| /* | 
 |  * 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. | 
 |  */ | 
 |  | 
 | #ifndef SkMatrix_DEFINED | 
 | #define SkMatrix_DEFINED | 
 |  | 
 | #include "include/core/SkRect.h" | 
 | #include "include/private/SkMacros.h" | 
 | #include "include/private/SkTo.h" | 
 |  | 
 | struct SkRSXform; | 
 | struct SkPoint3; | 
 |  | 
 | // Remove when clients are updated to live without this | 
 | #define SK_SUPPORT_LEGACY_MATRIX_RECTTORECT | 
 |  | 
 | /** | 
 |  *  When we transform points through a matrix containing perspective (the bottom row is something | 
 |  *  other than 0,0,1), the bruteforce math can produce confusing results (since we might divide | 
 |  *  by 0, or a negative w value). By default, methods that map rects and paths will apply | 
 |  *  perspective clipping, but this can be changed by specifying kYes to those methods. | 
 |  */ | 
 | enum class SkApplyPerspectiveClip { | 
 |     kNo,    //!< Don't pre-clip the geometry before applying the (perspective) matrix | 
 |     kYes,   //!< Do pre-clip the geometry before applying the (perspective) matrix | 
 | }; | 
 |  | 
 | /** \class SkMatrix | 
 |     SkMatrix holds a 3x3 matrix for transforming coordinates. This allows mapping | 
 |     SkPoint and vectors with translation, scaling, skewing, rotation, and | 
 |     perspective. | 
 |  | 
 |     SkMatrix elements are in row major order. SkMatrix does not have a constructor, | 
 |     so it must be explicitly initialized. setIdentity() initializes SkMatrix | 
 |     so it has no effect. setTranslate(), setScale(), setSkew(), setRotate(), set9 and setAll() | 
 |     initializes all SkMatrix elements with the corresponding mapping. | 
 |  | 
 |     SkMatrix includes a hidden variable that classifies the type of matrix to | 
 |     improve performance. SkMatrix is not thread safe unless getType() is called first. | 
 |  | 
 |     example: https://fiddle.skia.org/c/@Matrix_063 | 
 | */ | 
 | SK_BEGIN_REQUIRE_DENSE | 
 | class SK_API SkMatrix { | 
 | public: | 
 |  | 
 |     /** Creates an identity SkMatrix: | 
 |  | 
 |             | 1 0 0 | | 
 |             | 0 1 0 | | 
 |             | 0 0 1 | | 
 |     */ | 
 |     constexpr SkMatrix() : SkMatrix(1,0,0, 0,1,0, 0,0,1, kIdentity_Mask | kRectStaysRect_Mask) {} | 
 |  | 
 |     /** Sets SkMatrix to scale by (sx, sy). Returned matrix is: | 
 |  | 
 |             | sx  0  0 | | 
 |             |  0 sy  0 | | 
 |             |  0  0  1 | | 
 |  | 
 |         @param sx  horizontal scale factor | 
 |         @param sy  vertical scale factor | 
 |         @return    SkMatrix with scale | 
 |     */ | 
 |     static SkMatrix SK_WARN_UNUSED_RESULT Scale(SkScalar sx, SkScalar sy) { | 
 |         SkMatrix m; | 
 |         m.setScale(sx, sy); | 
 |         return m; | 
 |     } | 
 |  | 
 |     /** Sets SkMatrix to translate by (dx, dy). Returned matrix is: | 
 |  | 
 |             | 1 0 dx | | 
 |             | 0 1 dy | | 
 |             | 0 0  1 | | 
 |  | 
 |         @param dx  horizontal translation | 
 |         @param dy  vertical translation | 
 |         @return    SkMatrix with translation | 
 |     */ | 
 |     static SkMatrix SK_WARN_UNUSED_RESULT Translate(SkScalar dx, SkScalar dy) { | 
 |         SkMatrix m; | 
 |         m.setTranslate(dx, dy); | 
 |         return m; | 
 |     } | 
 |     static SkMatrix SK_WARN_UNUSED_RESULT Translate(SkVector t) { return Translate(t.x(), t.y()); } | 
 |     static SkMatrix SK_WARN_UNUSED_RESULT Translate(SkIVector t) { return Translate(t.x(), t.y()); } | 
 |  | 
 |     /** Sets SkMatrix to rotate by |deg| about a pivot point at (0, 0). | 
 |  | 
 |         @param deg  rotation angle in degrees (positive rotates clockwise) | 
 |         @return     SkMatrix with rotation | 
 |     */ | 
 |     static SkMatrix SK_WARN_UNUSED_RESULT RotateDeg(SkScalar deg) { | 
 |         SkMatrix m; | 
 |         m.setRotate(deg); | 
 |         return m; | 
 |     } | 
 |     static SkMatrix SK_WARN_UNUSED_RESULT RotateDeg(SkScalar deg, SkPoint pt) { | 
 |         SkMatrix m; | 
 |         m.setRotate(deg, pt.x(), pt.y()); | 
 |         return m; | 
 |     } | 
 |     static SkMatrix SK_WARN_UNUSED_RESULT RotateRad(SkScalar rad) { | 
 |         return RotateDeg(SkRadiansToDegrees(rad)); | 
 |     } | 
 |  | 
 |     /** Sets SkMatrix to skew by (kx, ky) about pivot point (0, 0). | 
 |  | 
 |         @param kx  horizontal skew factor | 
 |         @param ky  vertical skew factor | 
 |         @return    SkMatrix with skew | 
 |     */ | 
 |     static SkMatrix SK_WARN_UNUSED_RESULT Skew(SkScalar kx, SkScalar ky) { | 
 |         SkMatrix m; | 
 |         m.setSkew(kx, ky); | 
 |         return m; | 
 |     } | 
 |  | 
 |     /** \enum SkMatrix::ScaleToFit | 
 |         ScaleToFit describes how SkMatrix is constructed to map one SkRect to another. | 
 |         ScaleToFit may allow SkMatrix to have unequal horizontal and vertical scaling, | 
 |         or may restrict SkMatrix to square scaling. If restricted, ScaleToFit specifies | 
 |         how SkMatrix maps to the side or center of the destination SkRect. | 
 |     */ | 
 |     enum ScaleToFit { | 
 |         kFill_ScaleToFit,   //!< scales in x and y to fill destination SkRect | 
 |         kStart_ScaleToFit,  //!< scales and aligns to left and top | 
 |         kCenter_ScaleToFit, //!< scales and aligns to center | 
 |         kEnd_ScaleToFit,    //!< scales and aligns to right and bottom | 
 |     }; | 
 |  | 
 |     /** Returns SkMatrix set to scale and translate src to dst. ScaleToFit selects | 
 |         whether mapping completely fills dst or preserves the aspect ratio, and how to | 
 |         align src within dst. Returns the identity SkMatrix if src is empty. If dst is | 
 |         empty, returns SkMatrix set to: | 
 |  | 
 |             | 0 0 0 | | 
 |             | 0 0 0 | | 
 |             | 0 0 1 | | 
 |  | 
 |         @param src  SkRect to map from | 
 |         @param dst  SkRect to map to | 
 |         @param mode How to handle the mapping | 
 |         @return     SkMatrix mapping src to dst | 
 |     */ | 
 |     static SkMatrix SK_WARN_UNUSED_RESULT RectToRect(const SkRect& src, const SkRect& dst, | 
 |                                                      ScaleToFit mode = kFill_ScaleToFit) { | 
 |         return MakeRectToRect(src, dst, mode); | 
 |     } | 
 |  | 
 |     /** Sets SkMatrix to: | 
 |  | 
 |             | scaleX  skewX transX | | 
 |             |  skewY scaleY transY | | 
 |             |  pers0  pers1  pers2 | | 
 |  | 
 |         @param scaleX  horizontal scale factor | 
 |         @param skewX   horizontal skew factor | 
 |         @param transX  horizontal translation | 
 |         @param skewY   vertical skew factor | 
 |         @param scaleY  vertical scale factor | 
 |         @param transY  vertical translation | 
 |         @param pers0   input x-axis perspective factor | 
 |         @param pers1   input y-axis perspective factor | 
 |         @param pers2   perspective scale factor | 
 |         @return        SkMatrix constructed from parameters | 
 |     */ | 
 |     static SkMatrix SK_WARN_UNUSED_RESULT MakeAll(SkScalar scaleX, SkScalar skewX,  SkScalar transX, | 
 |                                                   SkScalar skewY,  SkScalar scaleY, SkScalar transY, | 
 |                                                   SkScalar pers0, SkScalar pers1, SkScalar pers2) { | 
 |         SkMatrix m; | 
 |         m.setAll(scaleX, skewX, transX, skewY, scaleY, transY, pers0, pers1, pers2); | 
 |         return m; | 
 |     } | 
 |  | 
 |     /** \enum SkMatrix::TypeMask | 
 |         Enum of bit fields for mask returned by getType(). | 
 |         Used to identify the complexity of SkMatrix, to optimize performance. | 
 |     */ | 
 |     enum TypeMask { | 
 |         kIdentity_Mask    = 0,    //!< identity SkMatrix; all bits clear | 
 |         kTranslate_Mask   = 0x01, //!< translation SkMatrix | 
 |         kScale_Mask       = 0x02, //!< scale SkMatrix | 
 |         kAffine_Mask      = 0x04, //!< skew or rotate SkMatrix | 
 |         kPerspective_Mask = 0x08, //!< perspective SkMatrix | 
 |     }; | 
 |  | 
 |     /** Returns a bit field describing the transformations the matrix may | 
 |         perform. The bit field is computed conservatively, so it may include | 
 |         false positives. For example, when kPerspective_Mask is set, all | 
 |         other bits are set. | 
 |  | 
 |         @return  kIdentity_Mask, or combinations of: kTranslate_Mask, kScale_Mask, | 
 |                  kAffine_Mask, kPerspective_Mask | 
 |     */ | 
 |     TypeMask getType() const { | 
 |         if (fTypeMask & kUnknown_Mask) { | 
 |             fTypeMask = this->computeTypeMask(); | 
 |         } | 
 |         // only return the public masks | 
 |         return (TypeMask)(fTypeMask & 0xF); | 
 |     } | 
 |  | 
 |     /** Returns true if SkMatrix is identity.  Identity matrix is: | 
 |  | 
 |             | 1 0 0 | | 
 |             | 0 1 0 | | 
 |             | 0 0 1 | | 
 |  | 
 |         @return  true if SkMatrix has no effect | 
 |     */ | 
 |     bool isIdentity() const { | 
 |         return this->getType() == 0; | 
 |     } | 
 |  | 
 |     /** Returns true if SkMatrix at most scales and translates. SkMatrix may be identity, | 
 |         contain only scale elements, only translate elements, or both. SkMatrix form is: | 
 |  | 
 |             | scale-x    0    translate-x | | 
 |             |    0    scale-y translate-y | | 
 |             |    0       0         1      | | 
 |  | 
 |         @return  true if SkMatrix is identity; or scales, translates, or both | 
 |     */ | 
 |     bool isScaleTranslate() const { | 
 |         return !(this->getType() & ~(kScale_Mask | kTranslate_Mask)); | 
 |     } | 
 |  | 
 |     /** Returns true if SkMatrix is identity, or translates. SkMatrix form is: | 
 |  | 
 |             | 1 0 translate-x | | 
 |             | 0 1 translate-y | | 
 |             | 0 0      1      | | 
 |  | 
 |         @return  true if SkMatrix is identity, or translates | 
 |     */ | 
 |     bool isTranslate() const { return !(this->getType() & ~(kTranslate_Mask)); } | 
 |  | 
 |     /** Returns true SkMatrix maps SkRect to another SkRect. If true, SkMatrix is identity, | 
 |         or scales, or rotates a multiple of 90 degrees, or mirrors on axes. In all | 
 |         cases, SkMatrix may also have translation. SkMatrix form is either: | 
 |  | 
 |             | scale-x    0    translate-x | | 
 |             |    0    scale-y translate-y | | 
 |             |    0       0         1      | | 
 |  | 
 |         or | 
 |  | 
