat[kMPersp0] = scross_dscale(fMat[kMSkewY], fMat[kMPersp1], fMat[kMScaleY], fMat[kMPersp0], scale); |
| inv->fMat[kMPersp1] = scross_dscale(fMat[kMSkewX], fMat[kMPersp0], fMat[kMScaleX], fMat[kMPersp1], scale); |
| inv->fMat[kMPersp2] = scross_dscale(fMat[kMScaleX], fMat[kMScaleY], fMat[kMSkewX], fMat[kMSkewY], scale); |
| } else { // not perspective |
| inv->fMat[kMScaleX] = SkDoubleToScalar(fMat[kMScaleY] * scale); |
| inv->fMat[kMSkewX] = SkDoubleToScalar(-fMat[kMSkewX] * scale); |
| inv->fMat[kMTransX] = dcross_dscale(fMat[kMSkewX], fMat[kMTransY], fMat[kMScaleY], fMat[kMTransX], scale); |
| |
| inv->fMat[kMSkewY] = SkDoubleToScalar(-fMat[kMSkewY] * scale); |
| inv->fMat[kMScaleY] = SkDoubleToScalar(fMat[kMScaleX] * scale); |
| inv->fMat[kMTransY] = dcross_dscale(fMat[kMSkewY], fMat[kMTransX], fMat[kMScaleX], fMat[kMTransY], scale); |
| |
| inv->fMat[kMPersp0] = 0; |
| inv->fMat[kMPersp1] = 0; |
| inv->fMat[kMPersp2] = 1; |
| } |
| |
| inv->setTypeMask(fTypeMask); |
| |
| if (inv == &tmp) { |
| *(SkMatrix*)this = tmp; |
| } |
| } |
| 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() == kTranslate_Mask); |
| |
| if (count > 0) { |
| SkScalar tx = m.fMat[kMTransX]; |
| SkScalar ty = m.fMat[kMTransY]; |
| do { |
| dst->fY = src->fY + ty; |
| dst->fX = src->fX + tx; |
| src += 1; |
| dst += 1; |
| } while (--count); |
| } |
| } |
| |
| void SkMatrix::Scale_pts(const SkMatrix& m, SkPoint dst[], |
| const SkPoint src[], int count) { |
| SkASSERT(m.getType() == kScale_Mask); |
| |
| if (count > 0) { |
| SkScalar mx = m.fMat[kMScaleX]; |
| SkScalar my = m.fMat[kMScaleY]; |
| do { |
| dst->fY = src->fY * my; |
| dst->fX = src->fX * mx; |
| src += 1; |
| dst += 1; |
| } while (--count); |
| } |
| } |
| |
| void SkMatrix::ScaleTrans_pts(const SkMatrix& m, SkPoint dst[], |
| const SkPoint src[], int count) { |
| SkASSERT(m.getType() == (kScale_Mask | kTranslate_Mask)); |
| |
| if (count > 0) { |
| SkScalar mx = m.fMat[kMScaleX]; |
| SkScalar my = m.fMat[kMScaleY]; |
| SkScalar tx = m.fMat[kMTransX]; |
| SkScalar ty = m.fMat[kMTransY]; |
| do { |
| dst->fY = src->fY * my + ty; |
| dst->fX = src->fX * mx + tx; |
| src += 1; |
| dst += 1; |
| } while (--count); |
| } |
| } |
| |
| void SkMatrix::Rot_pts(const SkMatrix& m, SkPoint dst[], |
| const SkPoint src[], int count) { |
| SkASSERT((m.getType() & (kPerspective_Mask | kTranslate_Mask)) == 0); |
| |
| if (count > 0) { |
| SkScalar mx = m.fMat[kMScaleX]; |
| SkScalar my = m.fMat[kMScaleY]; |
| SkScalar kx = m.fMat[kMSkewX]; |
| SkScalar ky = m.fMat[kMSkewY]; |
| do { |
| SkScalar sy = src->fY; |
| SkScalar sx = src->fX; |
| src += 1; |
| dst->fY = sdot(sx, ky, sy, my); |
| dst->fX = sdot(sx, mx, sy, kx); |
| dst += 1; |
| } while (--count); |
| } |
| } |
| |
| void SkMatrix::RotTrans_pts(const SkMatrix& m, SkPoint dst[], |
| const SkPoint src[], int count) { |
| SkASSERT(!m.hasPerspective()); |
| |
| if (count > 0) { |
| SkScalar mx = m.fMat[kMScaleX]; |
| SkScalar my = m.fMat[kMScaleY]; |
| SkScalar kx = m.fMat[kMSkewX]; |
| SkScalar ky = m.fMat[kMSkewY]; |
| SkScalar tx = m.fMat[kMTransX]; |
| SkScalar ty = m.fMat[kMTransY]; |
| do { |
| SkScalar sy = src->fY; |
| SkScalar sx = src->fX; |
| src += 1; |
| #ifdef SK_LEGACY_MATRIX_MATH_ORDER |
| dst->fY = sx * ky + (sy * my + ty); |
| dst->fX = sx * mx + (sy * kx + tx); |
| #else |
| dst->fY = sdot(sx, ky, sy, my) + ty; |
| dst->fX = sdot(sx, mx, sy, kx) + tx; |
| #endif |
| dst += 1; |
| } while (--count); |
| } |
| } |
| |
