SkMatrix Reference === # Matrix # Class SkMatrix Matrix holds a 3x3 matrix for transforming coordinates. This allows mapping Points and Vectors with translation, scaling, skewing, rotation, and perspective. Matrix elements are in row major order. Matrix does not have a constructor, so it must be explicitly initialized. setIdentity initializes Matrix so it has no effect. setTranslate, setScale, setSkew, setRotate, set9 and setAll initializes all Matrix elements with the corresponding mapping. Matrix includes a hidden variable that classifies the type of matrix to improve performance. Matrix is not thread safe unless getType is called first. # Overview ## Subtopics | topics | description | | --- | --- | ## Operators | function | description | | --- | --- | | operator!=(const SkMatrix& a, const SkMatrix& b) | Returns true if members are unequal. | | operator==(const SkMatrix& a, const SkMatrix& b) | Returns true if members are equal. | | operator[](int index) const | Returns Matrix value. | | operator[](int index) | Returns writable reference to Matrix value. | ## Member Functions | function | description | | --- | --- | | Concat | Returns the concatenation of Matrix pair. | | I | Returns a reference to a const identity Matrix. | | InvalidMatrix | Returns a reference to a const invalid Matrix. | | MakeAll | Constructs all nine values. | | MakeRectToRect | Constructs from source Rect to destination Rect. | | MakeScale | Constructs from scale in x and y. | | MakeTrans | Constructs from translate in x and y. | | SetAffineIdentity | Sets 3x2 array to identity. | | asAffine | Copies to 3x2 array. | | cheapEqualTo | Compares Matrix pair using memcmp(). | | decomposeScale | Separates scale if possible. | | dirtyMatrixTypeCache | Sets internal cache to unknown state. | | dump | Sends text representation using floats to standard output. | | fixedStepInX | Returns step in x for a position in y. | | get | Returns one of nine Matrix values. | | get9 | Returns all nine Matrix values. | | getMaxScale | Returns maximum scaling, if possible. | | getMinMaxScales | Returns minimum and maximum scaling, if possible. | | getMinScale | Returns minimum scaling, if possible. | | getPerspX | Returns input x perspective factor. | | getPerspY | Returns input y perspective factor. | | getScaleX | Returns horizontal scale factor. | | getScaleY | Returns vertical scale factor. | | getSkewX | Returns horizontal skew factor. | | getSkewY | Returns vertical skew factor. | | getTranslateX | Returns horizontal translation. | | getTranslateY | Returns vertical translation. | | getType | Returns transform complexity. | | hasPerspective | Returns if transform includes perspective. | | invert | Returns inverse, if possible. | | isFinite | Returns if all Matrix values are not infinity, NaN. | | isFixedStepInX | Returns if transformation supports fixed step in x. | | isIdentity | Returns if matrix equals the identity Matrix . | | isScaleTranslate | Returns if transform is limited to scale and translate. | | isSimilarity | Returns if transform is limited to square scale and rotation. | | isTranslate | Returns if transform is limited to translate. | | mapHomogeneousPoints | Maps Point3 array. | | mapPoints | Maps Point array. | | mapRadius | Returns mean radius of mapped Circle. | | mapRect | Returns bounds of mapped Rect. | | mapRectScaleTranslate | Returns bounds of mapped Rect. | | mapRectToQuad | Maps Rect to Point array. | | mapVector | Maps Vector. | | mapVectors | Maps Vector array. | | mapXY | Maps Point. | | postConcat | Post-multiplies Matrix by Matrix parameter. | | postIDiv | Post-multiplies Matrix by inverse scale. | | postRotate | Post-multiplies Matrix by rotation. | | postScale | Post-multiplies Matrix by scale. | | postSkew | Post-multiplies Matrix by skew. | | postTranslate | Post-multiplies Matrix by translation. | | preConcat | Pre-multiplies Matrix by Matrix parameter. | | preRotate | Pre-multiplies Matrix by rotation. | | preScale | Pre-multiplies Matrix by scale. | | preSkew | Pre-multiplies Matrix by skew. | | preTranslate | Pre-multiplies Matrix by translation. | | preservesAxisAlignment | Returns if mapping restricts to 90 degree multiples and mirroring. | | preservesRightAngles | Returns if mapped 90 angle remains 90 degrees. | | rectStaysRect | Returns if mapped Rect can be represented by another Rect. | | reset | Sets Matrix to identity. | | set | Sets one value. | | set9 | Sets all values from Scalar array. | | setAffine | Sets left two columns. | | setAll | Sets all values from parameters. | | setConcat | Sets to Matrix parameter multiplied by Matrix parameter. | | setIdentity | Sets Matrix to identity. | | setPerspX | Sets input x perspective factor. | | setPerspY | Sets input y perspective factor. | | setPolyToPoly | Sets to map one to four points to an equal array of points. | | setRSXform | Sets to rotate, scale, and translate. | | setRectToRect | Sets to map one Rect to another. | | setRotate | Sets to rotate about a point. | | setScale | Sets to scale about a point. | | setScaleTranslate | Sets to scale and translate. | | setScaleX | Sets horizontal scale factor. | | setScaleY | Sets vertical scale factor | | setSinCos | Sets to rotate and scale about a point. | | setSkew | Sets to skew about a point. | | setSkewX | Sets horizontal skew factor. | | setSkewY | Sets vertical skew factor. | | setTranslate | Sets to translate in x and y. | | setTranslateX | Sets horizontal translation. | | setTranslateY | Sets vertical translation. | | toString | Converts Matrix to machine readable form. | ## MakeScale

static SkMatrix SK_WARN_UNUSED_RESULT MakeScale(SkScalar sx, SkScalar sy)

Sets Matrix to scale by (sx, sy). Returned matrix is:

| sx  0  0 |
|  0 sy  0 |
|  0  0  1 |

### Parameters

`sx`	horizontal scale factor
`sy`	vertical scale factor

### Return Value Matrix with scale ### Example

### See Also setScale postScale preScale ---

static SkMatrix SK_WARN_UNUSED_RESULT MakeScale(SkScalar scale)

Sets Matrix to scale by (scale, scale). Returned matrix is:

| scale   0   0 |
|   0   scale 0 |
|   0     0   1 |

### Parameters

scale horizontal and vertical scale factor

### Return Value Matrix with scale ### Example

### See Also setScale postScale preScale --- ## MakeTrans

static SkMatrix SK_WARN_UNUSED_RESULT MakeTrans(SkScalar dx, SkScalar dy)

Sets Matrix to translate by (dx, dy). Returned matrix is:

| 1 0 dx |
| 0 1 dy |
| 0 0  1 |

### Parameters

`dx`	horizontal translation
`dy`	vertical translation

### Return Value Matrix with translation ### Example

### See Also setTranslate postTranslate preTranslate --- ## MakeAll

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)

Sets Matrix to:

| scaleX  skewX transX |
|  skewY scaleY transY |
|  pers0  pers1  pers2 |

### Parameters

`scaleX`	horizontal scale factor
`skewX`	horizontal skew factor
`transX`	horizontal translation
`skewY`	vertical skew factor
`scaleY`	vertical scale factor
`transY`	vertical translation
`pers0`	input x perspective factor
`pers1`	input y perspective factor
`pers2`	perspective scale factor