 |             |    0     rotate-x translate-x | | 
 |             | rotate-y    0     translate-y | | 
 |             |    0        0          1      | | 
 |  | 
 |         for non-zero values of scale-x, scale-y, rotate-x, and rotate-y. | 
 |  | 
 |         Also called preservesAxisAlignment(); use the one that provides better inline | 
 |         documentation. | 
 |  | 
 |         @return  true if SkMatrix maps one SkRect into another | 
 |     */ | 
 |     bool rectStaysRect() const { | 
 |         if (fTypeMask & kUnknown_Mask) { | 
 |             fTypeMask = this->computeTypeMask(); | 
 |         } | 
 |         return (fTypeMask & kRectStaysRect_Mask) != 0; | 
 |     } | 
 |  | 
 |     /** Returns true SkMatrix maps SkRect to another SkRect. If true, SkMatrix is identity, | 
 |         or scales, or rotates a multiple of 90 degrees, or mirrors on axes. In all | 
 |         cases, SkMatrix may also have translation. SkMatrix form is either: | 
 |  | 
 |             | scale-x    0    translate-x | | 
 |             |    0    scale-y translate-y | | 
 |             |    0       0         1      | | 
 |  | 
 |         or | 
 |  | 
 |             |    0     rotate-x translate-x | | 
 |             | rotate-y    0     translate-y | | 
 |             |    0        0          1      | | 
 |  | 
 |         for non-zero values of scale-x, scale-y, rotate-x, and rotate-y. | 
 |  | 
 |         Also called rectStaysRect(); use the one that provides better inline | 
 |         documentation. | 
 |  | 
 |         @return  true if SkMatrix maps one SkRect into another | 
 |     */ | 
 |     bool preservesAxisAlignment() const { return this->rectStaysRect(); } | 
 |  | 
 |     /** Returns true if the matrix contains perspective elements. SkMatrix form is: | 
 |  | 
 |             |       --            --              --          | | 
 |             |       --            --              --          | | 
 |             | perspective-x  perspective-y  perspective-scale | | 
 |  | 
 |         where perspective-x or perspective-y is non-zero, or perspective-scale is | 
 |         not one. All other elements may have any value. | 
 |  | 
 |         @return  true if SkMatrix is in most general form | 
 |     */ | 
 |     bool hasPerspective() const { | 
 |         return SkToBool(this->getPerspectiveTypeMaskOnly() & | 
 |                         kPerspective_Mask); | 
 |     } | 
 |  | 
 |     /** Returns true if SkMatrix contains only translation, rotation, reflection, and | 
 |         uniform scale. | 
 |         Returns false if SkMatrix contains different scales, skewing, perspective, or | 
 |         degenerate forms that collapse to a line or point. | 
 |  | 
 |         Describes that the SkMatrix makes rendering with and without the matrix are | 
 |         visually alike; a transformed circle remains a circle. Mathematically, this is | 
 |         referred to as similarity of a Euclidean space, or a similarity transformation. | 
 |  | 
 |         Preserves right angles, keeping the arms of the angle equal lengths. | 
 |  | 
 |         @param tol  to be deprecated | 
 |         @return     true if SkMatrix only rotates, uniformly scales, translates | 
 |  | 
 |         example: https://fiddle.skia.org/c/@Matrix_isSimilarity | 
 |     */ | 
 |     bool isSimilarity(SkScalar tol = SK_ScalarNearlyZero) const; | 
 |  | 
 |     /** Returns true if SkMatrix contains only translation, rotation, reflection, and | 
 |         scale. Scale may differ along rotated axes. | 
 |         Returns false if SkMatrix skewing, perspective, or degenerate forms that collapse | 
 |         to a line or point. | 
 |  | 
 |         Preserves right angles, but not requiring that the arms of the angle | 
 |         retain equal lengths. | 
 |  | 
 |         @param tol  to be deprecated | 
 |         @return     true if SkMatrix only rotates, scales, translates | 
 |  | 
 |         example: https://fiddle.skia.org/c/@Matrix_preservesRightAngles | 
 |     */ | 
 |     bool preservesRightAngles(SkScalar tol = SK_ScalarNearlyZero) const; | 
 |  | 
 |     /** SkMatrix organizes its values in row-major order. These members correspond to | 
 |         each value in SkMatrix. | 
 |     */ | 
 |     static constexpr int kMScaleX = 0; //!< horizontal scale factor | 
 |     static constexpr int kMSkewX  = 1; //!< horizontal skew factor | 
 |     static constexpr int kMTransX = 2; //!< horizontal translation | 
 |     static constexpr int kMSkewY  = 3; //!< vertical skew factor | 
 |     static constexpr int kMScaleY = 4; //!< vertical scale factor | 
 |     static constexpr int kMTransY = 5; //!< vertical translation | 
 |     static constexpr int kMPersp0 = 6; //!< input x perspective factor | 
 |     static constexpr int kMPersp1 = 7; //!< input y perspective factor | 
 |     static constexpr int kMPersp2 = 8; //!< perspective bias | 
 |  | 
 |     /** Affine arrays are in column-major order to match the matrix used by | 
 |         PDF and XPS. | 
 |     */ | 
 |     static constexpr int kAScaleX = 0; //!< horizontal scale factor | 
 |     static constexpr int kASkewY  = 1; //!< vertical skew factor | 
 |     static constexpr int kASkewX  = 2; //!< horizontal skew factor | 
 |     static constexpr int kAScaleY = 3; //!< vertical scale factor | 
 |     static constexpr int kATransX = 4; //!< horizontal translation | 
 |     static constexpr int kATransY = 5; //!< vertical translation | 
 |  | 
 |     /** Returns one matrix value. Asserts if index is out of range and SK_DEBUG is | 
 |         defined. | 
 |  | 
 |         @param index  one of: kMScaleX, kMSkewX, kMTransX, kMSkewY, kMScaleY, kMTransY, | 
 |                       kMPersp0, kMPersp1, kMPersp2 | 
 |         @return       value corresponding to index | 
 |     */ | 
 |     SkScalar operator[](int index) const { | 
 |         SkASSERT((unsigned)index < 9); | 
 |         return fMat[index]; | 
 |     } | 
 |  | 
 |     /** Returns one matrix value. Asserts if index is out of range and SK_DEBUG is | 
 |         defined. | 
 |  | 
 |         @param index  one of: kMScaleX, kMSkewX, kMTransX, kMSkewY, kMScaleY, kMTransY, | 
 |                       kMPersp0, kMPersp1, kMPersp2 | 
 |         @return       value corresponding to index | 
 |     */ | 
 |     SkScalar get(int index) const { | 
 |         SkASSERT((unsigned)index < 9); | 
 |         return fMat[index]; | 
 |     } | 
 |  | 
 |     /** Returns one matrix value from a particular row/column. Asserts if index is out | 
 |         of range and SK_DEBUG is defined. | 
 |  | 
 |         @param r  matrix row to fetch | 
 |         @param c  matrix column to fetch | 
 |         @return   value at the given matrix position | 
 |     */ | 
 |     SkScalar rc(int r, int c) const { | 
 |         SkASSERT(r >= 0 && r <= 2); | 
 |         SkASSERT(c >= 0 && c <= 2); | 
 |         return fMat[r*3 + c]; | 
 |     } | 
 |  | 
 |     /** Returns scale factor multiplied by x-axis input, contributing to x-axis output. | 
 |         With mapPoints(), scales SkPoint along the x-axis. | 
 |  | 
 |         @return  horizontal scale factor | 
 |     */ | 
 |     SkScalar getScaleX() const { return fMat[kMScaleX]; } | 
 |  | 
 |     /** Returns scale factor multiplied by y-axis input, contributing to y-axis output. | 
 |         With mapPoints(), scales SkPoint along the y-axis. | 
 |  | 
 |         @return  vertical scale factor | 
 |     */ | 
 |     SkScalar getScaleY() const { return fMat[kMScaleY]; } | 
 |  | 
 |     /** Returns scale factor multiplied by x-axis input, contributing to y-axis output. | 
 |         With mapPoints(), skews SkPoint along the y-axis. | 
 |         Skewing both axes can rotate SkPoint. | 
 |  | 
 |         @return  vertical skew factor | 
 |     */ | 
 |     SkScalar getSkewY() const { return fMat[kMSkewY]; } | 
 |  | 
 |     /** Returns scale factor multiplied by y-axis input, contributing to x-axis output. | 
 |         With mapPoints(), skews SkPoint along the x-axis. | 
 |         Skewing both axes can rotate SkPoint. | 
 |  | 
 |         @return  horizontal scale factor | 
 |     */ | 
 |     SkScalar getSkewX() const { return fMat[kMSkewX]; } | 
 |  | 
 |     /** Returns translation contributing to x-axis output. | 
 |         With mapPoints(), moves SkPoint along the x-axis. | 
 |  | 
 |         @return  horizontal translation factor | 
 |     */ | 
 |     SkScalar getTranslateX() const { return fMat[kMTransX]; } | 
 |  | 
 |     /** Returns translation contributing to y-axis output. | 
 |         With mapPoints(), moves SkPoint along the y-axis. | 
 |  | 
 |         @return  vertical translation factor | 
 |     */ | 
 |     SkScalar getTranslateY() const { return fMat[kMTransY]; } | 
 |  | 
 |     /** Returns factor scaling input x-axis relative to input y-axis. | 
 |  | 
 |         @return  input x-axis perspective factor | 
 |     */ | 
 |     SkScalar getPerspX() const { return fMat[kMPersp0]; } | 
 |  | 
 |     /** Returns factor scaling input y-axis relative to input x-axis. | 
 |  | 
 |         @return  input y-axis perspective factor | 
 |     */ | 
 |     SkScalar getPerspY() const { return fMat[kMPersp1]; } | 
 |  | 
 |     /** Returns writable SkMatrix value. Asserts if index is out of range and SK_DEBUG is | 
 |         defined. Clears internal cache anticipating that caller will change SkMatrix value. | 
 |  | 
 |         Next call to read SkMatrix state may recompute cache; subsequent writes to SkMatrix | 
 |         value must be followed by dirtyMatrixTypeCache(). | 
 |  | 
 |         @param index  one of: kMScaleX, kMSkewX, kMTransX, kMSkewY, kMScaleY, kMTransY, | 
 |                       kMPersp0, kMPersp1, kMPersp2 | 
 |         @return       writable value corresponding to index | 
 |     */ | 
 |     SkScalar& operator[](int index) { | 
 |         SkASSERT((unsigned)index < 9); | 
 |         this->setTypeMask(kUnknown_Mask); | 
 |         return fMat[index]; | 
 |     } | 
 |  | 
 |     /** Sets SkMatrix value. Asserts if index is out of range and SK_DEBUG is | 
 |         defined. Safer than operator[]; internal cache is always maintained. | 
 |  | 
 |         @param index  one of: kMScaleX, kMSkewX, kMTransX, kMSkewY, kMScaleY, kMTransY, | 
 |                       kMPersp0, kMPersp1, kMPersp2 | 
 |         @param value  scalar to store in SkMatrix | 
 |     */ | 
 |     SkMatrix& set(int index, SkScalar value) { | 
 |         SkASSERT((unsigned)index < 9); | 
 |         fMat[index] = value; | 
 |         this->setTypeMask(kUnknown_Mask); | 
 |         return *this; | 
 |     } | 
 |  | 
 |     /** Sets horizontal scale factor. | 
 |  | 