| 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); |
| } |
| } |
| |
| const SkMatrix::MapPtsProc SkMatrix::gMapPtsProcs[] = { |
| SkMatrix::Identity_pts, SkMatrix::Trans_pts, |
| SkMatrix::Scale_pts, SkMatrix::ScaleTrans_pts, |
| SkMatrix::Rot_pts, SkMatrix::RotTrans_pts, |
| SkMatrix::Rot_pts, SkMatrix::RotTrans_pts, |
| // 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 SkMatrix::mapPoints(SkPoint dst[], const SkPoint src[], int count) const { |
| SkASSERT((dst && src && count > 0) || 0 == count); |
| // no partial overlap |
| SkASSERT(src == dst || &dst[count] <= &src[0] || &src[count] <= &dst[0]); |
| |
| this->getMapPtsProc()(*this, dst, src, count); |
| } |
| |
| /////////////////////////////////////////////////////////////////////////////// |
| |
| void SkMatrix::mapHomogeneousPoints(SkScalar dst[], const SkScalar src[], int count) const { |
| SkASSERT((dst && src && count > 0) || 0 == count); |
| // no partial overlap |
| SkASSERT(src == dst || SkAbs32((int32_t)(src - dst)) >= 3*count); |
| |
| if (count > 0) { |
| if (this->isIdentity()) { |
| memcpy(dst, src, 3*count*sizeof(SkScalar)); |
| return; |
| } |
| do { |
| SkScalar sx = src[0]; |
| SkScalar sy = src[1]; |
| SkScalar sw = src[2]; |
| src += 3; |
| |
| SkScalar x = sdot(sx, fMat[kMScaleX], sy, fMat[kMSkewX], sw, fMat[kMTransX]); |
| SkScalar y = sdot(sx, fMat[kMSkewY], sy, fMat[kMScaleY], sw, fMat[kMTransY]); |
| SkScalar w = sdot(sx, fMat[kMPersp0], sy, fMat[kMPersp1], sw, fMat[kMPersp2]); |
| |
| dst[0] = x; |
| dst[1] = y; |
| dst[2] = w; |
| dst += 3; |
| } while (--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); |
| } |
| } |
| |
| bool SkMatrix::mapRect(SkRect* dst, const SkRect& src) const { |
| SkASSERT(dst && &src); |
| |
| if (this->rectStaysRect()) { |
| this->mapPoints((SkPoint*)dst, (const SkPoint*)&src, 2); |
| dst->sort(); |
| return true; |
| } else { |
| SkPoint quad[4]; |
| |
| src.toQuad(quad); |
| this->mapPoints(quad, quad, 4); |
| dst->set(quad, 4); |
| return false; |
| } |
| } |
| |
| 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::fixedStepInX(SkScalar y, SkFixed* stepX, SkFixed* stepY) const { |
| if (PerspNearlyZero(fMat[kMPersp0])) { |
| if (stepX || stepY) { |
| if (PerspNearlyZero(fMat[kMPersp1]) && |
| PerspNearlyZero(fMat[kMPersp2] - 1)) { |
| if (stepX) { |
| *stepX = SkScalarToFixed(fMat[kMScaleX]); |
| } |
| if (stepY) { |
| *stepY = SkScalarToFixed(fMat[kMSkewY]); |
| } |
| } else { |
| SkScalar z = y * fMat[kMPersp1] + fMat[kMPersp2]; |
| if (stepX) { |
| *stepX = SkScalarToFixed(fMat[kMScaleX] / z); |
| } |
| if (stepY) { |
| *stepY = SkScalarToFixed(fMat[kMSkewY] / z); |
| } |
| } |
| } |
| return true; |
| } |
| return false; |
| } |
| |
| /////////////////////////////////////////////////////////////////////////////// |
| |
| #include "SkPerspIter.h" |
| |
| SkPerspIter::SkPerspIter(const SkMatrix& m, SkScalar x0, SkScalar y0, int count) |
| : fMatrix(m), fSX(x0), fSY(y0), fCount(count) { |
| SkPoint pt; |
| |
| SkMatrix::Persp_xy(m, x0, y0, &pt); |
| fX = SkScalarToFixed(pt.fX); |
| fY = SkScalarToFixed(pt.fY); |
| } |
| |
| int SkPerspIter::next() { |
| int n = fCount; |
| |
| if (0 == n) { |
| return 0; |
| } |
| SkPoint pt; |
| SkFixed x = fX; |
| SkFixed y = fY; |
| SkFixed dx, dy; |
| |
| if (n >= kCount) { |
| n = kCount; |
| fSX += SkIntToScalar(kCount); |
| SkMatrix::Persp_xy(fMatrix, fSX, fSY, &pt); |
| fX = SkScalarToFixed(pt.fX); |
| fY = SkScalarToFixed(pt.fY); |