### Return Value Matrix constructed from parameters ### Example

### See Also setAll set9 postConcat preConcat --- ## Enum SkMatrix::TypeMask

enum TypeMask {
kIdentity Mask = 0,
kTranslate Mask = 0x01,
kScale Mask = 0x02,
kAffine Mask = 0x04,
kPerspective Mask = 0x08,
};

Enum of bit fields for mask returned by getType. Used to identify the complexity of Matrix, to optimize performance. ### Constants

`SkMatrix::kIdentity_Mask`	0	all bits clear if Matrix is identity
`SkMatrix::kTranslate_Mask`	1	set if Matrix has translation
`SkMatrix::kScale_Mask`	2	set if Matrix has x or y scale
`SkMatrix::kAffine_Mask`	4	set if Matrix skews or rotates
`SkMatrix::kPerspective_Mask`	8	set if Matrix has perspective

### Example

#### Example Output ~~~~ after reset: kIdentity_Mask after postTranslate: kTranslate_Mask after postScale: kTranslate_Mask kScale_Mask after postScale: kTranslate_Mask kScale_Mask kAffine_Mask after setPolyToPoly: kTranslate_Mask kScale_Mask kAffine_Mask kPerspective_Mask ~~~~

### See Also getType ## getType

TypeMask getType() const

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 Value kIdentity Mask, or combinations of: kTranslate Mask, kScale Mask, kAffine Mask, kPerspective Mask ### Example

#### Example Output ~~~~ identity flags hex: 0 decimal: 0 set all flags hex: f decimal: 15 ~~~~

### See Also TypeMask --- ## isIdentity

bool isIdentity() const

Returns true if Matrix is identity. Identity matrix is:

| 1 0 0 |
| 0 1 0 |
| 0 0 1 |

### Return Value true if Matrix has no effect ### Example

#### Example Output ~~~~ is identity: true is identity: false ~~~~

### See Also reset setIdentity getType --- ## isScaleTranslate

bool isScaleTranslate() const

Returns true if Matrix at most scales and translates. Matrix may be identity, contain only scale elements, only translate elements, or both. Matrix form is:

| scale-x    0    translate-x |
|    0    scale-y translate-y |
|    0       0         1      |

### Return Value true if Matrix is identity; or scales, translates, or both ### Example

#### Example Output ~~~~ is scale-translate: true is scale-translate: true is scale-translate: true is scale-translate: true ~~~~

### See Also setScale isTranslate setTranslate getType --- ## isTranslate

bool isTranslate() const

Returns true if Matrix is identity, or translates. Matrix form is:

| 1 0 translate-x |
| 0 1 translate-y |
| 0 0      1      |

### Return Value true if Matrix is identity, or translates ### Example

#### Example Output ~~~~ is translate: true is translate: true is translate: false is translate: false ~~~~

### See Also setTranslate getType --- ## rectStaysRect

bool rectStaysRect() const

Returns true Matrix maps Rect to another Rect. If true, Matrix is identity, or scales, or rotates a multiple of 90 degrees, or mirrors in x or y. In all cases, Matrix may also have translation. Matrix form is either:

| scale-x    0    translate-x |
|    0    scale-y translate-y |
|    0       0         1      |

|    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 Value true if Matrix maps one Rect into another ### Example

#### Example Output ~~~~ rectStaysRect: true rectStaysRect: true rectStaysRect: true rectStaysRect: true ~~~~

### See Also preservesAxisAlignment preservesRightAngles --- ## preservesAxisAlignment

bool preservesAxisAlignment() const

| scale-x    0    translate-x |
|    0    scale-y translate-y |
|    0       0         1      |

|    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 Value true if Matrix maps one Rect into another ### Example

#### Example Output ~~~~ preservesAxisAlignment: true preservesAxisAlignment: true preservesAxisAlignment: true preservesAxisAlignment: true ~~~~

### See Also rectStaysRect preservesRightAngles --- ## hasPerspective

bool hasPerspective() const

Returns true if the matrix contains perspective elements. Matrix 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 Value true if Matrix is in most general form ### Example

### See Also setAll set9 MakeAll --- ## isSimilarity

bool isSimilarity(SkScalar tol = SK_ScalarNearlyZero) const

Returns true if Matrix contains only translation, rotation, reflection, and uniform scale. Returns false if Matrix contains different scales, skewing, perspective, or degenerate forms that collapse to a line or point. Describes that the Matrix 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. ### Parameters

tol to be deprecated

### Return Value true if Matrix only rotates, uniformly scales, translates ### Example

String is drawn four times through but only two are visible. Drawing the pair with isSimilarity false reveals the pair not visible through the matrix.

### See Also isScaleTranslate preservesRightAngles rectStaysRect isFixedStepInX --- ## preservesRightAngles

bool preservesRightAngles(SkScalar tol = SK_ScalarNearlyZero) const

Returns true if Matrix contains only translation, rotation, reflection, and scale. Scale may differ along rotated axes. Returns false if Matrix 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. ### Parameters

tol to be deprecated

### Return Value true if Matrix only rotates, scales, translates ### Example

Equal scale is both similar and preserves right angles. Unequal scale is not similar but preserves right angles. Skews are not similar and do not preserve right angles.

### See Also isScaleTranslate isSimilarity rectStaysRect isFixedStepInX --- ## Enum SkMatrix::_anonymous

enum {
kMScaleX,
kMSkewX,
kMTransX,
kMSkewY,
kMScaleY,
kMTransY,
kMPersp0,
kMPersp1,
kMPersp2,
};

Matrix organizes its values in row order. These members correspond to each value in Matrix. ### Constants

`SkMatrix::kMScaleX`	0	horizontal scale factor
`SkMatrix::kMSkewX`	1	horizontal skew factor
`SkMatrix::kMTransX`	2	horizontal translation
`SkMatrix::kMSkewY`	3	vertical skew factor
`SkMatrix::kMScaleY`	4	vertical scale factor
`SkMatrix::kMTransY`	5	vertical translation
`SkMatrix::kMPersp0`	6	input x perspective factor
`SkMatrix::kMPersp1`	7	input y perspective factor
`SkMatrix::kMPersp2`	8	perspective bias

### Example

### See Also get set ## Enum SkMatrix::_anonymous_2

enum {
kAScaleX,
kASkewY,
kASkewX,
kAScaleY,
kATransX,
kATransY,
};

Affine arrays are in column major order to match the matrix used by PDF and XPS. ### Constants

`SkMatrix::kAScaleX`	0	horizontal scale factor
`SkMatrix::kASkewY`	1	vertical skew factor
`SkMatrix::kASkewX`	2	horizontal skew factor
`SkMatrix::kAScaleY`	3	vertical scale factor
`SkMatrix::kATransX`	4	horizontal translation
`SkMatrix::kATransY`	5	vertical translation

### See Also SetAffineIdentity asAffine setAffine ## operator[]

SkScalar operator[](int index) _const

Returns one matrix value. Asserts if index is out of range and SK_DEBUG is defined. ### Parameters

index one of: kMScaleX, kMSkewX, kMTransX, kMSkewY, kMScaleY, kMTransY, kMPersp0, kMPersp1, kMPersp2

### Return Value value corresponding to index ### Example

#### Example Output ~~~~ matrix[SkMatrix::kMScaleX] == 42 matrix[SkMatrix::kMScaleY] == 24 ~~~~

### See Also get set --- ## get

SkScalar get(int index) const

Returns one matrix value. Asserts if index is out of range and SK_DEBUG is defined. ### Parameters

index one of: kMScaleX, kMSkewX, kMTransX, kMSkewY, kMScaleY, kMTransY, kMPersp0, kMPersp1, kMPersp2