 |         @param v  horizontal scale factor to store | 
 |     */ | 
 |     SkMatrix& setScaleX(SkScalar v) { return this->set(kMScaleX, v); } | 
 |  | 
 |     /** Sets vertical scale factor. | 
 |  | 
 |         @param v  vertical scale factor to store | 
 |     */ | 
 |     SkMatrix& setScaleY(SkScalar v) { return this->set(kMScaleY, v); } | 
 |  | 
 |     /** Sets vertical skew factor. | 
 |  | 
 |         @param v  vertical skew factor to store | 
 |     */ | 
 |     SkMatrix& setSkewY(SkScalar v) { return this->set(kMSkewY, v); } | 
 |  | 
 |     /** Sets horizontal skew factor. | 
 |  | 
 |         @param v  horizontal skew factor to store | 
 |     */ | 
 |     SkMatrix& setSkewX(SkScalar v) { return this->set(kMSkewX, v); } | 
 |  | 
 |     /** Sets horizontal translation. | 
 |  | 
 |         @param v  horizontal translation to store | 
 |     */ | 
 |     SkMatrix& setTranslateX(SkScalar v) { return this->set(kMTransX, v); } | 
 |  | 
 |     /** Sets vertical translation. | 
 |  | 
 |         @param v  vertical translation to store | 
 |     */ | 
 |     SkMatrix& setTranslateY(SkScalar v) { return this->set(kMTransY, v); } | 
 |  | 
 |     /** Sets input x-axis perspective factor, which causes mapXY() to vary input x-axis values | 
 |         inversely proportional to input y-axis values. | 
 |  | 
 |         @param v  perspective factor | 
 |     */ | 
 |     SkMatrix& setPerspX(SkScalar v) { return this->set(kMPersp0, v); } | 
 |  | 
 |     /** Sets input y-axis perspective factor, which causes mapXY() to vary input y-axis values | 
 |         inversely proportional to input x-axis values. | 
 |  | 
 |         @param v  perspective factor | 
 |     */ | 
 |     SkMatrix& setPerspY(SkScalar v) { return this->set(kMPersp1, v); } | 
 |  | 
 |     /** Sets all values from parameters. Sets matrix to: | 
 |  | 
 |             | scaleX  skewX transX | | 
 |             |  skewY scaleY transY | | 
 |             | persp0 persp1 persp2 | | 
 |  | 
 |         @param scaleX  horizontal scale factor to store | 
 |         @param skewX   horizontal skew factor to store | 
 |         @param transX  horizontal translation to store | 
 |         @param skewY   vertical skew factor to store | 
 |         @param scaleY  vertical scale factor to store | 
 |         @param transY  vertical translation to store | 
 |         @param persp0  input x-axis values perspective factor to store | 
 |         @param persp1  input y-axis values perspective factor to store | 
 |         @param persp2  perspective scale factor to store | 
 |     */ | 
 |     SkMatrix& setAll(SkScalar scaleX, SkScalar skewX,  SkScalar transX, | 
 |                      SkScalar skewY,  SkScalar scaleY, SkScalar transY, | 
 |                      SkScalar persp0, SkScalar persp1, SkScalar persp2) { | 
 |         fMat[kMScaleX] = scaleX; | 
 |         fMat[kMSkewX]  = skewX; | 
 |         fMat[kMTransX] = transX; | 
 |         fMat[kMSkewY]  = skewY; | 
 |         fMat[kMScaleY] = scaleY; | 
 |         fMat[kMTransY] = transY; | 
 |         fMat[kMPersp0] = persp0; | 
 |         fMat[kMPersp1] = persp1; | 
 |         fMat[kMPersp2] = persp2; | 
 |         this->setTypeMask(kUnknown_Mask); | 
 |         return *this; | 
 |     } | 
 |  | 
 |     /** Copies nine scalar values contained by SkMatrix into buffer, in member value | 
 |         ascending order: kMScaleX, kMSkewX, kMTransX, kMSkewY, kMScaleY, kMTransY, | 
 |         kMPersp0, kMPersp1, kMPersp2. | 
 |  | 
 |         @param buffer  storage for nine scalar values | 
 |     */ | 
 |     void get9(SkScalar buffer[9]) const { | 
 |         memcpy(buffer, fMat, 9 * sizeof(SkScalar)); | 
 |     } | 
 |  | 
 |     /** Sets SkMatrix to nine scalar values in buffer, in member value ascending order: | 
 |         kMScaleX, kMSkewX, kMTransX, kMSkewY, kMScaleY, kMTransY, kMPersp0, kMPersp1, | 
 |         kMPersp2. | 
 |  | 
 |         Sets matrix to: | 
 |  | 
 |             | buffer[0] buffer[1] buffer[2] | | 
 |             | buffer[3] buffer[4] buffer[5] | | 
 |             | buffer[6] buffer[7] buffer[8] | | 
 |  | 
 |         In the future, set9 followed by get9 may not return the same values. Since SkMatrix | 
 |         maps non-homogeneous coordinates, scaling all nine values produces an equivalent | 
 |         transformation, possibly improving precision. | 
 |  | 
 |         @param buffer  nine scalar values | 
 |     */ | 
 |     SkMatrix& set9(const SkScalar buffer[9]); | 
 |  | 
 |     /** Sets SkMatrix to identity; which has no effect on mapped SkPoint. Sets SkMatrix to: | 
 |  | 
 |             | 1 0 0 | | 
 |             | 0 1 0 | | 
 |             | 0 0 1 | | 
 |  | 
 |         Also called setIdentity(); use the one that provides better inline | 
 |         documentation. | 
 |     */ | 
 |     SkMatrix& reset(); | 
 |  | 
 |     /** Sets SkMatrix to identity; which has no effect on mapped SkPoint. Sets SkMatrix to: | 
 |  | 
 |             | 1 0 0 | | 
 |             | 0 1 0 | | 
 |             | 0 0 1 | | 
 |  | 
 |         Also called reset(); use the one that provides better inline | 
 |         documentation. | 
 |     */ | 
 |     SkMatrix& setIdentity() { return this->reset(); } | 
 |  | 
 |     /** Sets SkMatrix to translate by (dx, dy). | 
 |  | 
 |         @param dx  horizontal translation | 
 |         @param dy  vertical translation | 
 |     */ | 
 |     SkMatrix& setTranslate(SkScalar dx, SkScalar dy); | 
 |  | 
 |     /** Sets SkMatrix to translate by (v.fX, v.fY). | 
 |  | 
 |         @param v  vector containing horizontal and vertical translation | 
 |     */ | 
 |     SkMatrix& setTranslate(const SkVector& v) { return this->setTranslate(v.fX, v.fY); } | 
 |  | 
 |     /** Sets SkMatrix to scale by sx and sy, about a pivot point at (px, py). | 
 |         The pivot point is unchanged when mapped with SkMatrix. | 
 |  | 
 |         @param sx  horizontal scale factor | 
 |         @param sy  vertical scale factor | 
 |         @param px  pivot on x-axis | 
 |         @param py  pivot on y-axis | 
 |     */ | 
 |     SkMatrix& setScale(SkScalar sx, SkScalar sy, SkScalar px, SkScalar py); | 
 |  | 
 |     /** Sets SkMatrix to scale by sx and sy about at pivot point at (0, 0). | 
 |  | 
 |         @param sx  horizontal scale factor | 
 |         @param sy  vertical scale factor | 
 |     */ | 
 |     SkMatrix& setScale(SkScalar sx, SkScalar sy); | 
 |  | 
 |     /** Sets SkMatrix to rotate by degrees about a pivot point at (px, py). | 
 |         The pivot point is unchanged when mapped with SkMatrix. | 
 |  | 
 |         Positive degrees rotates clockwise. | 
 |  | 
 |         @param degrees  angle of axes relative to upright axes | 
 |         @param px       pivot on x-axis | 
 |         @param py       pivot on y-axis | 
 |     */ | 
 |     SkMatrix& setRotate(SkScalar degrees, SkScalar px, SkScalar py); | 
 |  | 
 |     /** Sets SkMatrix to rotate by degrees about a pivot point at (0, 0). | 
 |         Positive degrees rotates clockwise. | 
 |  | 
 |         @param degrees  angle of axes relative to upright axes | 
 |     */ | 
 |     SkMatrix& setRotate(SkScalar degrees); | 
 |  | 
 |     /** Sets SkMatrix to rotate by sinValue and cosValue, about a pivot point at (px, py). | 
 |         The pivot point is unchanged when mapped with SkMatrix. | 
 |  | 
 |         Vector (sinValue, cosValue) describes the angle of rotation relative to (0, 1). | 
 |         Vector length specifies scale. | 
 |  | 
 |         @param sinValue  rotation vector x-axis component | 
 |         @param cosValue  rotation vector y-axis component | 
 |         @param px        pivot on x-axis | 
 |         @param py        pivot on y-axis | 
 |     */ | 
 |     SkMatrix& setSinCos(SkScalar sinValue, SkScalar cosValue, | 
 |                    SkScalar px, SkScalar py); | 
 |  | 
 |     /** Sets SkMatrix to rotate by sinValue and cosValue, about a pivot point at (0, 0). | 
 |  | 
 |         Vector (sinValue, cosValue) describes the angle of rotation relative to (0, 1). | 
 |         Vector length specifies scale. | 
 |  | 
 |         @param sinValue  rotation vector x-axis component | 
 |         @param cosValue  rotation vector y-axis component | 
 |     */ | 
 |     SkMatrix& setSinCos(SkScalar sinValue, SkScalar cosValue); | 
 |  | 
 |     /** Sets SkMatrix to rotate, scale, and translate using a compressed matrix form. | 
 |  | 
 |         Vector (rsxForm.fSSin, rsxForm.fSCos) describes the angle of rotation relative | 
 |         to (0, 1). Vector length specifies scale. Mapped point is rotated and scaled | 
 |         by vector, then translated by (rsxForm.fTx, rsxForm.fTy). | 
 |  | 
 |         @param rsxForm  compressed SkRSXform matrix | 
 |         @return         reference to SkMatrix | 
 |  | 
 |         example: https://fiddle.skia.org/c/@Matrix_setRSXform | 
 |     */ | 
 |     SkMatrix& setRSXform(const SkRSXform& rsxForm); | 
 |  | 
 |     /** Sets SkMatrix to skew by kx and ky, about a pivot point at (px, py). | 
 |         The pivot point is unchanged when mapped with SkMatrix. | 
 |  | 
 |         @param kx  horizontal skew factor | 
 |         @param ky  vertical skew factor | 
 |         @param px  pivot on x-axis | 
 |         @param py  pivot on y-axis | 
 |     */ | 
 |     SkMatrix& setSkew(SkScalar kx, SkScalar ky, SkScalar px, SkScalar py); | 
 |  | 
 |     /** Sets SkMatrix to skew by kx and ky, about a pivot point at (0, 0). | 
 |  | 
 |         @param kx  horizontal skew factor | 
 |         @param ky  vertical skew factor | 
 |     */ | 
 |     SkMatrix& setSkew(SkScalar kx, SkScalar ky); | 
 |  | 
 |     /** Sets SkMatrix to SkMatrix a multiplied by SkMatrix b. Either a or b may be this. | 
 |  | 
 |         Given: | 
 |  | 
 |                 | A B C |      | J K L | | 
 |             a = | D E F |, b = | M N O | | 
 |                 | G H I |      | P Q R | | 
 |  | 
 |         sets SkMatrix to: | 
 |  | 
 |                     | A B C |   | J K L |   | AJ+BM+CP AK+BN+CQ AL+BO+CR | | 
 |             a * b = | D E F | * | M N O | = | DJ+EM+FP DK+EN+FQ DL+EO+FR | | 
 |                     | G H I |   | P Q R |   | GJ+HM+IP GK+HN+IQ GL+HO+IR | | 
 |  | 
 |         @param a  SkMatrix on left side of multiply expression | 
 |         @param b  SkMatrix on right side of multiply expression | 
 |     */ | 
 |     SkMatrix& setConcat(const SkMatrix& a, const SkMatrix& b); | 
 |  | 
 |     /** Sets SkMatrix to SkMatrix multiplied by SkMatrix constructed from translation (dx, dy). | 
 |         This can be thought of as moving the point to be mapped before applying SkMatrix. | 
 |  | 
 |         Given: | 
 |  | 
 |                      | A B C |               | 1 0 dx | | 
