A value class that defines a 2D affine transformation matrix. More...

#include <Wt/WTransform>

Inheritance diagram for Wt::WTransform:

Classes
struct	TRSRDecomposition
	Result of a TRSR decomposition. More...

struct	TRSSDecomposition
	Result of a TRSS decomposition. More...

Public Member Functions
	WTransform ()
	Default constructor. More...

	WTransform (double m11, double m12, double m21, double m22, double dx, double dy)
	Construct a custom matrix by specifying the parameters. More...

	WTransform (const WTransform &other)
	Copy constructor.

WTransform &	operator= (const WTransform &rhs)
	Assignment operator. More...

bool	operator== (const WTransform &rhs) const
	Comparison operator. More...

bool	operator!= (const WTransform &rhs) const
	Comparison operator. More...

bool	isIdentity () const
	Identity check. More...

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. More...

double	m32 () const
	Returns the vertical translation factor. More...

double	m33 () const
	Returns m33 = 1.

double	dx () const
	Returns the horizontal translation factor. More...

double	dy () const
	Returns the vertical translation factor. More...

WPointF	map (const WPointF &p) const
	Applys the transformation to a point. More...

void	map (double x, double y, double tx, double ty) const
	Applys the transformation to a point. More...

WRectF	map (const WRectF &rect) const
	Applies the transformation to a rectangle. More...

WPainterPath	map (const WPainterPath &path) const
	Applies the transformation to a painter path. More...

void	reset ()
	Resets the transformation to the identity. More...

WTransform &	rotate (double angle)
	Rotates the transformation. More...

WTransform &	rotateRadians (double angle)
	Rotates the transformation. More...

WTransform &	scale (double sx, double sy)
	Scales the transformation. More...

WTransform &	shear (double sh, double sv)
	Shears the transformation. More...

WTransform &	translate (double dx, double dy)
	Translates the transformation. More...

WTransform &	translate (const WPointF &p)
	Translates the transformation. More...

WTransform &	operator*= (const WTransform &rhs)
	Adds a transform that is conceptually applied after this transform.

WTransform	operator* (const WTransform &rhs) const
	Multiply 2 transform objects.

double	determinant () const
	Returns the determinant.

WTransform	adjoint () const
	Returns the adjoint.

WTransform	inverted () const
	Returns the inverted transformation. More...

void	decomposeTranslateRotateScaleSkew (TRSSDecomposition &result) const
	Decomposes the transformation. More...

void	decomposeTranslateRotateScaleRotate (TRSRDecomposition &result) const
	Decomposes the transformation. More...

virtual std::string	jsValue () const WT_CXX11ONLY(override)
	Returns a JavaScript representation of the value of this object. More...

Public Member Functions inherited from Wt::WJavaScriptExposableObject
bool	isJavaScriptBound () const
	Returns whether this object is JavaScript bound. More...

std::string	jsRef () const
	Returns a JavaScript reference to this object. More...

Static Public Member Functions
static double	degreesToRadians (double angle)
	Utility method to convert degrees to radians.

Static Public Attributes
static const WTransform	Identity
	A constant that represents the identity transform. More...

Detailed Description

A value class that defines 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.

The transformation is used to represent a tansformed coordinate system, and provides methods to rotate(), scale(), shear() or translate() this coordinate system.

There are also 2 methods to decompose an arbitrary matrix into elementary operations:

decomposeTranslateRotateScaleSkew() decomposes into a T ∘ R ∘ Sxx ∘ Sxy
decomposeTranslateRotateScaleRotate() decomposes into a T ∘ R1 ∘ Sxx ∘ R2

with T a translation, R a rotation, Sxx a scale, and Sxy a skew component.

JavaScript exposability

A WTransform is JavaScript exposable. If a WTransform is JavaScript bound, it can be accessed in your custom JavaScript code through its handle's jsRef(). A transform is represented as a JavaScript array, e.g. a WTransform(m11, m12, m21, m22, dx, dy) will be represented in JavaScript by:

[m11, m12, m21, m22, dx, dy]

As an exception to the general rule that JavaScript bound objects should not be modified, WTransform does support many modifications. These modifications will then accumulate in the JavaScript representation of the transform.