### Return Value value corresponding to index ### Example

#### Example Output ~~~~ matrix.get(SkMatrix::kMSkewX) == 42 matrix.get(SkMatrix::kMSkewY) == 24 ~~~~

### See Also operator[](int index) set --- ## getScaleX

SkScalar getScaleX() const

Returns scale factor multiplied by x input, contributing to x output. With mapPoints, scales Points along the x-axis. ### Return Value horizontal scale factor ### Example

#### Example Output ~~~~ matrix.getScaleX() == 42 ~~~~

### See Also get getScaleY setScaleX setScale --- ## getScaleY

SkScalar getScaleY() const

Returns scale factor multiplied by y input, contributing to y output. With mapPoints, scales Points along the y-axis. ### Return Value vertical scale factor ### Example

#### Example Output ~~~~ matrix.getScaleY() == 24 ~~~~

### See Also get getScaleX setScaleY setScale --- ## getSkewY

SkScalar getSkewY() const

Returns scale factor multiplied by x input, contributing to y output. With mapPoints, skews Points along the y-axis. Skew x and y together can rotate Points. ### Return Value vertical skew factor ### Example

#### Example Output ~~~~ matrix.getSkewY() == 24 ~~~~

### See Also get getSkewX setSkewY setSkew --- ## getSkewX

SkScalar getSkewX() const

Returns scale factor multiplied by y input, contributing to x output. With mapPoints, skews Points along the x-axis. Skew x and y together can rotate Points. ### Return Value horizontal scale factor ### Example

#### Example Output ~~~~ matrix.getSkewX() == 42 ~~~~

### See Also get getSkewY setSkewX setSkew --- ## getTranslateX

SkScalar getTranslateX() const

Returns translation contributing to x output. With mapPoints, moves Points along the x-axis. ### Return Value horizontal translation factor ### Example

#### Example Output ~~~~ matrix.getTranslateX() == 42 ~~~~

### See Also get getTranslateY setTranslateX setTranslate --- ## getTranslateY

SkScalar getTranslateY() const

Returns translation contributing to y output. With mapPoints, moves Points along the y-axis. ### Return Value vertical translation factor ### Example

#### Example Output ~~~~ matrix.getTranslateY() == 24 ~~~~

### See Also get getTranslateX setTranslateY setTranslate --- ## getPerspX

SkScalar getPerspX() const

Returns factor scaling input x relative to input y. ### Return Value input x perspective factor ### Example

### See Also kMPersp0 getPerspY --- ## getPerspY

SkScalar getPerspY() const

Returns factor scaling input y relative to input x. ### Return Value input y perspective factor ### Example

### See Also kMPersp1 getPerspX --- ## operator[]

SkScalar& operator[](int index)

Returns writable Matrix value. Asserts if index is out of range and SK_DEBUG is defined. Clears internal cache anticipating that caller will change Matrix value. Next call to read Matrix state may recompute cache; subsequent writes to Matrix value must be followed by dirtyMatrixTypeCache. ### Parameters

index one of: kMScaleX, kMSkewX, kMTransX, kMSkewY, kMScaleY, kMTransY, kMPersp0, kMPersp1, kMPersp2

### Return Value writable value corresponding to index ### Example

#### Example Output ~~~~ with identity matrix: x = 24 after skew x mod: x = 24 after 2nd skew x mod: x = 24 after dirty cache: x = 66 ~~~~

### See Also get dirtyMatrixTypeCache set --- ## set

void set(int index, SkScalar value)

Sets Matrix value. Asserts if index is out of range and SK_DEBUG is defined. Safer than operator[]; internal cache is always maintained. ### Parameters

`index`	one of: kMScaleX, kMSkewX, kMTransX, kMSkewY, kMScaleY, kMTransY, kMPersp0, kMPersp1, kMPersp2
`value`	Scalar to store in Matrix

### Example

#### Example Output ~~~~ with identity matrix: x = 24 after skew x mod: x = 24 after 2nd skew x mod: x = 66 ~~~~

### See Also operator[] get --- ## setScaleX

void setScaleX(SkScalar v)

Sets horizontal scale factor. ### Parameters

`v`	horizontal scale factor to store

### Example

### See Also set setScale setScaleY --- ## setScaleY

void setScaleY(SkScalar v)

Sets vertical scale factor. ### Parameters

`v`	vertical scale factor to store

### Example

### See Also set setScale setScaleX --- ## setSkewY

void setSkewY(SkScalar v)

Sets vertical skew factor. ### Parameters

`v`	vertical skew factor to store

### Example

### See Also set setSkew setSkewX --- ## setSkewX

void setSkewX(SkScalar v)

Sets horizontal skew factor. ### Parameters

`v`	horizontal skew factor to store

### Example

### See Also set setSkew setSkewX --- ## setTranslateX

void setTranslateX(SkScalar v)

Sets horizontal translation. ### Parameters

`v`	horizontal translation to store

### Example

### See Also set setTranslate setTranslateY --- ## setTranslateY

void setTranslateY(SkScalar v)

Sets vertical translation. ### Parameters

`v`	vertical translation to store

### Example

### See Also set setTranslate setTranslateX --- ## setPerspX

void setPerspX(SkScalar v)

Sets input x perspective factor, which causes mapXY to vary input x inversely proportional to input y. ### Parameters

`v`	perspective factor

### Example

### See Also getPerspX set setAll set9 MakeAll --- ## setPerspY

void setPerspY(SkScalar v)

Sets input y perspective factor, which causes mapXY to vary input y inversely proportional to input x. ### Parameters

`v`	perspective factor

### Example

### See Also getPerspY set setAll set9 MakeAll --- ## setAll

void setAll(SkScalar scaleX, SkScalar skewX, SkScalar transX, SkScalar skewY, SkScalar scaleY,
            SkScalar transY, SkScalar persp0, SkScalar persp1, SkScalar persp2)

Sets all values from parameters. Sets matrix to:

| scaleX  skewX transX |
|  skewY scaleY transY |
| persp0 persp1 persp2 |

### Parameters

`scaleX`	horizontal scale factor to store
`skewX`	horizontal skew factor to store
`transX`	horizontal translation to store
`skewY`	vertical skew factor to store
`scaleY`	vertical scale factor to store
`transY`	vertical translation to store
`persp0`	input x perspective factor to store
`persp1`	input y perspective factor to store
`persp2`	perspective scale factor to store

### Example

### See Also set9 MakeAll --- ## get9

void get9(SkScalar buffer[9]) const

Copies nine Scalar values contained by Matrix into buffer, in member value ascending order: kMScaleX, kMSkewX, kMTransX, kMSkewY, kMScaleY, kMTransY, kMPersp0, kMPersp1, kMPersp2. ### Parameters

buffer storage for nine Scalar values

### Example

#### Example Output ~~~~ {4, 0, 3}, {0, 5, 4}, {0, 0, 1} ~~~~

### See Also set9 --- ## set9

void set9(const SkScalar buffer[9])

Sets Matrix 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 Matrix maps non-homogeneous coordinates, scaling all nine values produces an equivalent transformation, possibly improving precision. ### Parameters

buffer nine Scalar values

### Example

### See Also setAll get9 MakeAll --- ## reset

void reset()

Sets Matrix to identity; which has no effect on mapped Points. Sets Matrix to:

| 1 0 0 |
| 0 1 0 |
| 0 0 1 |

Also called setIdentity; use the one that provides better inline documentation. ### Example