 |             Matrix = | D E F |,  T(dx, dy) = | 0 1 dy | | 
 |                      | G H I |               | 0 0  1 | | 
 |  | 
 |         sets SkMatrix to: | 
 |  | 
 |                                  | A B C | | 1 0 dx |   | A B A*dx+B*dy+C | | 
 |             Matrix * T(dx, dy) = | D E F | | 0 1 dy | = | D E D*dx+E*dy+F | | 
 |                                  | G H I | | 0 0  1 |   | G H G*dx+H*dy+I | | 
 |  | 
 |         @param dx  x-axis translation before applying SkMatrix | 
 |         @param dy  y-axis translation before applying SkMatrix | 
 |     */ | 
 |     SkMatrix& preTranslate(SkScalar dx, SkScalar dy); | 
 |  | 
 |     /** Sets SkMatrix to SkMatrix multiplied by SkMatrix constructed from scaling by (sx, sy) | 
 |         about pivot point (px, py). | 
 |         This can be thought of as scaling about a pivot point before applying SkMatrix. | 
 |  | 
 |         Given: | 
 |  | 
 |                      | A B C |                       | sx  0 dx | | 
 |             Matrix = | D E F |,  S(sx, sy, px, py) = |  0 sy dy | | 
 |                      | G H I |                       |  0  0  1 | | 
 |  | 
 |         where | 
 |  | 
 |             dx = px - sx * px | 
 |             dy = py - sy * py | 
 |  | 
 |         sets SkMatrix to: | 
 |  | 
 |                                          | A B C | | sx  0 dx |   | A*sx B*sy A*dx+B*dy+C | | 
 |             Matrix * S(sx, sy, px, py) = | D E F | |  0 sy dy | = | D*sx E*sy D*dx+E*dy+F | | 
 |                                          | G H I | |  0  0  1 |   | G*sx H*sy G*dx+H*dy+I | | 
 |  | 
 |         @param sx  horizontal scale factor | 
 |         @param sy  vertical scale factor | 
 |         @param px  pivot on x-axis | 
 |         @param py  pivot on y-axis | 
 |     */ | 
 |     SkMatrix& preScale(SkScalar sx, SkScalar sy, SkScalar px, SkScalar py); | 
 |  | 
 |     /** Sets SkMatrix to SkMatrix multiplied by SkMatrix constructed from scaling by (sx, sy) | 
 |         about pivot point (0, 0). | 
 |         This can be thought of as scaling about the origin before applying SkMatrix. | 
 |  | 
 |         Given: | 
 |  | 
 |                      | A B C |               | sx  0  0 | | 
 |             Matrix = | D E F |,  S(sx, sy) = |  0 sy  0 | | 
 |                      | G H I |               |  0  0  1 | | 
 |  | 
 |         sets SkMatrix to: | 
 |  | 
 |                                  | A B C | | sx  0  0 |   | A*sx B*sy C | | 
 |             Matrix * S(sx, sy) = | D E F | |  0 sy  0 | = | D*sx E*sy F | | 
 |                                  | G H I | |  0  0  1 |   | G*sx H*sy I | | 
 |  | 
 |         @param sx  horizontal scale factor | 
 |         @param sy  vertical scale factor | 
 |     */ | 
 |     SkMatrix& preScale(SkScalar sx, SkScalar sy); | 
 |  | 
 |     /** Sets SkMatrix to SkMatrix multiplied by SkMatrix constructed from rotating by degrees | 
 |         about pivot point (px, py). | 
 |         This can be thought of as rotating about a pivot point before applying SkMatrix. | 
 |  | 
 |         Positive degrees rotates clockwise. | 
 |  | 
 |         Given: | 
 |  | 
 |                      | A B C |                        | c -s dx | | 
 |             Matrix = | D E F |,  R(degrees, px, py) = | s  c dy | | 
 |                      | G H I |                        | 0  0  1 | | 
 |  | 
 |         where | 
 |  | 
 |             c  = cos(degrees) | 
 |             s  = sin(degrees) | 
 |             dx =  s * py + (1 - c) * px | 
 |             dy = -s * px + (1 - c) * py | 
 |  | 
 |         sets SkMatrix to: | 
 |  | 
 |                                           | A B C | | c -s dx |   | Ac+Bs -As+Bc A*dx+B*dy+C | | 
 |             Matrix * R(degrees, px, py) = | D E F | | s  c dy | = | Dc+Es -Ds+Ec D*dx+E*dy+F | | 
 |                                           | G H I | | 0  0  1 |   | Gc+Hs -Gs+Hc G*dx+H*dy+I | | 
 |  | 
 |         @param degrees  angle of axes relative to upright axes | 
 |         @param px       pivot on x-axis | 
 |         @param py       pivot on y-axis | 
 |     */ | 
 |     SkMatrix& preRotate(SkScalar degrees, SkScalar px, SkScalar py); | 
 |  | 
 |     /** Sets SkMatrix to SkMatrix multiplied by SkMatrix constructed from rotating by degrees | 
 |         about pivot point (0, 0). | 
 |         This can be thought of as rotating about the origin before applying SkMatrix. | 
 |  | 
 |         Positive degrees rotates clockwise. | 
 |  | 
 |         Given: | 
 |  | 
 |                      | A B C |                        | c -s 0 | | 
 |             Matrix = | D E F |,  R(degrees, px, py) = | s  c 0 | | 
 |                      | G H I |                        | 0  0 1 | | 
 |  | 
 |         where | 
 |  | 
 |             c  = cos(degrees) | 
 |             s  = sin(degrees) | 
 |  | 
 |         sets SkMatrix to: | 
 |  | 
 |                                           | A B C | | c -s 0 |   | Ac+Bs -As+Bc C | | 
 |             Matrix * R(degrees, px, py) = | D E F | | s  c 0 | = | Dc+Es -Ds+Ec F | | 
 |                                           | G H I | | 0  0 1 |   | Gc+Hs -Gs+Hc I | | 
 |  | 
 |         @param degrees  angle of axes relative to upright axes | 
 |     */ | 
 |     SkMatrix& preRotate(SkScalar degrees); | 
 |  | 
 |     /** Sets SkMatrix to SkMatrix multiplied by SkMatrix constructed from skewing by (kx, ky) | 
 |         about pivot point (px, py). | 
 |         This can be thought of as skewing about a pivot point before applying SkMatrix. | 
 |  | 
 |         Given: | 
 |  | 
 |                      | A B C |                       |  1 kx dx | | 
 |             Matrix = | D E F |,  K(kx, ky, px, py) = | ky  1 dy | | 
 |                      | G H I |                       |  0  0  1 | | 
 |  | 
 |         where | 
 |  | 
 |             dx = -kx * py | 
 |             dy = -ky * px | 
 |  | 
 |         sets SkMatrix to: | 
 |  | 
 |                                          | A B C | |  1 kx dx |   | A+B*ky A*kx+B A*dx+B*dy+C | | 
 |             Matrix * K(kx, ky, px, py) = | D E F | | ky  1 dy | = | D+E*ky D*kx+E D*dx+E*dy+F | | 
 |                                          | G H I | |  0  0  1 |   | G+H*ky G*kx+H G*dx+H*dy+I | | 
 |  | 
 |         @param kx  horizontal skew factor | 
 |         @param ky  vertical skew factor | 
 |         @param px  pivot on x-axis | 
 |         @param py  pivot on y-axis | 
 |     */ | 
 |     SkMatrix& preSkew(SkScalar kx, SkScalar ky, SkScalar px, SkScalar py); | 
 |  | 
 |     /** Sets SkMatrix to SkMatrix multiplied by SkMatrix constructed from skewing by (kx, ky) | 
 |         about pivot point (0, 0). | 
 |         This can be thought of as skewing about the origin before applying SkMatrix. | 
 |  | 
 |         Given: | 
 |  | 
 |                      | A B C |               |  1 kx 0 | | 
 |             Matrix = | D E F |,  K(kx, ky) = | ky  1 0 | | 
 |                      | G H I |               |  0  0 1 | | 
 |  | 
 |         sets SkMatrix to: | 
 |  | 
 |                                  | A B C | |  1 kx 0 |   | A+B*ky A*kx+B C | | 
 |             Matrix * K(kx, ky) = | D E F | | ky  1 0 | = | D+E*ky D*kx+E F | | 
 |                                  | G H I | |  0  0 1 |   | G+H*ky G*kx+H I | | 
 |  | 
 |         @param kx  horizontal skew factor | 
 |         @param ky  vertical skew factor | 
 |     */ | 
 |     SkMatrix& preSkew(SkScalar kx, SkScalar ky); | 
 |  | 
 |     /** Sets SkMatrix to SkMatrix multiplied by SkMatrix other. | 
 |         This can be thought of mapping by other before applying SkMatrix. | 
 |  | 
 |         Given: | 
 |  | 
 |                      | A B C |          | J K L | | 
 |             Matrix = | D E F |, other = | M N O | | 
 |                      | G H I |          | P Q R | | 
 |  | 
 |         sets SkMatrix to: | 
 |  | 
 |                              | A B C |   | J K L |   | AJ+BM+CP AK+BN+CQ AL+BO+CR | | 
 |             Matrix * other = | D E F | * | M N O | = | DJ+EM+FP DK+EN+FQ DL+EO+FR | | 
 |                              | G H I |   | P Q R |   | GJ+HM+IP GK+HN+IQ GL+HO+IR | | 
 |  | 
 |         @param other  SkMatrix on right side of multiply expression | 
 |     */ | 
 |     SkMatrix& preConcat(const SkMatrix& other); | 
 |  | 
 |     /** Sets SkMatrix to SkMatrix constructed from translation (dx, dy) multiplied by SkMatrix. | 
 |         This can be thought of as moving the point to be mapped after applying SkMatrix. | 
 |  | 
 |         Given: | 
 |  | 
 |                      | J K L |               | 1 0 dx | | 
 |             Matrix = | M N O |,  T(dx, dy) = | 0 1 dy | | 
 |                      | P Q R |               | 0 0  1 | | 
 |  | 
 |         sets SkMatrix to: | 
 |  | 
 |                                  | 1 0 dx | | J K L |   | J+dx*P K+dx*Q L+dx*R | | 
 |             T(dx, dy) * Matrix = | 0 1 dy | | M N O | = | M+dy*P N+dy*Q O+dy*R | | 
 |                                  | 0 0  1 | | P Q R |   |      P      Q      R | | 
 |  | 
 |         @param dx  x-axis translation after applying SkMatrix | 
 |         @param dy  y-axis translation after applying SkMatrix | 
 |     */ | 
 |     SkMatrix& postTranslate(SkScalar dx, SkScalar dy); | 
 |  | 
 |     /** Sets SkMatrix to SkMatrix constructed from scaling by (sx, sy) about pivot point | 
 |         (px, py), multiplied by SkMatrix. | 
 |         This can be thought of as scaling about a pivot point after applying SkMatrix. | 
 |  | 
 |         Given: | 
 |  | 
 |                      | J K L |                       | sx  0 dx | | 
 |             Matrix = | M N O |,  S(sx, sy, px, py) = |  0 sy dy | | 
 |                      | P Q R |                       |  0  0  1 | | 
 |  | 
 |         where | 
 |  | 
 |             dx = px - sx * px | 
 |             dy = py - sy * py | 
 |  | 
 |         sets SkMatrix to: | 
 |  | 
 |                                          | sx  0 dx | | J K L |   | sx*J+dx*P sx*K+dx*Q sx*L+dx+R | | 
 |             S(sx, sy, px, py) * Matrix = |  0 sy dy | | M N O | = | sy*M+dy*P sy*N+dy*Q sy*O+dy*R | | 
 |                                          |  0  0  1 | | P Q R |   |         P         Q         R | | 
 |  | 
 |         @param sx  horizontal scale factor | 
 |         @param sy  vertical scale factor | 
 |         @param px  pivot on x-axis | 
 |         @param py  pivot on y-axis | 
 |     */ | 
 |     SkMatrix& postScale(SkScalar sx, SkScalar sy, SkScalar px, SkScalar py); | 
 |  | 
 |     /** Sets SkMatrix to SkMatrix constructed from scaling by (sx, sy) about pivot point | 
 |         (0, 0), multiplied by SkMatrix. | 
 |         This can be thought of as scaling about the origin after applying SkMatrix. | 