Constructor & Destructor Documentation

◆ WTransform() [1/2]

Wt::WTransform::WTransform ( )

Default constructor.

Creates the identity transformation matrix.

◆ WTransform() [2/2]

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

◆ decomposeTranslateRotateScaleRotate()

void Wt::WTransform::decomposeTranslateRotateScaleRotate ( TRSRDecomposition & result ) const

Decomposes 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 (SVD).

◆ decomposeTranslateRotateScaleSkew()

void Wt::WTransform::decomposeTranslateRotateScaleSkew ( TRSSDecomposition & result ) const

Decomposes 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.

◆ dx()

double Wt::WTransform::dx ( ) const

Returns the horizontal translation factor.

Is equivalent to m31()

◆ dy()

double Wt::WTransform::dy ( ) const

Returns the vertical translation factor.

Is equivalent to m32()

◆ inverted()

WTransform Wt::WTransform::inverted ( ) const

Returns the inverted transformation.

Returns this if the transformation could not be inverted (determinant() == 0), and logs an error instead.

◆ isIdentity()

bool Wt::WTransform::isIdentity ( ) const

Identity check.

Returns true if the transform represents an identity transformation.

Note: This is always false if the transform is JavaScript bound.

◆ jsValue()

std::string Wt::WTransform::jsValue ( ) const

overridevirtual

Returns a JavaScript representation of the value of this object.

Note: The value returned will reflect the current server side value of the object. If this object is JavaScript bound, this value may not reflect the actual client side value. If you need access to the client side value, use jsRef() intead.

Implements Wt::WJavaScriptExposableObject.

◆ m31()

double Wt::WTransform::m31 ( ) const

Returns the horizontal translation factor.

Is equivalent to dx()

◆ m32()

double Wt::WTransform::m32 ( ) const

Returns the vertical translation factor.

Is equivalent to dy()

◆ map() [1/4]

WPointF Wt::WTransform::map ( const WPointF & p ) const

Applys the transformation to a point.

Returns the transformed point.

Note: If this transform or the given point are JavaScript bound, the resulting point will also be JavaScript bound.

See also: map(double x, double y, double *tx, double *ty) const

◆ map() [2/4]

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

Applys the transformation to a point.

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

See also: map(const WPointF&) const

◆ map() [3/4]

WRectF Wt::WTransform::map ( const WRectF & rect ) const

Applies the transformation to a rectangle.

Since the rectangle is aligned with X and Y axes, this may increase the size of the rectangle even for a transformation that only rotates.

Note: If this transform or the given rectangle are JavaScript bound, the resulting rectangle will also be JavaScript bound.

◆ map() [4/4]

WPainterPath Wt::WTransform::map ( const WPainterPath & path ) const

Applies the transformation to a painter path.

This will transform all individual points according to the transformation. The radius of arcs will be unaffected.

Note: If this transform or the given path are JavaScript bound, the resulting path will also be JavaScript bound.

◆ operator!=()

bool Wt::WTransform::operator!= ( const WTransform & rhs ) const

Comparison operator.

Returns true if the transforms are different.

◆ operator=()

WTransform & Wt::WTransform::operator= ( const WTransform & rhs )

Assignment operator.

Copies the transformation from the rhs.

◆ operator==()

bool Wt::WTransform::operator== ( const WTransform & rhs ) const

Comparison operator.

Returns true if the transforms are exactly the same.

◆ reset()

void Wt::WTransform::reset ( )

Resets the transformation to the identity.

Exceptions

WException if the transform is JavaScript bound

See also: isIdentity(), WTransform()

◆ rotate()

WTransform & Wt::WTransform::rotate ( double angle )

Rotates the transformation.

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

See also: rotateRadians()

◆ rotateRadians()

WTransform & Wt::WTransform::rotateRadians ( double angle )

Rotates the transformation.

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

See also: rotate()

◆ scale()

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

Scales the transformation.

Scales the current transformation.

See also: shear()

◆ shear()

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

Shears the transformation.

Shears the current transformation.

See also: scale(), rotate()

◆ translate() [1/2]

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

Translates the transformation.

Translates the current transformation.

◆ translate() [2/2]

WTransform & Wt::WTransform::translate ( const WPointF & p )