#### Example Output ~~~~ m.isIdentity(): true ~~~~

### See Also isIdentity setIdentity --- ## setIdentity

void setIdentity()

Sets Matrix to identity; which has no effect on mapped Points. Sets Matrix to:

| 1 0 0 |
| 0 1 0 |
| 0 0 1 |

Also called reset; use the one that provides better inline documentation. ### Example

#### Example Output ~~~~ m.isIdentity(): true ~~~~

### See Also isIdentity reset --- ## setTranslate

void setTranslate(SkScalar dx, SkScalar dy)

Sets Matrix to translate by (dx, dy). ### Parameters

`dx`	horizontal translation
`dy`	vertical translation

### Example

### See Also setTranslateX setTranslateY ---

void setTranslate(const SkVector& v)

Sets Matrix to translate by (v.fX, v.fY). ### Parameters

`v`	Vector containing horizontal and vertical translation

### Example

### See Also setTranslateX setTranslateY MakeTrans --- ## setScale

void setScale(SkScalar sx, SkScalar sy, SkScalar px, SkScalar py)

Sets Matrix to scale by sx and sy, about a pivot point at (px, py). The pivot point is unchanged when mapped with Matrix. ### Parameters

`sx`	horizontal scale factor
`sy`	vertical scale factor
`px`	pivot x
`py`	pivot y

### Example

### See Also setScaleX setScaleY MakeScale preScale postScale ---

void setScale(SkScalar sx, SkScalar sy)

Sets Matrix to scale by sx and sy about at pivot point at (0, 0). ### Parameters

`sx`	horizontal scale factor
`sy`	vertical scale factor

### Example

### See Also setScaleX setScaleY MakeScale preScale postScale --- ## setRotate

void setRotate(SkScalar degrees, SkScalar px, SkScalar py)

Sets Matrix to rotate by degrees about a pivot point at (px, py). The pivot point is unchanged when mapped with Matrix. Positive degrees rotates clockwise. ### Parameters

`degrees`	angle of axes relative to upright axes
`px`	pivot x
`py`	pivot y

### Example

### See Also setSinCos preRotate postRotate ---

void setRotate(SkScalar degrees)

Sets Matrix to rotate by degrees about a pivot point at (0, 0). Positive degrees rotates clockwise. ### Parameters

degrees angle of axes relative to upright axes

### Example

### See Also setSinCos preRotate postRotate --- ## setSinCos

void setSinCos(SkScalar sinValue, SkScalar cosValue, SkScalar px, SkScalar py)

Sets Matrix to rotate by sinValue and cosValue, about a pivot point at (px, py). The pivot point is unchanged when mapped with Matrix. Vector (sinValue, cosValue) describes the angle of rotation relative to (0, 1). Vector length specifies scale. ### Parameters

`sinValue`	rotation vector x component
`cosValue`	rotation vector y component
`px`	pivot x
`py`	pivot y

### Example

### See Also setRotate setScale setRSXform ---

void setSinCos(SkScalar sinValue, SkScalar cosValue)

Sets Matrix 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. ### Parameters

`sinValue`	rotation vector x component
`cosValue`	rotation vector y component

### Example

Canvas needs offset after applying Matrix to pivot about Rect center.

### See Also setRotate setScale setRSXform --- ## setRSXform

SkMatrix& setRSXform(const SkRSXform& rsxForm)

Sets Matrix 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). ### Parameters

rsxForm compressed RSXform matrix

### Return Value reference to Matrix ### Example

Canvas needs offset after applying Matrix to pivot about Rect center.

### See Also setSinCos setScale setTranslate --- ## setSkew

void setSkew(SkScalar kx, SkScalar ky, SkScalar px, SkScalar py)

Sets Matrix to skew by kx and ky, about a pivot point at (px, py). The pivot point is unchanged when mapped with Matrix. ### Parameters

`kx`	horizontal skew factor
`ky`	vertical skew factor
`px`	pivot x
`py`	pivot y

### Example

### See Also setSkewX setSkewY preSkew postSkew ---

void setSkew(SkScalar kx, SkScalar ky)

Sets Matrix to skew by kx and ky, about a pivot point at (0, 0). ### Parameters

`kx`	horizontal skew factor
`ky`	vertical skew factor

### Example

### See Also setSkewX setSkewY preSkew postSkew --- ## setConcat

void setConcat(const SkMatrix& a, const SkMatrix& b)

Sets Matrix to Matrix a multiplied by Matrix 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 Matrix 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 |

### Parameters

`a`	Matrix on left side of multiply expression
`b`	Matrix on right side of multiply expression

### Example

setPolyToPoly creates perspective matrices, one the inverse of the other. Multiplying the matrix by its inverse turns into an identity matrix.

### See Also Concat preConcat postConcat SkCanvas::concat --- ## preTranslate

void preTranslate(SkScalar dx, SkScalar dy)

Sets Matrix to Matrix multiplied by Matrix constructed from translation (dx, dy). This can be thought of as moving the point to be mapped before applying Matrix. Given:

         | A B C |               | 1 0 dx |
Matrix = | D E F |,  T(dx, dy) = | 0 1 dy |
         | G H I |               | 0 0  1 |

sets Matrix 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 |

### Parameters

`dx`	x translation before applying Matrix
`dy`	y translation before applying Matrix

### Example

### See Also postTranslate setTranslate MakeTrans --- ## preScale

void preScale(SkScalar sx, SkScalar sy, SkScalar px, SkScalar py)

Sets Matrix to Matrix multiplied by Matrix constructed from scaling by (sx, sy) about pivot point (px, py). This can be thought of as scaling about a pivot point before applying Matrix. 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 Matrix 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 |

### Parameters

`sx`	horizontal scale factor
`sy`	vertical scale factor
`px`	pivot x
`py`	pivot y

### Example

### See Also postScale setScale MakeScale ---

void preScale(SkScalar sx, SkScalar sy)

Sets Matrix to Matrix multiplied by Matrix constructed from scaling by (sx, sy) about pivot point (0, 0). This can be thought of as scaling about the origin before applying Matrix. Given:

         | A B C |               | sx  0  0 |
Matrix = | D E F |,  S(sx, sy) = |  0 sy  0 |
         | G H I |               |  0  0  1 |

sets Matrix 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 |

### Parameters

`sx`	horizontal scale factor
`sy`	vertical scale factor

### Example

### See Also postScale setScale MakeScale --- ## preRotate

void preRotate(SkScalar degrees, SkScalar px, SkScalar py)

Sets Matrix to Matrix multiplied by Matrix constructed from rotating by degrees about pivot point (px, py). This can be thought of as rotating about a pivot point before applying Matrix. 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 Matrix 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 |

### Parameters

`degrees`	angle of axes relative to upright axes
`px`	pivot x
`py`	pivot y

### Example

### See Also postRotate setRotate ---

void preRotate(SkScalar degrees)

Sets Matrix to Matrix multiplied by Matrix constructed from rotating by degrees about pivot point (0, 0). This can be thought of as rotating about the origin before applying Matrix. 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 Matrix 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 |

### Parameters

degrees angle of axes relative to upright axes

### Example

### See Also postRotate setRotate --- ## preSkew

void preSkew(SkScalar kx, SkScalar ky, SkScalar px, SkScalar py)