 |  | 
 |         Given: | 
 |  | 
 |                      | J K L |               | sx  0  0 | | 
 |             Matrix = | M N O |,  S(sx, sy) = |  0 sy  0 | | 
 |                      | P Q R |               |  0  0  1 | | 
 |  | 
 |         sets SkMatrix to: | 
 |  | 
 |                                  | sx  0  0 | | J K L |   | sx*J sx*K sx*L | | 
 |             S(sx, sy) * Matrix = |  0 sy  0 | | M N O | = | sy*M sy*N sy*O | | 
 |                                  |  0  0  1 | | P Q R |   |    P    Q    R | | 
 |  | 
 |         @param sx  horizontal scale factor | 
 |         @param sy  vertical scale factor | 
 |     */ | 
 |     SkMatrix& postScale(SkScalar sx, SkScalar sy); | 
 |  | 
 |     /** Sets SkMatrix to SkMatrix constructed from rotating by degrees about pivot point | 
 |         (px, py), multiplied by SkMatrix. | 
 |         This can be thought of as rotating about a pivot point after applying SkMatrix. | 
 |  | 
 |         Positive degrees rotates clockwise. | 
 |  | 
 |         Given: | 
 |  | 
 |                      | J K L |                        | c -s dx | | 
 |             Matrix = | M N O |,  R(degrees, px, py) = | s  c dy | | 
 |                      | P Q R |                        | 0  0  1 | | 
 |  | 
 |         where | 
 |  | 
 |             c  = cos(degrees) | 
 |             s  = sin(degrees) | 
 |             dx =  s * py + (1 - c) * px | 
 |             dy = -s * px + (1 - c) * py | 
 |  | 
 |         sets SkMatrix to: | 
 |  | 
 |                                           |c -s dx| |J K L|   |cJ-sM+dx*P cK-sN+dx*Q cL-sO+dx+R| | 
 |             R(degrees, px, py) * Matrix = |s  c dy| |M N O| = |sJ+cM+dy*P sK+cN+dy*Q sL+cO+dy*R| | 
 |                                           |0  0  1| |P Q R|   |         P          Q          R| | 
 |  | 
 |         @param degrees  angle of axes relative to upright axes | 
 |         @param px       pivot on x-axis | 
 |         @param py       pivot on y-axis | 
 |     */ | 
 |     SkMatrix& postRotate(SkScalar degrees, SkScalar px, SkScalar py); | 
 |  | 
 |     /** Sets SkMatrix to SkMatrix constructed from rotating by degrees about pivot point | 
 |         (0, 0), multiplied by SkMatrix. | 
 |         This can be thought of as rotating about the origin after applying SkMatrix. | 
 |  | 
 |         Positive degrees rotates clockwise. | 
 |  | 
 |         Given: | 
 |  | 
 |                      | J K L |                        | c -s 0 | | 
 |             Matrix = | M N O |,  R(degrees, px, py) = | s  c 0 | | 
 |                      | P Q R |                        | 0  0 1 | | 
 |  | 
 |         where | 
 |  | 
 |             c  = cos(degrees) | 
 |             s  = sin(degrees) | 
 |  | 
 |         sets SkMatrix to: | 
 |  | 
 |                                           | c -s dx | | J K L |   | cJ-sM cK-sN cL-sO | | 
 |             R(degrees, px, py) * Matrix = | s  c dy | | M N O | = | sJ+cM sK+cN sL+cO | | 
 |                                           | 0  0  1 | | P Q R |   |     P     Q     R | | 
 |  | 
 |         @param degrees  angle of axes relative to upright axes | 
 |     */ | 
 |     SkMatrix& postRotate(SkScalar degrees); | 
 |  | 
 |     /** Sets SkMatrix to SkMatrix constructed from skewing by (kx, ky) about pivot point | 
 |         (px, py), multiplied by SkMatrix. | 
 |         This can be thought of as skewing about a pivot point after applying SkMatrix. | 
 |  | 
 |         Given: | 
 |  | 
 |                      | J K L |                       |  1 kx dx | | 
 |             Matrix = | M N O |,  K(kx, ky, px, py) = | ky  1 dy | | 
 |                      | P Q R |                       |  0  0  1 | | 
 |  | 
 |         where | 
 |  | 
 |             dx = -kx * py | 
 |             dy = -ky * px | 
 |  | 
 |         sets SkMatrix to: | 
 |  | 
 |                                          | 1 kx dx| |J K L|   |J+kx*M+dx*P K+kx*N+dx*Q L+kx*O+dx+R| | 
 |             K(kx, ky, px, py) * Matrix = |ky  1 dy| |M N O| = |ky*J+M+dy*P ky*K+N+dy*Q ky*L+O+dy*R| | 
 |                                          | 0  0  1| |P Q R|   |          P           Q           R| | 
 |  | 
 |         @param kx  horizontal skew factor | 
 |         @param ky  vertical skew factor | 
 |         @param px  pivot on x-axis | 
 |         @param py  pivot on y-axis | 
 |     */ | 
 |     SkMatrix& postSkew(SkScalar kx, SkScalar ky, SkScalar px, SkScalar py); | 
 |  | 
 |     /** Sets SkMatrix to SkMatrix constructed from skewing by (kx, ky) about pivot point | 
 |         (0, 0), multiplied by SkMatrix. | 
 |         This can be thought of as skewing about the origin after applying SkMatrix. | 
 |  | 
 |         Given: | 
 |  | 
 |                      | J K L |               |  1 kx 0 | | 
 |             Matrix = | M N O |,  K(kx, ky) = | ky  1 0 | | 
 |                      | P Q R |               |  0  0 1 | | 
 |  | 
 |         sets SkMatrix to: | 
 |  | 
 |                                  |  1 kx 0 | | J K L |   | J+kx*M K+kx*N L+kx*O | | 
 |             K(kx, ky) * Matrix = | ky  1 0 | | M N O | = | ky*J+M ky*K+N ky*L+O | | 
 |                                  |  0  0 1 | | P Q R |   |      P      Q      R | | 
 |  | 
 |         @param kx  horizontal skew factor | 
 |         @param ky  vertical skew factor | 
 |     */ | 
 |     SkMatrix& postSkew(SkScalar kx, SkScalar ky); | 
 |  | 
 |     /** Sets SkMatrix to SkMatrix other multiplied by SkMatrix. | 
 |         This can be thought of mapping by other after applying SkMatrix. | 
 |  | 
 |         Given: | 
 |  | 
 |                      | J K L |           | A B C | | 
 |             Matrix = | M N O |,  other = | D E F | | 
 |                      | P Q R |           | G H I | | 
 |  | 
 |         sets SkMatrix to: | 
 |  | 
 |                              | A B C |   | J K L |   | AJ+BM+CP AK+BN+CQ AL+BO+CR | | 
 |             other * Matrix = | D E F | * | M N O | = | DJ+EM+FP DK+EN+FQ DL+EO+FR | | 
 |                              | G H I |   | P Q R |   | GJ+HM+IP GK+HN+IQ GL+HO+IR | | 
 |  | 
 |         @param other  SkMatrix on left side of multiply expression | 
 |     */ | 
 |     SkMatrix& postConcat(const SkMatrix& other); | 
 |  | 
 | #ifndef SK_SUPPORT_LEGACY_MATRIX_RECTTORECT | 
 | private: | 
 | #endif | 
 |     /** Sets SkMatrix to scale and translate src SkRect to dst SkRect. stf selects whether | 
 |         mapping completely fills dst or preserves the aspect ratio, and how to align | 
 |         src within dst. Returns false if src is empty, and sets SkMatrix to identity. | 
 |         Returns true if dst is empty, and sets SkMatrix to: | 
 |  | 
 |             | 0 0 0 | | 
 |             | 0 0 0 | | 
 |             | 0 0 1 | | 
 |  | 
 |         @param src  SkRect to map from | 
 |         @param dst  SkRect to map to | 
 |         @return     true if SkMatrix can represent SkRect mapping | 
 |  | 
 |         example: https://fiddle.skia.org/c/@Matrix_setRectToRect | 
 |     */ | 
 |     bool setRectToRect(const SkRect& src, const SkRect& dst, ScaleToFit stf); | 
 |  | 
 |     /** Returns SkMatrix set to scale and translate src SkRect to dst SkRect. stf selects | 
 |         whether mapping completely fills dst or preserves the aspect ratio, and how to | 
 |         align src within dst. Returns the identity SkMatrix if src is empty. If dst is | 
 |         empty, returns SkMatrix set to: | 
 |  | 
 |             | 0 0 0 | | 
 |             | 0 0 0 | | 
 |             | 0 0 1 | | 
 |  | 
 |         @param src  SkRect to map from | 
 |         @param dst  SkRect to map to | 
 |         @return     SkMatrix mapping src to dst | 
 |     */ | 
 |     static SkMatrix MakeRectToRect(const SkRect& src, const SkRect& dst, ScaleToFit stf) { | 
 |         SkMatrix m; | 
 |         m.setRectToRect(src, dst, stf); | 
 |         return m; | 
 |     } | 
 | #ifndef SK_SUPPORT_LEGACY_MATRIX_RECTTORECT | 
 | public: | 
 | #endif | 
 |  | 
 |     /** Sets SkMatrix to map src to dst. count must be zero or greater, and four or less. | 
 |  | 
 |         If count is zero, sets SkMatrix to identity and returns true. | 
 |         If count is one, sets SkMatrix to translate and returns true. | 
 |         If count is two or more, sets SkMatrix to map SkPoint if possible; returns false | 
 |         if SkMatrix cannot be constructed. If count is four, SkMatrix may include | 
 |         perspective. | 
 |  | 
 |         @param src    SkPoint to map from | 
 |         @param dst    SkPoint to map to | 
 |         @param count  number of SkPoint in src and dst | 
 |         @return       true if SkMatrix was constructed successfully | 
 |  | 
 |         example: https://fiddle.skia.org/c/@Matrix_setPolyToPoly | 
 |     */ | 
 |     bool setPolyToPoly(const SkPoint src[], const SkPoint dst[], int count); | 
 |  | 
 |     /** Sets inverse to reciprocal matrix, returning true if SkMatrix can be inverted. | 
 |         Geometrically, if SkMatrix maps from source to destination, inverse SkMatrix | 
 |         maps from destination to source. If SkMatrix can not be inverted, inverse is | 
 |         unchanged. | 
 |  | 
 |         @param inverse  storage for inverted SkMatrix; may be nullptr | 
 |         @return         true if SkMatrix can be inverted | 
 |     */ | 
 |     bool SK_WARN_UNUSED_RESULT invert(SkMatrix* inverse) const { | 
 |         // Allow the trivial case to be inlined. | 
 |         if (this->isIdentity()) { | 
 |             if (inverse) { | 
 |                 inverse->reset(); | 
 |             } | 
 |             return true; | 
 |         } | 
 |         return this->invertNonIdentity(inverse); | 
 |     } | 
 |  | 
 |     /** Fills affine with identity values in column major order. | 
 |         Sets affine to: | 
 |  | 
 |             | 1 0 0 | | 
 |             | 0 1 0 | | 
 |  | 
 |         Affine 3 by 2 matrices in column major order are used by OpenGL and XPS. | 
 |  | 
 |         @param affine  storage for 3 by 2 affine matrix | 
 |  | 
 |         example: https://fiddle.skia.org/c/@Matrix_SetAffineIdentity | 
 |     */ | 
 |     static void SetAffineIdentity(SkScalar affine[6]); | 
 |  | 
 |     /** Fills affine in column major order. Sets affine to: | 
 |  | 
 |             | scale-x  skew-x translate-x | | 
 |             | skew-y  scale-y translate-y | | 
 |  | 
 |         If SkMatrix contains perspective, returns false and leaves affine unchanged. | 
 |  | 
 |         @param affine  storage for 3 by 2 affine matrix; may be nullptr | 
 |         @return        true if SkMatrix does not contain perspective | 
 |     */ | 
 |     bool SK_WARN_UNUSED_RESULT asAffine(SkScalar affine[6]) const; | 
 |  | 