| dx = (fX - x) >> kShift; |
| dy = (fY - y) >> kShift; |
| } else { |
| fSX += SkIntToScalar(n); |
| SkMatrix::Persp_xy(fMatrix, fSX, fSY, &pt); |
| fX = SkScalarToFixed(pt.fX); |
| fY = SkScalarToFixed(pt.fY); |
| dx = (fX - x) / n; |
| dy = (fY - y) / n; |
| } |
| |
| SkFixed* p = fStorage; |
| for (int i = 0; i < n; i++) { |
| *p++ = x; x += dx; |
| *p++ = y; y += dy; |
| } |
| |
| fCount -= n; |
| return n; |
| } |
| |
| /////////////////////////////////////////////////////////////////////////////// |
| |
| static inline bool checkForZero(float x) { |
| return x*x == 0; |
| } |
| |
| static inline bool poly_to_point(SkPoint* pt, const SkPoint poly[], int count) { |
| float x = 1, y = 1; |
| SkPoint pt1, pt2; |
| |
| if (count > 1) { |
| pt1.fX = poly[1].fX - poly[0].fX; |
| pt1.fY = poly[1].fY - poly[0].fY; |
| y = SkPoint::Length(pt1.fX, pt1.fY); |
| if (checkForZero(y)) { |
| return false; |
| } |
| switch (count) { |
| case 2: |
| break; |
| case 3: |
| pt2.fX = poly[0].fY - poly[2].fY; |
| pt2.fY = poly[2].fX - poly[0].fX; |
| goto CALC_X; |
| default: |
| pt2.fX = poly[0].fY - poly[3].fY; |
| pt2.fY = poly[3].fX - poly[0].fX; |
| CALC_X: |
| x = sdot(pt1.fX, pt2.fX, pt1.fY, pt2.fY) / y; |
| break; |
| } |
| } |
| pt->set(x, y); |
| return true; |
| } |
| |
| bool SkMatrix::Poly2Proc(const SkPoint srcPt[], SkMatrix* dst, |
| const SkPoint& scale) { |
| float invScale = 1 / scale.fY; |
| |
| dst->fMat[kMScaleX] = (srcPt[1].fY - srcPt[0].fY) * invScale; |
| dst->fMat[kMSkewY] = (srcPt[0].fX - srcPt[1].fX) * invScale; |
| dst->fMat[kMPersp0] = 0; |
| dst->fMat[kMSkewX] = (srcPt[1].fX - srcPt[0].fX) * invScale; |
| dst->fMat[kMScaleY] = (srcPt[1].fY - srcPt[0].fY) * invScale; |
| 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, |
| const SkPoint& scale) { |
| float invScale = 1 / scale.fX; |
| dst->fMat[kMScaleX] = (srcPt[2].fX - srcPt[0].fX) * invScale; |
| dst->fMat[kMSkewY] = (srcPt[2].fY - srcPt[0].fY) * invScale; |
| dst->fMat[kMPersp0] = 0; |
| |
| invScale = 1 / scale.fY; |
| dst->fMat[kMSkewX] = (srcPt[1].fX - srcPt[0].fX) * invScale; |
| dst->fMat[kMScaleY] = (srcPt[1].fY - srcPt[0].fY) * invScale; |
| 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, |
| const SkPoint& scale) { |
| 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 = SkScalarMulDiv(x1, y2, x2) - y1; |
| if (checkForZero(denom)) { |
| return false; |
| } |
| a1 = (SkScalarMulDiv(x0 - x1, y2, x2) - y0 + y1) / denom; |
| } else { |
| float denom = x1 - SkScalarMulDiv(y1, x2, y2); |
| if (checkForZero(denom)) { |
| return false; |
| } |
| a1 = (x0 - x1 - SkScalarMulDiv(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 - SkScalarMulDiv(x2, y1, x1); |
| if (checkForZero(denom)) { |
| return false; |
| } |
| a2 = (y0 - y2 - SkScalarMulDiv(x0 - x2, y1, x1)) / denom; |
| } else { |
| float denom = SkScalarMulDiv(y2, x1, y1) - x2; |
| if (checkForZero(denom)) { |
| return false; |
| } |
| a2 = (SkScalarMulDiv(y0 - y2, x1, y1) - x0 + x2) / denom; |
| } |
| |
| float invScale = SkScalarInvert(scale.fX); |
| dst->fMat[kMScaleX] = (a2 * srcPt[3].fX + srcPt[3].fX - srcPt[0].fX) * invScale; |
| dst->fMat[kMSkewY] = (a2 * srcPt[3].fY + srcPt[3].fY - srcPt[0].fY) * invScale; |
| dst->fMat[kMPersp0] = a2 * invScale; |
| |
| invScale = SkScalarInvert(scale.fY); |
| dst->fMat[kMSkewX] = (a1 * srcPt[1].fX + srcPt[1].fX - srcPt[0].fX) * invScale; |
| dst->fMat[kMScaleY] = (a1 * srcPt[1].fY + srcPt[1].fY - srcPt[0].fY) * invScale; |
| dst->fMat[kMPersp1] = a1 * invScale; |