Sets Matrix to Matrix multiplied by Matrix constructed from skewing by (kx, ky) about pivot point (px, py). This can be thought of as skewing about a pivot point before applying Matrix. 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 Matrix 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 |

### Parameters

`kx`	horizontal skew factor
`ky`	vertical skew factor
`px`	pivot x
`py`	pivot y

### Example

### See Also postSkew setSkew ---

void preSkew(SkScalar kx, SkScalar ky)

Sets Matrix to Matrix multiplied by Matrix constructed from skewing by (kx, ky) about pivot point (0, 0). This can be thought of as skewing about the origin before applying Matrix. Given:

         | A B C |               |  1 kx 0 |
Matrix = | D E F |,  K(kx, ky) = | ky  1 0 |
         | G H I |               |  0  0 1 |

sets Matrix 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 |

### Parameters

`kx`	horizontal skew factor
`ky`	vertical skew factor

### Example

### See Also postSkew setSkew --- ## preConcat

void preConcat(const SkMatrix& other)

Sets Matrix to Matrix multiplied by Matrix other. This can be thought of mapping by other before applying Matrix. Given:

         | A B C |          | J K L |
Matrix = | D E F |, other = | M N O |
         | G H I |          | P Q R |

sets Matrix 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 |

### Parameters

other Matrix on right side of multiply expression

### Example

setPolyToPoly creates perspective matrices, one the inverse of the other. Multiplying the matrix by its inverse turns into an identity matrix.

### See Also postConcat setConcat Concat --- ## postTranslate

void postTranslate(SkScalar dx, SkScalar dy)

Sets Matrix to Matrix constructed from translation (dx, dy) multiplied by Matrix. This can be thought of as moving the point to be mapped after applying Matrix. Given:

         | J K L |               | 1 0 dx |
Matrix = | M N O |,  T(dx, dy) = | 0 1 dy |
         | P Q R |               | 0 0  1 |

sets Matrix 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 |

### Parameters

`dx`	x translation after applying Matrix
`dy`	y translation after applying Matrix

### Example

Compare with preTranslate example.

### See Also preTranslate setTranslate MakeTrans --- ## postScale

void postScale(SkScalar sx, SkScalar sy, SkScalar px, SkScalar py)

Sets Matrix to Matrix constructed from scaling by (sx, sy) about pivot point (px, py), multiplied by Matrix. This can be thought of as scaling about a pivot point after applying Matrix. 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 Matrix 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 |

### Parameters

`sx`	horizontal scale factor
`sy`	vertical scale factor
`px`	pivot x
`py`	pivot y

### Example

### See Also preScale setScale MakeScale ---

void postScale(SkScalar sx, SkScalar sy)

Sets Matrix to Matrix constructed from scaling by (sx, sy) about pivot point (0, 0), multiplied by Matrix. This can be thought of as scaling about the origin after applying Matrix. Given:

         | J K L |               | sx  0  0 |
Matrix = | M N O |,  S(sx, sy) = |  0 sy  0 |
         | P Q R |               |  0  0  1 |

sets Matrix 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 |

### Parameters

`sx`	horizontal scale factor
`sy`	vertical scale factor

### Example

### See Also preScale setScale MakeScale --- ## postIDiv

bool postIDiv(int divx, int divy)

Sets Matrix to Matrix constructed from scaling by(1/divx, 1/divy)about pivot point (px, py), multiplied by Matrix. Returns false if either divx or divy is zero. Given:

         | J K L |                   | sx  0  0 |
Matrix = | M N O |,  I(divx, divy) = |  0 sy  0 |
         | P Q R |                   |  0  0  1 |

where

sx = 1 / divx
sy = 1 / divy

sets Matrix to:

                         | sx  0  0 | | J K L |   | sx*J sx*K sx*L |
I(divx, divy) * Matrix = |  0 sy  0 | | M N O | = | sy*M sy*N sy*O |
                         |  0  0  1 | | P Q R |   |    P    Q    R |

### Parameters

`divx`	integer divisor for inverse scale in x
`divy`	integer divisor for inverse scale in y

### Return Value true on successful scale ### Example

### See Also postScale MakeScale --- ## postRotate

void postRotate(SkScalar degrees, SkScalar px, SkScalar py)

Sets Matrix to Matrix constructed from rotating by degrees about pivot point (px, py), multiplied by Matrix. This can be thought of as rotating about a pivot point after applying Matrix. 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 Matrix 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|

### Parameters

`degrees`	angle of axes relative to upright axes
`px`	pivot x
`py`	pivot y

### Example

### See Also preRotate setRotate ---

void postRotate(SkScalar degrees)

Sets Matrix to Matrix constructed from rotating by degrees about pivot point (0, 0), multiplied by Matrix. This can be thought of as rotating about the origin after applying Matrix. 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 Matrix 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 |

### Parameters

degrees angle of axes relative to upright axes

### Example

### See Also preRotate setRotate --- ## postSkew

void postSkew(SkScalar kx, SkScalar ky, SkScalar px, SkScalar py)

Sets Matrix to Matrix constructed from skewing by (kx, ky) about pivot point (px, py), multiplied by Matrix. This can be thought of as skewing about a pivot point after applying Matrix. 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 Matrix 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|

### Parameters

`kx`	horizontal skew factor
`ky`	vertical skew factor
`px`	pivot x
`py`	pivot y

### Example

### See Also preSkew setSkew ---

void postSkew(SkScalar kx, SkScalar ky)

Sets Matrix to Matrix constructed from skewing by (kx, ky) about pivot point (0, 0), multiplied by Matrix. This can be thought of as skewing about the origin after applying Matrix. Given:

         | J K L |               |  1 kx 0 |
Matrix = | M N O |,  K(kx, ky) = | ky  1 0 |
         | P Q R |               |  0  0 1 |

sets Matrix 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 |

### Parameters

`kx`	horizontal skew factor
`ky`	vertical skew factor

### Example

### See Also preSkew setSkew --- ## postConcat

void postConcat(const SkMatrix& other)

Sets Matrix to Matrix other multiplied by Matrix. This can be thought of mapping by other after applying Matrix. Given:

         | J K L |           | A B C |
Matrix = | M N O |,  other = | D E F |
         | P Q R |           | G H I |

sets Matrix 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 |

### Parameters

other Matrix on left side of multiply expression

### Example

### See Also preConcat setConcat Concat --- ## Enum SkMatrix::ScaleToFit

enum ScaleToFit {
kFill ScaleToFit,
kStart ScaleToFit,
kCenter ScaleToFit,
kEnd ScaleToFit,
};

ScaleToFit describes how Matrix is constructed to map one Rect to another. ScaleToFit may allow Matrix to have unequal horizontal and vertical scaling, or may restrict Matrix to square scaling. If restricted, ScaleToFit specifies how Matrix maps to the side or center of the destination Rect. ### Constants

`SkMatrix::kFill_ScaleToFit`	0	Computes Matrix that scales in x and y independently, so that source Rect is mapped to completely fill destination Rect. The aspect ratio of source Rect may change.
`SkMatrix::kStart_ScaleToFit`	1	Computes Matrix that maintains source Rect aspect ratio, mapping source Rect width or height to destination Rect. Aligns mapping to left and top edges of destination Rect.
`SkMatrix::kCenter_ScaleToFit`	2	Computes Matrix that maintains source Rect aspect ratio, mapping source Rect width or height to destination Rect. Aligns mapping to center of destination Rect.
`SkMatrix::kEnd_ScaleToFit`	3	Computes Matrix that maintains source Rect aspect ratio, mapping source Rect width or height to destination Rect. Aligns mapping to right and bottom edges of destination Rect.