 |     /** Sets SkMatrix to affine values, passed in column major order. Given affine, | 
 |         column, then row, as: | 
 |  | 
 |             | scale-x  skew-x translate-x | | 
 |             |  skew-y scale-y translate-y | | 
 |  | 
 |         SkMatrix is set, row, then column, to: | 
 |  | 
 |             | scale-x  skew-x translate-x | | 
 |             |  skew-y scale-y translate-y | | 
 |             |       0       0           1 | | 
 |  | 
 |         @param affine  3 by 2 affine matrix | 
 |     */ | 
 |     SkMatrix& setAffine(const SkScalar affine[6]); | 
 |  | 
 |     /** | 
 |      *  A matrix is categorized as 'perspective' if the bottom row is not [0, 0, 1]. | 
 |      *  However, for most uses (e.g. mapPoints) a bottom row of [0, 0, X] behaves like a | 
 |      *  non-perspective matrix, though it will be categorized as perspective. Calling | 
 |      *  normalizePerspective() will change the matrix such that, if its bottom row was [0, 0, X], | 
 |      *  it will be changed to [0, 0, 1] by scaling the rest of the matrix by 1/X. | 
 |      * | 
 |      *  | A B C |    | A/X B/X C/X | | 
 |      *  | D E F | -> | D/X E/X F/X |   for X != 0 | 
 |      *  | 0 0 X |    |  0   0   1  | | 
 |      */ | 
 |     void normalizePerspective() { | 
 |         if (fMat[8] != 1) { | 
 |             this->doNormalizePerspective(); | 
 |         } | 
 |     } | 
 |  | 
 |     /** Maps src SkPoint array of length count to dst SkPoint array of equal or greater | 
 |         length. SkPoint are mapped by multiplying each SkPoint by SkMatrix. Given: | 
 |  | 
 |                      | A B C |        | x | | 
 |             Matrix = | D E F |,  pt = | y | | 
 |                      | G H I |        | 1 | | 
 |  | 
 |         where | 
 |  | 
 |             for (i = 0; i < count; ++i) { | 
 |                 x = src[i].fX | 
 |                 y = src[i].fY | 
 |             } | 
 |  | 
 |         each dst SkPoint is computed as: | 
 |  | 
 |                           |A B C| |x|                               Ax+By+C   Dx+Ey+F | 
 |             Matrix * pt = |D E F| |y| = |Ax+By+C Dx+Ey+F Gx+Hy+I| = ------- , ------- | 
 |                           |G H I| |1|                               Gx+Hy+I   Gx+Hy+I | 
 |  | 
 |         src and dst may point to the same storage. | 
 |  | 
 |         @param dst    storage for mapped SkPoint | 
 |         @param src    SkPoint to transform | 
 |         @param count  number of SkPoint to transform | 
 |  | 
 |         example: https://fiddle.skia.org/c/@Matrix_mapPoints | 
 |     */ | 
 |     void mapPoints(SkPoint dst[], const SkPoint src[], int count) const; | 
 |  | 
 |     /** Maps pts SkPoint array of length count in place. SkPoint are mapped by multiplying | 
 |         each SkPoint by SkMatrix. Given: | 
 |  | 
 |                      | A B C |        | x | | 
 |             Matrix = | D E F |,  pt = | y | | 
 |                      | G H I |        | 1 | | 
 |  | 
 |         where | 
 |  | 
 |             for (i = 0; i < count; ++i) { | 
 |                 x = pts[i].fX | 
 |                 y = pts[i].fY | 
 |             } | 
 |  | 
 |         each resulting pts SkPoint is computed as: | 
 |  | 
 |                           |A B C| |x|                               Ax+By+C   Dx+Ey+F | 
 |             Matrix * pt = |D E F| |y| = |Ax+By+C Dx+Ey+F Gx+Hy+I| = ------- , ------- | 
 |                           |G H I| |1|                               Gx+Hy+I   Gx+Hy+I | 
 |  | 
 |         @param pts    storage for mapped SkPoint | 
 |         @param count  number of SkPoint to transform | 
 |     */ | 
 |     void mapPoints(SkPoint pts[], int count) const { | 
 |         this->mapPoints(pts, pts, count); | 
 |     } | 
 |  | 
 |     /** Maps src SkPoint3 array of length count to dst SkPoint3 array, which must of length count or | 
 |         greater. SkPoint3 array is mapped by multiplying each SkPoint3 by SkMatrix. Given: | 
 |  | 
 |                      | A B C |         | x | | 
 |             Matrix = | D E F |,  src = | y | | 
 |                      | G H I |         | z | | 
 |  | 
 |         each resulting dst SkPoint is computed as: | 
 |  | 
 |                            |A B C| |x| | 
 |             Matrix * src = |D E F| |y| = |Ax+By+Cz Dx+Ey+Fz Gx+Hy+Iz| | 
 |                            |G H I| |z| | 
 |  | 
 |         @param dst    storage for mapped SkPoint3 array | 
 |         @param src    SkPoint3 array to transform | 
 |         @param count  items in SkPoint3 array to transform | 
 |  | 
 |         example: https://fiddle.skia.org/c/@Matrix_mapHomogeneousPoints | 
 |     */ | 
 |     void mapHomogeneousPoints(SkPoint3 dst[], const SkPoint3 src[], int count) const; | 
 |  | 
 |     /** | 
 |      *  Returns homogeneous points, starting with 2D src points (with implied w = 1). | 
 |      */ | 
 |     void mapHomogeneousPoints(SkPoint3 dst[], const SkPoint src[], int count) const; | 
 |  | 
 |     /** Returns SkPoint pt multiplied by SkMatrix. Given: | 
 |  | 
 |                      | A B C |        | x | | 
 |             Matrix = | D E F |,  pt = | y | | 
 |                      | G H I |        | 1 | | 
 |  | 
 |         result is computed as: | 
 |  | 
 |                           |A B C| |x|                               Ax+By+C   Dx+Ey+F | 
 |             Matrix * pt = |D E F| |y| = |Ax+By+C Dx+Ey+F Gx+Hy+I| = ------- , ------- | 
 |                           |G H I| |1|                               Gx+Hy+I   Gx+Hy+I | 
 |  | 
 |         @param p  SkPoint to map | 
 |         @return   mapped SkPoint | 
 |     */ | 
 |     SkPoint mapPoint(SkPoint pt) const { | 
 |         SkPoint result; | 
 |         this->mapXY(pt.x(), pt.y(), &result); | 
 |         return result; | 
 |     } | 
 |  | 
 |     /** Maps SkPoint (x, y) to result. SkPoint is mapped by multiplying by SkMatrix. Given: | 
 |  | 
 |                      | A B C |        | x | | 
 |             Matrix = | D E F |,  pt = | y | | 
 |                      | G H I |        | 1 | | 
 |  | 
 |         result is computed as: | 
 |  | 
 |                           |A B C| |x|                               Ax+By+C   Dx+Ey+F | 
 |             Matrix * pt = |D E F| |y| = |Ax+By+C Dx+Ey+F Gx+Hy+I| = ------- , ------- | 
 |                           |G H I| |1|                               Gx+Hy+I   Gx+Hy+I | 
 |  | 
 |         @param x       x-axis value of SkPoint to map | 
 |         @param y       y-axis value of SkPoint to map | 
 |         @param result  storage for mapped SkPoint | 
 |  | 
 |         example: https://fiddle.skia.org/c/@Matrix_mapXY | 
 |     */ | 
 |     void mapXY(SkScalar x, SkScalar y, SkPoint* result) const; | 
 |  | 
 |     /** Returns SkPoint (x, y) multiplied by SkMatrix. Given: | 
 |  | 
 |                      | A B C |        | x | | 
 |             Matrix = | D E F |,  pt = | y | | 
 |                      | G H I |        | 1 | | 
 |  | 
 |         result is computed as: | 
 |  | 
 |                           |A B C| |x|                               Ax+By+C   Dx+Ey+F | 
 |             Matrix * pt = |D E F| |y| = |Ax+By+C Dx+Ey+F Gx+Hy+I| = ------- , ------- | 
 |                           |G H I| |1|                               Gx+Hy+I   Gx+Hy+I | 
 |  | 
 |         @param x  x-axis value of SkPoint to map | 
 |         @param y  y-axis value of SkPoint to map | 
 |         @return   mapped SkPoint | 
 |     */ | 
 |     SkPoint mapXY(SkScalar x, SkScalar y) const { | 
 |         SkPoint result; | 
 |         this->mapXY(x,y, &result); | 
 |         return result; | 
 |     } | 
 |  | 
 |  | 
 |     /** Returns (0, 0) multiplied by SkMatrix. Given: | 
 |  | 
 |                      | A B C |        | 0 | | 
 |             Matrix = | D E F |,  pt = | 0 | | 
 |                      | G H I |        | 1 | | 
 |  | 
 |         result is computed as: | 
 |  | 
 |                           |A B C| |0|             C    F | 
 |             Matrix * pt = |D E F| |0| = |C F I| = -  , - | 
 |                           |G H I| |1|             I    I | 
 |  | 
 |         @return   mapped (0, 0) | 
 |     */ | 
 |     SkPoint mapOrigin() const { | 
 |         SkScalar x = this->getTranslateX(), | 
 |                  y = this->getTranslateY(); | 
 |         if (this->hasPerspective()) { | 
 |             SkScalar w = fMat[kMPersp2]; | 
 |             if (w) { w = 1 / w; } | 
 |             x *= w; | 
 |             y *= w; | 
 |         } | 
 |         return {x, y}; | 
 |     } | 
 |  | 
 |     /** Maps src vector array of length count to vector SkPoint array of equal or greater | 
 |         length. Vectors are mapped by multiplying each vector by SkMatrix, treating | 
 |         SkMatrix translation as zero. Given: | 
 |  | 
 |                      | A B 0 |         | x | | 
 |             Matrix = | D E 0 |,  src = | y | | 
 |                      | G H I |         | 1 | | 
 |  | 
 |         where | 
 |  | 
 |             for (i = 0; i < count; ++i) { | 
 |                 x = src[i].fX | 
 |                 y = src[i].fY | 
 |             } | 
 |  | 
 |         each dst vector is computed as: | 
 |  | 
 |                            |A B 0| |x|                            Ax+By     Dx+Ey | 
 |             Matrix * src = |D E 0| |y| = |Ax+By Dx+Ey Gx+Hy+I| = ------- , ------- | 
 |                            |G H I| |1|                           Gx+Hy+I   Gx+Hy+I | 
 |  | 
 |         src and dst may point to the same storage. | 
 |  | 
 |         @param dst    storage for mapped vectors | 
 |         @param src    vectors to transform | 
 |         @param count  number of vectors to transform | 
 |  | 
 |         example: https://fiddle.skia.org/c/@Matrix_mapVectors | 
 |     */ | 
 |     void mapVectors(SkVector dst[], const SkVector src[], int count) const; | 
 |  | 
 |     /** Maps vecs vector array of length count in place, multiplying each vector by | 
 |         SkMatrix, treating SkMatrix translation as zero. Given: | 
 |  | 
 |                      | A B 0 |         | x | | 
 |             Matrix = | D E 0 |,  vec = | y | | 
 |                      | G H I |         | 1 | | 
 |  | 
 |         where | 
 |  | 
 |             for (i = 0; i < count; ++i) { | 
 |                 x = vecs[i].fX | 
 |                 y = vecs[i].fY | 
 |             } | 
 |  | 
 |         each result vector is computed as: | 
 |  | 
 |                            |A B 0| |x|                            Ax+By     Dx+Ey | 
 |             Matrix * vec = |D E 0| |y| = |Ax+By Dx+Ey Gx+Hy+I| = ------- , ------- | 
 |                            |G H I| |1|                           Gx+Hy+I   Gx+Hy+I | 
 |  | 
