Wt::WTransform Class Reference
[Painting system]

A 2D affine transformation matrix. More...

#include <Wt/WTransform>

List of all members.

Public Member Functions
	WTransform ()
	Default constructor.
	WTransform (double m11, double m12, double m21, double m22, double dx, double dy)
	Construct a custom matrix by specifying the parameters.
WTransform &	operator= (const WTransform &rhs)
	Assignment operator.
bool	operator== (const WTransform &rhs) const
	Comparison operator.
bool	operator!= (const WTransform &rhs) const
	Comparison operator.
bool	isIdentity () const
	Identity check.
double	m11 () const
	Returns the horizontal scaling factor.
double	m12 () const
	Returns the vertical shearing factor.
double	m13 () const
	Returns m13 = 0.
double	m21 () const
	Returns the horizontal shearing factor.
double	m22 () const
	Returns the vertical scaling factor.
double	m23 () const
	Returns m23 = 0.
double	m31 () const
	Returns the horizontal translation factor.
double	m32 () const
	Returns the vertical translation factor.
double	m33 () const
	Returns m33 = 1.
double	dx () const
	Returns the horizontal translation factor.
double	dy () const
	Returns the vertical translation factor.
WPointF	map (const WPointF &p) const
	Apply the transformation to a point.
void	map (double x, double y, double *tx, double *ty) const
	Apply the transformation to a point.
void	reset ()
	Resets the transformation to the identity.
WTransform &	rotate (double angle)
	Rotate the transformation.
WTransform &	rotateRadians (double angle)
	Rotate the transformation.
WTransform &	scale (double sx, double sy)
	Scale the transformation.
WTransform &	shear (double sh, double sv)
	Shear the transformation.
WTransform &	translate (double dx, double dy)
	Translate the transformation.
void	decomposeTranslateRotateScaleSkew (double &dx, double &dy, double &alpha, double &sx, double &sy, double &sh) const
	Decompose the transformation.
void	decomposeTranslateRotateScaleRotate (double &dx, double &dy, double &alpha1, double &sx, double &sy, double &alpha2) const
	Decompose the transformation.

---

Detailed Description

A 2D affine transformation matrix.

The matrix is encoded using 6 parameters:

    m11  m12   0
    m21  m22   0
    dx   dy    1
    

In this representation, dx (=m31) and dy (=m32) represent the translation components, and mxy represent a 2D matrix that contains the scale, rotation (and skew) components.

---

Constructor & Destructor Documentation

Wt::WTransform::WTransform

(

)

Default constructor.

Creates the identity transformation matrix.

Wt::WTransform::WTransform	(	double	m11,
		double	m12,
		double	m21,
		double	m22,
		double	dx,
		double	dy
	)

Construct a custom matrix by specifying the parameters.

Creates a matrix from the specified parameters.

---

Member Function Documentation

WTransform & Wt::WTransform::operator=

(

const WTransform &

rhs

)

Assignment operator.

Copies the transformation from the rhs.

bool Wt::WTransform::operator==

(

const WTransform &

rhs

)

const

Comparison operator.

Returns true if the transforms are exactly the same.

bool Wt::WTransform::operator!=

(

const WTransform &

rhs

)

const

Comparison operator.

Returns true if the transforms are different.

bool Wt::WTransform::isIdentity

(

)

const

Identity check.

Returns true if the transform represents an identity transformation.

double Wt::WTransform::m31

(

)

const [inline]

Returns the horizontal translation factor.

Is equivalent to dx()

double Wt::WTransform::m32

(

)

const [inline]

Returns the vertical translation factor.

Is equivalent to dy()

double Wt::WTransform::dx

(

)

const [inline]

Returns the horizontal translation factor.

Is equivalent to m31()

double Wt::WTransform::dy

(

)

const [inline]

Returns the vertical translation factor.

Is equivalent to m32()

WPointF Wt::WTransform::map

(

const WPointF &

p

)

const

Apply the transformation to a point.

Returns the transformed point.

See also:

map(double x, double y, double *tx, double *ty) const

void Wt::WTransform::map	(	double	x,
		double	y,
		double *	tx,
		double *	ty
	)			const

Apply the transformation to a point.

Sets the point (tx, ty) to the transformation of the point (x, y).

See also:

map(const WPointF&)

void Wt::WTransform::reset

(

)

Resets the transformation to the identity.

See also:

isIdentity(), WTransform()

WTransform & Wt::WTransform::rotate

(

double

angle

)

Rotate the transformation.

Applies a clock-wise rotation to the current transformation matrix, over angle degrees.

See also:

rotateRadians(double)

WTransform & Wt::WTransform::rotateRadians

(

double

angle

)

Rotate the transformation.

Applies a clock-wise rotation to the current transformation matrix, over angle radians.

See also:

rotate(double)

WTransform & Wt::WTransform::scale	(	double	sx,
		double	sy
	)

Scale the transformation.

Applies a clock-wise rotation to the current transformation matrix, over angle radians.

See also:

shear(double, double)

WTransform & Wt::WTransform::shear	(	double	sh,
		double	sv
	)

Shear the transformation.

Shears the current transformation

See also:

scale(double, double), rotate(double, double)

WTransform & Wt::WTransform::translate	(	double	dx,
		double	dy
	)

Translate the transformation.

Translates the current transformation

void Wt::WTransform::decomposeTranslateRotateScaleSkew	(	double &	dx,
		double &	dy,
		double &	alpha,
		double &	sx,
		double &	sy,
		double &	sh
	)			const

Decompose the transformation.

Decomposes the transformation into elementary operations: translation (dx, dy), followed by rotation (alpha), followed by scale (sx, sy) and vertical shearing factor (sh). The angle is expressed in radians.

This performs a Gram-Schmidt orthonormalization.

void Wt::WTransform::decomposeTranslateRotateScaleRotate	(	double &	dx,
		double &	dy,
		double &	alpha1,
		double &	sx,
		double &	sy,
		double &	alpha2
	)			const

Decompose the transformation.

Decomposes the transformation into elementary operations: translation (dx, dy), followed by rotation (alpha2), followed by scale (sx, sy) and again a rotation (alpha2). The angles are expressed in radians.

This performs a Singular Value Decomposition.