### Example

### See Also setRectToRect MakeRectToRect setPolyToPoly ## setRectToRect

bool setRectToRect(const SkRect& src, const SkRect& dst, ScaleToFit stf)

Sets Matrix to scale and translate src Rect to dst Rect. 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 Matrix to identity. Returns true if dst is empty, and sets Matrix to:

| 0 0 0 |
| 0 0 0 |
| 0 0 1 |

### Parameters

`src`	Rect to map from
`dst`	Rect to map to
`stf`	one of: kFill ScaleToFit, kStart ScaleToFit, kCenter ScaleToFit, kEnd ScaleToFit

### Return Value true if Matrix can represent Rect mapping ### Example

#### Example Output ~~~~ src: 0, 0, 0, 0 dst: 0, 0, 0, 0 success: false [ 1.0000 0.0000 0.0000][ 0.0000 1.0000 0.0000][ 0.0000 0.0000 1.0000] src: 0, 0, 0, 0 dst: 5, 6, 8, 9 success: false [ 1.0000 0.0000 0.0000][ 0.0000 1.0000 0.0000][ 0.0000 0.0000 1.0000] src: 1, 2, 3, 4 dst: 0, 0, 0, 0 success: true [ 0.0000 0.0000 0.0000][ 0.0000 0.0000 0.0000][ 0.0000 0.0000 1.0000] src: 1, 2, 3, 4 dst: 5, 6, 8, 9 success: true [ 1.5000 0.0000 3.5000][ 0.0000 1.5000 3.0000][ 0.0000 0.0000 1.0000] ~~~~

### See Also MakeRectToRect ScaleToFit setPolyToPoly SkRect::isEmpty --- ## MakeRectToRect

static SkMatrix MakeRectToRect(const SkRect& src, const SkRect& dst, ScaleToFit stf)

Returns Matrix set to scale and translate src Rect to dst Rect. stf selects whether mapping completely fills dst or preserves the aspect ratio, and how to align src within dst. Returns the identity Matrix if src is empty. If dst is empty, returns Matrix set to:

| 0 0 0 |
| 0 0 0 |
| 0 0 1 |

### Parameters

`src`	Rect to map from
`dst`	Rect to map to
`stf`	one of: kFill ScaleToFit, kStart ScaleToFit, kCenter ScaleToFit, kEnd ScaleToFit

### Return Value Matrix mapping src to dst ### Example

#### Example Output ~~~~ src: 0, 0, 0, 0 dst: 0, 0, 0, 0 [ 1.0000 0.0000 0.0000][ 0.0000 1.0000 0.0000][ 0.0000 0.0000 1.0000] src: 0, 0, 0, 0 dst: 5, 6, 8, 9 [ 1.0000 0.0000 0.0000][ 0.0000 1.0000 0.0000][ 0.0000 0.0000 1.0000] src: 1, 2, 3, 4 dst: 0, 0, 0, 0 [ 0.0000 0.0000 0.0000][ 0.0000 0.0000 0.0000][ 0.0000 0.0000 1.0000] src: 1, 2, 3, 4 dst: 5, 6, 8, 9 [ 1.5000 0.0000 3.5000][ 0.0000 1.5000 3.0000][ 0.0000 0.0000 1.0000] ~~~~

### See Also setRectToRect ScaleToFit setPolyToPoly SkRect::isEmpty --- ## setPolyToPoly

bool setPolyToPoly(const SkPoint src[], const SkPoint dst[], int count)

Sets Matrix to map src to dst. count must be zero or greater, and four or less. If count is zero, sets Matrix to identity and returns true. If count is one, sets Matrix to translate and returns true. If count is two or more, sets Matrix to map Points if possible; returns false if Matrix cannot be constructed. If count is four, Matrix may include perspective. ### Parameters

`src`	Points to map from
`dst`	Points to map to
`count`	number of Points in src and dst

### Return Value true if Matrix was constructed successfully ### Example

### See Also setRectToRect MakeRectToRect --- ## invert

bool SK_WARN_UNUSED_RESULT invert(SkMatrix* inverse) const

Sets inverse to reciprocal matrix, returning true if Matrix can be inverted. Geometrically, if Matrix maps from source to destination, inverse Matrix maps from destination to source. If Matrix can not be inverted, inverse is unchanged. ### Parameters

inverse storage for inverted Matrix; may be nullptr

### Return Value true if Matrix can be inverted ### Example

### See Also Concat --- ## SetAffineIdentity

static void SetAffineIdentity(SkScalar affine[6])

Fills affine with identity values in column major order. Sets affine to:

| 1 0 0 |
| 0 1 0 |

Affine 3x2 matrices in column major order are used by OpenGL and XPS. ### Parameters

affine storage for 3x2 affine matrix

### Example

#### Example Output ~~~~ ScaleX: 1 SkewY: 0 SkewX: 0 ScaleY: 1 TransX: 0 TransY: 0 ~~~~

### See Also setAffine asAffine --- ## asAffine

bool SK_WARN_UNUSED_RESULT asAffine(SkScalar affine[6]) const

Fills affine in column major order. Sets affine to:

| scale-x  skew-x translate-x |
| skew-y  scale-y translate-y |

If Matrix contains perspective, returns false and leaves affine unchanged. ### Parameters

affine storage for 3x2 affine matrix; may be nullptr

### Return Value true if Matrix does not contain perspective ### Example

#### Example Output ~~~~ ScaleX: 2 SkewY: 5 SkewX: 3 ScaleY: 6 TransX: 4 TransY: 7 ~~~~

### See Also setAffine SetAffineIdentity --- ## setAffine

void setAffine(const SkScalar affine[6])

Sets Matrix 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 |

Matrix is set, row, then column, to:

| scale-x  skew-x translate-x |
|  skew-y scale-y translate-y |
|       0       0           1 |

### Parameters

affine 3x2 affine matrix

### Example

#### Example Output ~~~~ ScaleX: 2 SkewY: 5 SkewX: 3 ScaleY: 6 TransX: 4 TransY: 7 [ 2.0000 3.0000 4.0000][ 5.0000 6.0000 7.0000][ 0.0000 0.0000 1.0000] ~~~~

### See Also asAffine SetAffineIdentity --- ## mapPoints

void mapPoints(SkPoint dst[], const SkPoint src[], int count) const

Maps src Point array of length count to dst Point array of equal or greater length. Points are mapped by multiplying each Point by Matrix. 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 Point 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. ### Parameters

`dst`	storage for mapped Points
`src`	Points to transform
`count`	number of Points to transform

### Example

### See Also mapXY mapHomogeneousPoints mapVectors ---

void mapPoints(SkPoint pts[], int count) const

Maps pts Point array of length count in place. Points are mapped by multiplying each Point by Matrix. 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 Point 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

### Parameters

`pts`	storage for mapped Points
`count`	number of Points to transform

### Example

### See Also mapXY mapHomogeneousPoints mapVectors --- ## mapHomogeneousPoints

void mapHomogeneousPoints(SkPoint3 dst[], const SkPoint3 src[], int count) const

Maps src Point3 array of length count to dst Point3 array, which must of length count or greater. Point3 array is mapped by multiplying each Point3 by Matrix. Given:

         | A B C |         | x |
Matrix = | D E F |,  src = | y |
         | G H I |         | z |

each resulting dst Point 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|

### Parameters

`dst`	storage for mapped Point3 array
`src`	Point3 array to transform
`count`	items in Point3 array to transform