 |         @param vecs   vectors to transform, and storage for mapped vectors | 
 |         @param count  number of vectors to transform | 
 |     */ | 
 |     void mapVectors(SkVector vecs[], int count) const { | 
 |         this->mapVectors(vecs, vecs, count); | 
 |     } | 
 |  | 
 |     /** Maps vector (dx, dy) to result. Vector is mapped by multiplying by SkMatrix, | 
 |         treating SkMatrix translation as zero. Given: | 
 |  | 
 |                      | A B 0 |         | dx | | 
 |             Matrix = | D E 0 |,  vec = | dy | | 
 |                      | G H I |         |  1 | | 
 |  | 
 |         each result vector is computed as: | 
 |  | 
 |                        |A B 0| |dx|                                        A*dx+B*dy     D*dx+E*dy | 
 |         Matrix * vec = |D E 0| |dy| = |A*dx+B*dy D*dx+E*dy G*dx+H*dy+I| = ----------- , ----------- | 
 |                        |G H I| | 1|                                       G*dx+H*dy+I   G*dx+*dHy+I | 
 |  | 
 |         @param dx      x-axis value of vector to map | 
 |         @param dy      y-axis value of vector to map | 
 |         @param result  storage for mapped vector | 
 |     */ | 
 |     void mapVector(SkScalar dx, SkScalar dy, SkVector* result) const { | 
 |         SkVector vec = { dx, dy }; | 
 |         this->mapVectors(result, &vec, 1); | 
 |     } | 
 |  | 
 |     /** Returns vector (dx, dy) multiplied by SkMatrix, treating SkMatrix translation as zero. | 
 |         Given: | 
 |  | 
 |                      | A B 0 |         | dx | | 
 |             Matrix = | D E 0 |,  vec = | dy | | 
 |                      | G H I |         |  1 | | 
 |  | 
 |         each result vector is computed as: | 
 |  | 
 |                        |A B 0| |dx|                                        A*dx+B*dy     D*dx+E*dy | 
 |         Matrix * vec = |D E 0| |dy| = |A*dx+B*dy D*dx+E*dy G*dx+H*dy+I| = ----------- , ----------- | 
 |                        |G H I| | 1|                                       G*dx+H*dy+I   G*dx+*dHy+I | 
 |  | 
 |         @param dx  x-axis value of vector to map | 
 |         @param dy  y-axis value of vector to map | 
 |         @return    mapped vector | 
 |     */ | 
 |     SkVector mapVector(SkScalar dx, SkScalar dy) const { | 
 |         SkVector vec = { dx, dy }; | 
 |         this->mapVectors(&vec, &vec, 1); | 
 |         return vec; | 
 |     } | 
 |  | 
 |     /** Sets dst to bounds of src corners mapped by SkMatrix. | 
 |         Returns true if mapped corners are dst corners. | 
 |  | 
 |         Returned value is the same as calling rectStaysRect(). | 
 |  | 
 |         @param dst  storage for bounds of mapped SkPoint | 
 |         @param src  SkRect to map | 
 |         @param pc   whether to apply perspective clipping | 
 |         @return     true if dst is equivalent to mapped src | 
 |  | 
 |         example: https://fiddle.skia.org/c/@Matrix_mapRect | 
 |     */ | 
 |     bool mapRect(SkRect* dst, const SkRect& src, | 
 |                  SkApplyPerspectiveClip pc = SkApplyPerspectiveClip::kYes) const; | 
 |  | 
 |     /** Sets rect to bounds of rect corners mapped by SkMatrix. | 
 |         Returns true if mapped corners are computed rect corners. | 
 |  | 
 |         Returned value is the same as calling rectStaysRect(). | 
 |  | 
 |         @param rect  rectangle to map, and storage for bounds of mapped corners | 
 |         @param pc    whether to apply perspective clipping | 
 |         @return      true if result is equivalent to mapped rect | 
 |     */ | 
 |     bool mapRect(SkRect* rect, SkApplyPerspectiveClip pc = SkApplyPerspectiveClip::kYes) const { | 
 |         return this->mapRect(rect, *rect, pc); | 
 |     } | 
 |  | 
 |     /** Returns bounds of src corners mapped by SkMatrix. | 
 |  | 
 |         @param src  rectangle to map | 
 |         @return     mapped bounds | 
 |     */ | 
 |     SkRect mapRect(const SkRect& src, | 
 |                    SkApplyPerspectiveClip pc = SkApplyPerspectiveClip::kYes) const { | 
 |         SkRect dst; | 
 |         (void)this->mapRect(&dst, src, pc); | 
 |         return dst; | 
 |     } | 
 |  | 
 |     /** Maps four corners of rect to dst. SkPoint are mapped by multiplying each | 
 |         rect corner by SkMatrix. rect corner is processed in this order: | 
 |         (rect.fLeft, rect.fTop), (rect.fRight, rect.fTop), (rect.fRight, rect.fBottom), | 
 |         (rect.fLeft, rect.fBottom). | 
 |  | 
 |         rect may be empty: rect.fLeft may be greater than or equal to rect.fRight; | 
 |         rect.fTop may be greater than or equal to rect.fBottom. | 
 |  | 
 |         Given: | 
 |  | 
 |                      | A B C |        | x | | 
 |             Matrix = | D E F |,  pt = | y | | 
 |                      | G H I |        | 1 | | 
 |  | 
 |         where pt is initialized from each of (rect.fLeft, rect.fTop), | 
 |         (rect.fRight, rect.fTop), (rect.fRight, rect.fBottom), (rect.fLeft, rect.fBottom), | 
 |         each dst SkPoint is computed as: | 
 |  | 
 |                           |A B C| |x|                               Ax+By+C   Dx+Ey+F | 
 |             Matrix * pt = |D E F| |y| = |Ax+By+C Dx+Ey+F Gx+Hy+I| = ------- , ------- | 
 |                           |G H I| |1|                               Gx+Hy+I   Gx+Hy+I | 
 |  | 
 |         @param dst   storage for mapped corner SkPoint | 
 |         @param rect  SkRect to map | 
 |  | 
 |         Note: this does not perform perspective clipping (as that might result in more than | 
 |               4 points, so results are suspect if the matrix contains perspective. | 
 |     */ | 
 |     void mapRectToQuad(SkPoint dst[4], const SkRect& rect) const { | 
 |         // This could potentially be faster if we only transformed each x and y of the rect once. | 
 |         rect.toQuad(dst); | 
 |         this->mapPoints(dst, 4); | 
 |     } | 
 |  | 
 |     /** Sets dst to bounds of src corners mapped by SkMatrix. If matrix contains | 
 |         elements other than scale or translate: asserts if SK_DEBUG is defined; | 
 |         otherwise, results are undefined. | 
 |  | 
 |         @param dst  storage for bounds of mapped SkPoint | 
 |         @param src  SkRect to map | 
 |  | 
 |         example: https://fiddle.skia.org/c/@Matrix_mapRectScaleTranslate | 
 |     */ | 
 |     void mapRectScaleTranslate(SkRect* dst, const SkRect& src) const; | 
 |  | 
 |     /** Returns geometric mean radius of ellipse formed by constructing circle of | 
 |         size radius, and mapping constructed circle with SkMatrix. The result squared is | 
 |         equal to the major axis length times the minor axis length. | 
 |         Result is not meaningful if SkMatrix contains perspective elements. | 
 |  | 
 |         @param radius  circle size to map | 
 |         @return        average mapped radius | 
 |  | 
 |         example: https://fiddle.skia.org/c/@Matrix_mapRadius | 
 |     */ | 
 |     SkScalar mapRadius(SkScalar radius) const; | 
 |  | 
 |     /** Compares a and b; returns true if a and b are numerically equal. Returns true | 
 |         even if sign of zero values are different. Returns false if either SkMatrix | 
 |         contains NaN, even if the other SkMatrix also contains NaN. | 
 |  | 
 |         @param a  SkMatrix to compare | 
 |         @param b  SkMatrix to compare | 
 |         @return   true if SkMatrix a and SkMatrix b are numerically equal | 
 |     */ | 
 |     friend SK_API bool operator==(const SkMatrix& a, const SkMatrix& b); | 
 |  | 
 |     /** Compares a and b; returns true if a and b are not numerically equal. Returns false | 
 |         even if sign of zero values are different. Returns true if either SkMatrix | 
 |         contains NaN, even if the other SkMatrix also contains NaN. | 
 |  | 
 |         @param a  SkMatrix to compare | 
 |         @param b  SkMatrix to compare | 
 |         @return   true if SkMatrix a and SkMatrix b are numerically not equal | 
 |     */ | 
 |     friend SK_API bool operator!=(const SkMatrix& a, const SkMatrix& b) { | 
 |         return !(a == b); | 
 |     } | 
 |  | 
 |     /** Writes text representation of SkMatrix to standard output. Floating point values | 
 |         are written with limited precision; it may not be possible to reconstruct | 
 |         original SkMatrix from output. | 
 |  | 
 |         example: https://fiddle.skia.org/c/@Matrix_dump | 
 |     */ | 
 |     void dump() const; | 
 |  | 
 |     /** Returns the minimum scaling factor of SkMatrix by decomposing the scaling and | 
 |         skewing elements. | 
 |         Returns -1 if scale factor overflows or SkMatrix contains perspective. | 
 |  | 
 |         @return  minimum scale factor | 
 |  | 
 |         example: https://fiddle.skia.org/c/@Matrix_getMinScale | 
 |     */ | 
 |     SkScalar getMinScale() const; | 
 |  | 
 |     /** Returns the maximum scaling factor of SkMatrix by decomposing the scaling and | 
 |         skewing elements. | 
 |         Returns -1 if scale factor overflows or SkMatrix contains perspective. | 
 |  | 
 |         @return  maximum scale factor | 
 |  | 
 |         example: https://fiddle.skia.org/c/@Matrix_getMaxScale | 
 |     */ | 
 |     SkScalar getMaxScale() const; | 
 |  | 
 |     /** Sets scaleFactors[0] to the minimum scaling factor, and scaleFactors[1] to the | 
 |         maximum scaling factor. Scaling factors are computed by decomposing | 
 |         the SkMatrix scaling and skewing elements. | 
 |  | 
 |         Returns true if scaleFactors are found; otherwise, returns false and sets | 
 |         scaleFactors to undefined values. | 
 |  | 
 |         @param scaleFactors  storage for minimum and maximum scale factors | 
 |         @return              true if scale factors were computed correctly | 
 |     */ | 
 |     bool SK_WARN_UNUSED_RESULT getMinMaxScales(SkScalar scaleFactors[2]) const; | 
 |  | 
 |     /** Decomposes SkMatrix into scale components and whatever remains. Returns false if | 
 |         SkMatrix could not be decomposed. | 
 |  | 
 |         Sets scale to portion of SkMatrix that scale axes. Sets remaining to SkMatrix | 
 |         with scaling factored out. remaining may be passed as nullptr | 
 |         to determine if SkMatrix can be decomposed without computing remainder. | 
 |  | 
 |         Returns true if scale components are found. scale and remaining are | 
 |         unchanged if SkMatrix contains perspective; scale factors are not finite, or | 
 |         are nearly zero. | 
 |  | 
 |         On success: Matrix = Remaining * scale. | 
 |  | 
 |         @param scale      axes scaling factors; may be nullptr | 
 |         @param remaining  SkMatrix without scaling; may be nullptr | 