| |
| 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*, const SkPoint&); |
| |
| /* Taken 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; |
| } |
| |
| SkPoint scale; |
| if (!poly_to_point(&scale, src, count) || |
| SkScalarNearlyZero(scale.fX) || |
| SkScalarNearlyZero(scale.fY)) { |
| return false; |
| } |
| |
| static const PolyMapProc gPolyMapProcs[] = { |
| SkMatrix::Poly2Proc, SkMatrix::Poly3Proc, SkMatrix::Poly4Proc |
| }; |
| PolyMapProc proc = gPolyMapProcs[count - 2]; |
| |
| SkMatrix tempMap, result; |
| tempMap.setTypeMask(kUnknown_Mask); |
| |
| if (!proc(src, &tempMap, scale)) { |
| return false; |
| } |
| if (!tempMap.invert(&result)) { |
| return false; |
| } |
| if (!proc(dst, &tempMap, scale)) { |
| 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]) { |
| SkTSwap(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]) { |
| SkTSwap(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; |
| } |
| } |
| SkASSERT(results[0] >= 0); |
| results[0] = SkScalarSqrt(results[0]); |
| if (kBoth_MinMaxOrBoth == MIN_MAX_OR_BOTH) { |
| SkASSERT(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 { |
| |
| struct PODMatrix { |
| SkScalar matrix[9]; |
| uint32_t typemask; |
| |
| const SkMatrix& asSkMatrix() const { return *reinterpret_cast<const SkMatrix*>(this); } |
| }; |
| SK_COMPILE_ASSERT(sizeof(PODMatrix) == sizeof(SkMatrix), PODMatrixSizeMismatch); |
| |
| } // namespace |
| |
| const SkMatrix& SkMatrix::I() { |
| SK_COMPILE_ASSERT(offsetof(SkMatrix, fMat) == offsetof(PODMatrix, matrix), BadfMat); |
| SK_COMPILE_ASSERT(offsetof(SkMatrix, fTypeMask) == offsetof(PODMatrix, typemask), BadfTypeMask); |
| |
| static const PODMatrix 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() { |
| SK_COMPILE_ASSERT(offsetof(SkMatrix, fMat) == offsetof(PODMatrix, matrix), BadfMat); |
| SK_COMPILE_ASSERT(offsetof(SkMatrix, fTypeMask) == offsetof(PODMatrix, typemask), BadfTypeMask); |
| |
| static const PODMatrix 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(); |
| } |
| |
| /////////////////////////////////////////////////////////////////////////////// |
| |
| 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; |
| } |
| if (buffer) { |
| memcpy(fMat, buffer, sizeInMemory); |
| this->setTypeMask(kUnknown_Mask); |
| } |
| return sizeInMemory; |
| } |
| |
| #ifdef SK_DEVELOPER |
| void SkMatrix::dump() const { |
| SkString str; |
| this->toString(&str); |
| SkDebugf("%s\n", str.c_str()); |
| } |
| #endif |
| |
| #ifndef SK_IGNORE_TO_STRING |
| void SkMatrix::toString(SkString* str) const { |
| 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]); |
| } |
| #endif |
| |
| /////////////////////////////////////////////////////////////////////////////// |
| |
| #include "SkMatrixUtils.h" |
| |
| bool SkTreatAsSprite(const SkMatrix& mat, int width, int height, |
| unsigned subpixelBits) { |
| // 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 = { 0, 0, width, height }; |
| |
| { |
| 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 <<= subpixelBits; |
| isrc.fTop <<= subpixelBits; |
| isrc.fRight <<= subpixelBits; |
| 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 (NULL != scale) { |
| scale->fX = SkDoubleToScalar(w1); |
| scale->fY = SkDoubleToScalar(w2); |
| } |
| if (NULL != rotation1) { |
| rotation1->fX = cos1; |
| rotation1->fY = sin1; |
| } |
| if (NULL != rotation2) { |
| rotation2->fX = cos2; |
| rotation2->fY = sin2; |
| } |
| |
| return true; |
| } |