### Example

### See Also mapPoints mapXY mapVectors --- ## mapXY

void mapXY(SkScalar x, SkScalar y, SkPoint* result) const

Maps Point (x, y) to result. Point is mapped by multiplying by Matrix. 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

### Parameters

`x`	x-coordinate of Point to map
`y`	y-coordinate of Point to map
`result`	storage for mapped Point

### Example

### See Also mapPoints mapVectors ---

SkPoint mapXY(SkScalar x, SkScalar y) const

Returns Point (x, y) multiplied by Matrix. 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

### Parameters

`x`	x-coordinate of Point to map
`y`	y-coordinate of Point to map

### Return Value mapped Point ### Example

### See Also mapPoints mapVectors --- ## mapVectors

void mapVectors(SkVector dst[], const SkVector src[], int count) const

Maps src Vector array of length count to Vector Point array of equal or greater length. Vectors are mapped by multiplying each Vector by Matrix, treating Matrix 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. ### Parameters

`dst`	storage for mapped Vectors
`src`	Vectors to transform
`count`	number of Vectors to transform

### Example

### See Also mapVector mapPoints mapXY ---

void mapVectors(SkVector vecs[], int count) const

Maps vecs Vector array of length count in place, multiplying each Vector by Matrix, treating Matrix 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

### Parameters

`vecs`	Vectors to transform, and storage for mapped Vectors
`count`	number of Vectors to transform

### Example

### See Also mapVector mapPoints mapXY --- ## mapVector

void mapVector(SkScalar dx, SkScalar dy, SkVector* result) const

Maps Vector (x, y) to result. Vector is mapped by multiplying by Matrix, treating Matrix 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

### Parameters

`dx`	x-coordinate of Vector to map
`dy`	y-coordinate of Vector to map
`result`	storage for mapped Vector

### Example

### See Also mapVectors mapPoints mapXY ---

SkVector mapVector(SkScalar dx, SkScalar dy) const

Returns Vector (x, y) multiplied by Matrix, treating Matrix 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

### Parameters

`dx`	x-coordinate of Vector to map
`dy`	y-coordinate of Vector to map

### Return Value mapped Vector ### Example

### See Also mapVectors mapPoints mapXY --- ## mapRect

bool mapRect(SkRect* dst, const SkRect& src) const

Sets dst to bounds of src corners mapped by Matrix. Returns true if mapped corners are dst corners. Returned value is the same as calling rectStaysRect. ### Parameters

`dst`	storage for bounds of mapped Points
`src`	Rect to map

### Return Value true if dst is equivalent to mapped src ### Example

### See Also mapPoints rectStaysRect ---

bool mapRect(SkRect* rect) const

Sets rect to bounds of rect corners mapped by Matrix. Returns true if mapped corners are computed rect corners. Returned value is the same as calling rectStaysRect. ### Parameters

rect rectangle to map, and storage for bounds of mapped corners

### Return Value true if result is equivalent to mapped src ### Example

### See Also mapRectScaleTranslate mapPoints rectStaysRect --- ## mapRectToQuad

void mapRectToQuad(SkPoint dst[4], const SkRect& rect) const

Maps four corners of rect to dst. Points are mapped by multiplying each rect corner by Matrix. 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 Point 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

### Parameters

`dst`	storage for mapped corner Points
`rect`	Rect to map

### Example

### See Also mapRect mapRectScaleTranslate --- ## mapRectScaleTranslate

void mapRectScaleTranslate(SkRect* dst, const SkRect& src) const

Sets dst to bounds of src corners mapped by Matrix. If matrix contains elements other than scale or translate: asserts if SK_DEBUG is defined; otherwise, results are undefined. ### Parameters

`dst`	storage for bounds of mapped Points
`src`	Rect to map

### Example

### See Also mapRect mapRectToQuad isScaleTranslate rectStaysRect --- ## mapRadius

SkScalar mapRadius(SkScalar radius) const

Returns geometric mean radius of ellipse formed by constructing Circle of size radius, and mapping constructed Circle with Matrix. The result squared is equal to the major axis length times the minor axis length. Result is not meaningful if Matrix contains perspective elements. ### Parameters

radius Circle size to map

### Return Value average mapped radius ### Example

The area enclosed by a square with sides equal to mappedRadius is the same as the area enclosed by the ellipse major and minor axes.

### See Also mapVector --- ## isFixedStepInX

bool isFixedStepInX() const

Returns true if a unit step in x at some y mapped through Matrix can be represented by a constant Vector. Returns true if getType returns kIdentity Mask, or combinations of: kTranslate Mask, kScale Mask, and kAffine Mask. May return true if getType returns kPerspective Mask, but only when Matrix does not include rotation or skewing along the y-axis. ### Return Value true if Matrix does not have complex perspective ### Example

#### Example Output ~~~~ [ 1.0000 0.0000 0.0000][ 0.0000 1.0000 0.0000][ 0.0000 0.0000 1.0000] isFixedStepInX: true [ 1.0000 0.0000 0.0000][ 0.0000 2.0000 0.0000][ 0.0000 0.0000 1.0000] isFixedStepInX: true [ 1.0000 0.0000 0.0000][ 0.0000 1.0000 0.0000][ 0.0000 0.1000 1.0000] isFixedStepInX: true [ 1.0000 0.0000 0.0000][ 0.0000 2.0000 0.0000][ 0.0000 0.1000 1.0000] isFixedStepInX: true [ 1.0000 0.0000 0.0000][ 0.0000 1.0000 0.0000][ 0.1000 0.0000 1.0000] isFixedStepInX: false [ 1.0000 0.0000 0.0000][ 0.0000 2.0000 0.0000][ 0.1000 0.0000 1.0000] isFixedStepInX: false [ 1.0000 0.0000 0.0000][ 0.0000 1.0000 0.0000][ 0.1000 0.1000 1.0000] isFixedStepInX: false [ 1.0000 0.0000 0.0000][ 0.0000 2.0000 0.0000][ 0.1000 0.1000 1.0000] isFixedStepInX: false ~~~~

### See Also fixedStepInX getType --- ## fixedStepInX

SkVector fixedStepInX(SkScalar y) const

Returns Vector representing a unit step in x at y mapped through Matrix. If isFixedStepInX is false, returned value is undefined. ### Parameters

`y`	position of line parallel to x-axis

### Return Value Vector advance of mapped unit step in x ### Example

### See Also isFixedStepInX getType --- ## cheapEqualTo

bool cheapEqualTo(const SkMatrix& m) const

Returns true if Matrix equals m, using an efficient comparison. Returns false when the sign of zero values is the different; when one matrix has positive zero value and the other has negative zero value. Returns true even when both Matrices contain NaN. NaN never equals any value, including itself. To improve performance, NaN values are treated as bit patterns that are equal if their bit patterns are equal. ### Parameters

`m`	Matrix to compare

### Return Value true if m and Matrix are represented by identical bit patterns ### Example

#### Example Output ~~~~ identity: a == b a.cheapEqualTo(b): true neg zero: a == b a.cheapEqualTo(b): false one NaN: a != b a.cheapEqualTo(b): false both NaN: a != b a.cheapEqualTo(b): true ~~~~

### See Also operator==(const SkMatrix& a, const SkMatrix& b) --- ## operator==

bool operator==(const SkMatrix& a, const SkMatrix& b)