 |         @return           true if scale can be computed | 
 |  | 
 |         example: https://fiddle.skia.org/c/@Matrix_decomposeScale | 
 |     */ | 
 |     bool decomposeScale(SkSize* scale, SkMatrix* remaining = nullptr) const; | 
 |  | 
 |     /** Returns reference to const identity SkMatrix. Returned SkMatrix is set to: | 
 |  | 
 |             | 1 0 0 | | 
 |             | 0 1 0 | | 
 |             | 0 0 1 | | 
 |  | 
 |         @return  const identity SkMatrix | 
 |  | 
 |         example: https://fiddle.skia.org/c/@Matrix_I | 
 |     */ | 
 |     static const SkMatrix& I(); | 
 |  | 
 |     /** Returns reference to a const SkMatrix with invalid values. Returned SkMatrix is set | 
 |         to: | 
 |  | 
 |             | SK_ScalarMax SK_ScalarMax SK_ScalarMax | | 
 |             | SK_ScalarMax SK_ScalarMax SK_ScalarMax | | 
 |             | SK_ScalarMax SK_ScalarMax SK_ScalarMax | | 
 |  | 
 |         @return  const invalid SkMatrix | 
 |  | 
 |         example: https://fiddle.skia.org/c/@Matrix_InvalidMatrix | 
 |     */ | 
 |     static const SkMatrix& InvalidMatrix(); | 
 |  | 
 |     /** Returns SkMatrix a multiplied by SkMatrix b. | 
 |  | 
 |         Given: | 
 |  | 
 |                 | A B C |      | J K L | | 
 |             a = | D E F |, b = | M N O | | 
 |                 | G H I |      | P Q R | | 
 |  | 
 |         sets SkMatrix to: | 
 |  | 
 |                     | A B C |   | J K L |   | AJ+BM+CP AK+BN+CQ AL+BO+CR | | 
 |             a * b = | D E F | * | M N O | = | DJ+EM+FP DK+EN+FQ DL+EO+FR | | 
 |                     | G H I |   | P Q R |   | GJ+HM+IP GK+HN+IQ GL+HO+IR | | 
 |  | 
 |         @param a  SkMatrix on left side of multiply expression | 
 |         @param b  SkMatrix on right side of multiply expression | 
 |         @return   SkMatrix computed from a times b | 
 |     */ | 
 |     static SkMatrix Concat(const SkMatrix& a, const SkMatrix& b) { | 
 |         SkMatrix result; | 
 |         result.setConcat(a, b); | 
 |         return result; | 
 |     } | 
 |  | 
 |     friend SkMatrix operator*(const SkMatrix& a, const SkMatrix& b) { | 
 |         return Concat(a, b); | 
 |     } | 
 |  | 
 |     /** Sets internal cache to unknown state. Use to force update after repeated | 
 |         modifications to SkMatrix element reference returned by operator[](int index). | 
 |     */ | 
 |     void dirtyMatrixTypeCache() { | 
 |         this->setTypeMask(kUnknown_Mask); | 
 |     } | 
 |  | 
 |     /** Initializes SkMatrix with scale and translate elements. | 
 |  | 
 |             | sx  0 tx | | 
 |             |  0 sy ty | | 
 |             |  0  0  1 | | 
 |  | 
 |         @param sx  horizontal scale factor to store | 
 |         @param sy  vertical scale factor to store | 
 |         @param tx  horizontal translation to store | 
 |         @param ty  vertical translation to store | 
 |     */ | 
 |     void setScaleTranslate(SkScalar sx, SkScalar sy, SkScalar tx, SkScalar ty) { | 
 |         fMat[kMScaleX] = sx; | 
 |         fMat[kMSkewX]  = 0; | 
 |         fMat[kMTransX] = tx; | 
 |  | 
 |         fMat[kMSkewY]  = 0; | 
 |         fMat[kMScaleY] = sy; | 
 |         fMat[kMTransY] = ty; | 
 |  | 
 |         fMat[kMPersp0] = 0; | 
 |         fMat[kMPersp1] = 0; | 
 |         fMat[kMPersp2] = 1; | 
 |  | 
 |         int mask = 0; | 
 |         if (sx != 1 || sy != 1) { | 
 |             mask |= kScale_Mask; | 
 |         } | 
 |         if (tx || ty) { | 
 |             mask |= kTranslate_Mask; | 
 |         } | 
 |         this->setTypeMask(mask | kRectStaysRect_Mask); | 
 |     } | 
 |  | 
 |     /** Returns true if all elements of the matrix are finite. Returns false if any | 
 |         element is infinity, or NaN. | 
 |  | 
 |         @return  true if matrix has only finite elements | 
 |     */ | 
 |     bool isFinite() const { return SkScalarsAreFinite(fMat, 9); } | 
 |  | 
 | private: | 
 |     /** Set if the matrix will map a rectangle to another rectangle. This | 
 |         can be true if the matrix is scale-only, or rotates a multiple of | 
 |         90 degrees. | 
 |  | 
 |         This bit will be set on identity matrices | 
 |     */ | 
 |     static constexpr int kRectStaysRect_Mask = 0x10; | 
 |  | 
 |     /** Set if the perspective bit is valid even though the rest of | 
 |         the matrix is Unknown. | 
 |     */ | 
 |     static constexpr int kOnlyPerspectiveValid_Mask = 0x40; | 
 |  | 
 |     static constexpr int kUnknown_Mask = 0x80; | 
 |  | 
 |     static constexpr int kORableMasks = kTranslate_Mask | | 
 |                                         kScale_Mask | | 
 |                                         kAffine_Mask | | 
 |                                         kPerspective_Mask; | 
 |  | 
 |     static constexpr int kAllMasks = kTranslate_Mask | | 
 |                                      kScale_Mask | | 
 |                                      kAffine_Mask | | 
 |                                      kPerspective_Mask | | 
 |                                      kRectStaysRect_Mask; | 
 |  | 
 |     SkScalar        fMat[9]; | 
 |     mutable int32_t fTypeMask; | 
 |  | 
 |     constexpr SkMatrix(SkScalar sx, SkScalar kx, SkScalar tx, | 
 |                        SkScalar ky, SkScalar sy, SkScalar ty, | 
 |                        SkScalar p0, SkScalar p1, SkScalar p2, int typeMask) | 
 |         : fMat{sx, kx, tx, | 
 |                ky, sy, ty, | 
 |                p0, p1, p2} | 
 |         , fTypeMask(typeMask) {} | 
 |  | 
 |     static void ComputeInv(SkScalar dst[9], const SkScalar src[9], double invDet, bool isPersp); | 
 |  | 
 |     uint8_t computeTypeMask() const; | 
 |     uint8_t computePerspectiveTypeMask() const; | 
 |  | 
 |     void setTypeMask(int mask) { | 
 |         // allow kUnknown or a valid mask | 
 |         SkASSERT(kUnknown_Mask == mask || (mask & kAllMasks) == mask || | 
 |                  ((kUnknown_Mask | kOnlyPerspectiveValid_Mask) & mask) | 
 |                  == (kUnknown_Mask | kOnlyPerspectiveValid_Mask)); | 
 |         fTypeMask = mask; | 
 |     } | 
 |  | 
 |     void orTypeMask(int mask) { | 
 |         SkASSERT((mask & kORableMasks) == mask); | 
 |         fTypeMask |= mask; | 
 |     } | 
 |  | 
 |     void clearTypeMask(int mask) { | 
 |         // only allow a valid mask | 
 |         SkASSERT((mask & kAllMasks) == mask); | 
 |         fTypeMask &= ~mask; | 
 |     } | 
 |  | 
 |     TypeMask getPerspectiveTypeMaskOnly() const { | 
 |         if ((fTypeMask & kUnknown_Mask) && | 
 |             !(fTypeMask & kOnlyPerspectiveValid_Mask)) { | 
 |             fTypeMask = this->computePerspectiveTypeMask(); | 
 |         } | 
 |         return (TypeMask)(fTypeMask & 0xF); | 
 |     } | 
 |  | 
 |     /** Returns true if we already know that the matrix is identity; | 
 |         false otherwise. | 
 |     */ | 
 |     bool isTriviallyIdentity() const { | 
 |         if (fTypeMask & kUnknown_Mask) { | 
 |             return false; | 
 |         } | 
 |         return ((fTypeMask & 0xF) == 0); | 
 |     } | 
 |  | 
 |     inline void updateTranslateMask() { | 
 |         if ((fMat[kMTransX] != 0) | (fMat[kMTransY] != 0)) { | 
 |             fTypeMask |= kTranslate_Mask; | 
 |         } else { | 
 |             fTypeMask &= ~kTranslate_Mask; | 
 |         } | 
 |     } | 
 |  | 
 |     typedef void (*MapXYProc)(const SkMatrix& mat, SkScalar x, SkScalar y, | 
 |                                  SkPoint* result); | 
 |  | 
 |     static MapXYProc GetMapXYProc(TypeMask mask) { | 
 |         SkASSERT((mask & ~kAllMasks) == 0); | 
 |         return gMapXYProcs[mask & kAllMasks]; | 
 |     } | 
 |  | 
 |     MapXYProc getMapXYProc() const { | 
 |         return GetMapXYProc(this->getType()); | 
 |     } | 
 |  | 
 |     typedef void (*MapPtsProc)(const SkMatrix& mat, SkPoint dst[], | 
 |                                   const SkPoint src[], int count); | 
 |  | 
 |     static MapPtsProc GetMapPtsProc(TypeMask mask) { | 
 |         SkASSERT((mask & ~kAllMasks) == 0); | 
 |         return gMapPtsProcs[mask & kAllMasks]; | 
 |     } | 
 |  | 
 |     MapPtsProc getMapPtsProc() const { | 
 |         return GetMapPtsProc(this->getType()); | 
 |     } | 
 |  | 
 |     bool SK_WARN_UNUSED_RESULT invertNonIdentity(SkMatrix* inverse) const; | 
 |  | 
 |     static bool Poly2Proc(const SkPoint[], SkMatrix*); | 
 |     static bool Poly3Proc(const SkPoint[], SkMatrix*); | 
 |     static bool Poly4Proc(const SkPoint[], SkMatrix*); | 
 |  | 
 |     static void Identity_xy(const SkMatrix&, SkScalar, SkScalar, SkPoint*); | 
 |     static void Trans_xy(const SkMatrix&, SkScalar, SkScalar, SkPoint*); | 
 |     static void Scale_xy(const SkMatrix&, SkScalar, SkScalar, SkPoint*); | 
 |     static void ScaleTrans_xy(const SkMatrix&, SkScalar, SkScalar, SkPoint*); | 
 |     static void Rot_xy(const SkMatrix&, SkScalar, SkScalar, SkPoint*); | 
 |     static void RotTrans_xy(const SkMatrix&, SkScalar, SkScalar, SkPoint*); | 
 |     static void Persp_xy(const SkMatrix&, SkScalar, SkScalar, SkPoint*); | 
 |  | 
 |     static const MapXYProc gMapXYProcs[]; | 
 |  | 
 |     static void Identity_pts(const SkMatrix&, SkPoint[], const SkPoint[], int); | 
 |     static void Trans_pts(const SkMatrix&, SkPoint dst[], const SkPoint[], int); | 
 |     static void Scale_pts(const SkMatrix&, SkPoint dst[], const SkPoint[], int); | 
 |     static void ScaleTrans_pts(const SkMatrix&, SkPoint dst[], const SkPoint[], | 
 |                                int count); | 
 |     static void Persp_pts(const SkMatrix&, SkPoint dst[], const SkPoint[], int); | 
 |  | 
 |     static void Affine_vpts(const SkMatrix&, SkPoint dst[], const SkPoint[], int); | 
 |  | 
 |     static const MapPtsProc gMapPtsProcs[]; | 
 |  | 
 |     // return the number of bytes written, whether or not buffer is null | 
 |     size_t writeToMemory(void* buffer) const; | 
 |     /** | 
 |      * Reads data from the buffer parameter | 
 |      * | 
 |      * @param buffer Memory to read from | 
 |      * @param length Amount of memory available in the buffer | 
 |      * @return number of bytes read (must be a multiple of 4) or | 
 |      *         0 if there was not enough memory available | 
 |      */ | 
 |     size_t readFromMemory(const void* buffer, size_t length); | 
 |  | 
 |     // legacy method -- still needed? why not just postScale(1/divx, ...)? | 
 |     bool postIDiv(int divx, int divy); | 
 |     void doNormalizePerspective(); | 
 |  | 
 |     friend class SkPerspIter; | 
 |     friend class SkMatrixPriv; | 
 |     friend class SerializationTest; | 
 | }; | 
 | SK_END_REQUIRE_DENSE | 
 |  | 
 | #endif |