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 Matrix contains NaN, even if the other Matrix also contains NaN. ### Parameters

`a`	Matrix to compare
`b`	Matrix to compare

### Return Value true if m and Matrix are numerically equal ### Example

#### Example Output ~~~~ identity: a == b a.cheapEqualTo(b): true ~~~~

### See Also cheapEqualTo operator!=(const SkMatrix& a, const SkMatrix& b) --- ## operator!=

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 Matrix contains NaN, even if the other Matrix also contains NaN. ### Parameters

`a`	Matrix to compare
`b`	Matrix to compare

### Return Value true if m and Matrix are numerically not equal ### Example

### See Also cheapEqualTo operator==(const SkMatrix& a, const SkMatrix& b) --- ## dump

void dump() const

Writes text representation of Matrix to standard output. Floating point values are written with limited precision; it may not be possible to reconstruct original Matrix from output. ### Example

#### Example Output ~~~~ [ 0.7071 -0.7071 0.0000][ 0.7071 0.7071 0.0000][ 0.0000 0.0000 1.0000] [ 0.7071 -0.7071 0.0000][ 0.7071 0.7071 0.0000][ 0.0000 0.0000 1.0000] matrix != nearlyEqual ~~~~

### See Also toString --- ## toString

void toString(SkString* str) const

Creates string representation of Matrix. Floating point values are written with limited precision; it may not be possible to reconstruct original Matrix from output. ### Parameters

str storage for string representation of Matrix

### Example

#### Example Output ~~~~ mStr [ 0.7071 -0.7071 0.0000][ 0.7071 0.7071 0.0000][ 0.0000 0.0000 1.0000] neStr [ 0.7071 -0.7071 0.0000][ 0.7071 0.7071 0.0000][ 0.0000 0.0000 1.0000] matrix != nearlyEqual ~~~~

### See Also dump --- ## getMinScale

SkScalar getMinScale() const

Returns the minimum scaling factor of Matrix by decomposing the scaling and skewing elements. Returns -1 if scale factor overflows or Matrix contains perspective. ### Return Value minimum scale factor ### Example

#### Example Output ~~~~ matrix.getMinScale() 24 ~~~~

### See Also getMaxScale getMinMaxScales --- ## getMaxScale

SkScalar getMaxScale() const

Returns the maximum scaling factor of Matrix by decomposing the scaling and skewing elements. Returns -1 if scale factor overflows or Matrix contains perspective. ### Return Value maximum scale factor ### Example

#### Example Output ~~~~ matrix.getMaxScale() 42 ~~~~

### See Also getMinScale getMinMaxScales --- ## getMinMaxScales

bool SK_WARN_UNUSED_RESULT getMinMaxScales(SkScalar scaleFactors[2]) const

Sets scaleFactors[0] to the minimum scaling factor, and scaleFactors[1] to the maximum scaling factor. Scaling factors are computed by decomposing the Matrix scaling and skewing elements. Returns true if scaleFactors are found; otherwise, returns false and sets scaleFactors to undefined values. ### Parameters

scaleFactors storage for minimum and maximum scale factors

### Return Value true if scale factors were computed correctly ### Example

#### Example Output ~~~~ matrix.getMinMaxScales() false 2 2 ~~~~

### See Also getMinScale getMaxScale --- ## decomposeScale

bool decomposeScale(SkSize* scale, SkMatrix* remaining = nullptr) const

Decomposes Matrix into scale components and whatever remains. Returns false if Matrix could not be decomposed. Sets scale to portion of Matrix that scales in x and y. Sets remaining to Matrix with x and y scaling factored out. remaining may be passed as nullptr to determine if Matrix can be decomposed without computing remainder. Returns true if scale components are found. scale and remaining are unchanged if Matrix contains perspective; scale factors are not finite, or are nearly zero. On successMatrix = scale * Remaining ### Parameters

`scale`	x and y scaling factors; may be nullptr
`remaining`	Matrix without scaling; may be nullptr

### Return Value true if scale can be computed ### Example

#### Example Output ~~~~ [ 0.0000 -0.2500 0.0000][ 0.5000 0.0000 0.0000][ 0.0000 0.0000 1.0000] success: true scale: 0.5, 0.25 [ 0.0000 -0.5000 0.0000][ 2.0000 0.0000 0.0000][ 0.0000 0.0000 1.0000] [ 0.0000 -0.2500 0.0000][ 0.5000 0.0000 0.0000][ 0.0000 0.0000 1.0000] ~~~~

### See Also setScale MakeScale --- ## I

static const SkMatrix& I()

Returns reference to const identity Matrix. Returned Matrix is set to:

| 1 0 0 |
| 0 1 0 |
| 0 0 1 |

### Return Value const identity Matrix ### Example

#### Example Output ~~~~ m1 == m2 m2 == m3 ~~~~

### See Also reset setIdentity --- ## InvalidMatrix

static const SkMatrix& InvalidMatrix()

Returns reference to a const Matrix with invalid values. Returned Matrix is set to:

| SK_ScalarMax SK_ScalarMax SK_ScalarMax |
| SK_ScalarMax SK_ScalarMax SK_ScalarMax |
| SK_ScalarMax SK_ScalarMax SK_ScalarMax |

### Return Value const invalid Matrix ### Example

#### Example Output ~~~~ scaleX 3.40282e+38 ~~~~

### See Also SeeAlso getType --- ## Concat

static SkMatrix Concat(const SkMatrix& a, const SkMatrix& b)

Returns Matrix a multiplied by Matrix b. Given:

    | A B C |      | J K L |
a = | D E F |, b = | M N O |
    | G H I |      | P Q R |

sets Matrix 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 |

### Parameters

`a`	Matrix on left side of multiply expression
`b`	Matrix on right side of multiply expression

### Return Value Matrix computed from a times b ### Example

setPolyToPoly creates perspective matrices, one the inverse of the other. Multiplying the matrix by its inverse turns into an identity matrix.

### See Also preConcat postConcat --- ## dirtyMatrixTypeCache

void dirtyMatrixTypeCache()

Sets internal cache to unknown state. Use to force update after repeated modifications to Matrix element reference returned by operator[](int index). ### Example

#### Example Output ~~~~ with identity matrix: x = 24 after skew x mod: x = 24 after 2nd skew x mod: x = 24 after dirty cache: x = 66 ~~~~

### See Also operator[](int index) getType --- ## setScaleTranslate

void setScaleTranslate(SkScalar sx, SkScalar sy, SkScalar tx, SkScalar ty)

Initializes Matrix with scale and translate elements.

| sx  0 tx |
|  0 sy ty |
|  0  0  1 |

### Parameters

`sx`	horizontal scale factor to store
`sy`	vertical scale factor to store
`tx`	horizontal translation to store
`ty`	vertical translation to store

### Example

#### Example Output ~~~~ [ 1.0000 0.0000 3.0000][ 0.0000 2.0000 4.0000][ 0.0000 0.0000 1.0000] ~~~~

### See Also setScale preTranslate postTranslate --- ## isFinite

bool isFinite() const

Returns true if all elements of the matrix are finite. Returns false if any element is infinity, or NaN. ### Return Value true if matrix has only finite elements ### Example

#### Example Output ~~~~ [ 1.0000 0.0000 nan][ 0.0000 1.0000 0.0000][ 0.0000 0.0000 1.0000] matrix is finite: false matrix != matrix ~~~~

### See Also operator== ---