A Transformation matrix. More...

#include <cairomm/matrix.h>

Inheritance diagram for Cairo::Matrix:

Public Member Functions
	Matrix ()
	Creates an uninitialized matrix. More...

	Matrix (double xx, double yx, double xy, double yy, double x0, double y0)
	Creates a matrix Sets to be the affine transformation given by xx, yx, xy, yy, x0, y0. More...

void	translate (double tx, double ty)
	Applies a translation by tx, ty to the transformation in matrix. More...

void	scale (double sx, double sy)
	Applies scaling by sx, sy to the transformation in matrix. More...

void	rotate (double radians)
	Applies rotation by radians to the transformation in matrix. More...

void	invert ()
	Changes matrix to be the inverse of it's original value. More...

void	multiply (Matrix & a, Matrix & b)
	Multiplies the affine transformations in a and b together and stores the result in this matrix. More...

void	transform_distance (double & dx, double & dy) const
	Transforms the distance vector (dx,dy) by matrix. More...

void	transform_point (double & x, double & y) const
	Transforms the point (x, y) by this matrix. More...

Related Functions
(Note that these are not member functions.)
Matrix	identity_matrix ()
	Returns a Matrix initialized to the identity matrix. More...

Matrix	translation_matrix (double tx, double ty)
	Returns a Matrix initialized to a transformation that translates by tx and ty in the X and Y dimensions, respectively. More...

Matrix	scaling_matrix (double sx, double sy)
	Returns a Matrix initialized to a transformation that scales by sx and sy in the X and Y dimensions, respectively. More...

Matrix	rotation_matrix (double radians)
	Returns a Matrix initialized to a transformation that rotates by radians. More...

Matrix	operator* (const Matrix & a, const Matrix & b)
	Multiplies the affine transformations in a and b together and returns the result. More...

Detailed Description

A Transformation matrix.

Cairo::Matrix is used throughout cairomm to convert between different coordinate spaces. A Matrix holds an affine transformation, such as a scale, rotation, shear, or a combination of these. The transformation of a point (x,y) is given by:

x_new = xx * x + xy * y + x0;

y_new = yx * x + yy * y + y0;

The current transformation matrix of a Context, represented as a Matrix, defines the transformation from user-space coordinates to device-space coordinates.

See also: Context::get_matrix(); Context::set_matrix()

Constructor & Destructor Documentation

◆ Matrix() [1/2]

Cairo::Matrix::Matrix ( )

Creates an uninitialized matrix.

If you want a matrix initialized to a certain value, either specify the values explicitly with the other constructor or use one of the free functions for initializing matrices with specific scales, rotations, etc.

See also: identity_matrix(); rotation_matrix(); translation_matrix(); scaling_matrix()

◆ Matrix() [2/2]

Cairo::Matrix::Matrix	(	double	xx,
		double	yx,
		double	xy,
		double	yy,
		double	x0,
		double	y0
	)

Creates a matrix Sets to be the affine transformation given by xx, yx, xy, yy, x0, y0.

The transformation is given by:

x_new = xx * x + xy * y + x0;

y_new = yx * x + yy * y + y0;

Parameters

xx	xx component of the affine transformation
yx	yx component of the affine transformation
xy	xy component of the affine transformation
yy	yy component of the affine transformation
x0	X translation component of the affine transformation
y0	Y translation component of the affine transformation

Member Function Documentation

◆ invert()

void Cairo::Matrix::invert ( )

Changes matrix to be the inverse of it's original value.

Not all transformation matrices have inverses; if the matrix collapses points together (it is degenerate), then it has no inverse and this function will throw an exception.

Exceptions

◆ multiply()

void Cairo::Matrix::multiply	(	Matrix &	a,
		Matrix &	b
	)

Multiplies the affine transformations in a and b together and stores the result in this matrix.

The effect of the resulting transformation is to first apply the transformation in a to the coordinates and then apply the transformation in b to the coordinates.

It is allowable for result to be identical to either a or b.

Parameters

a	a Matrix
b	a Matrix

See also: operator*()

◆ rotate()

void Cairo::Matrix::rotate ( double radians )

Applies rotation by radians to the transformation in matrix.

The effect of the new transformation is to first rotate the coordinates by radians, then apply the original transformation to the coordinates.

Parameters

radians angle of rotation, in radians. The direction of rotation is defined such that positive angles rotate in the direction from the positive X axis toward the positive Y axis. With the default axis orientation of cairo, positive angles rotate in a clockwise direction.

◆ scale()

void Cairo::Matrix::scale	(	double	sx,
		double	sy
	)

Applies scaling by sx, sy to the transformation in matrix.

The effect of the new transformation is to first scale the coordinates by sx and sy, then apply the original transformation to the coordinates.

Parameters

sx	scale factor in the X direction
sy	scale factor in the Y direction

◆ transform_distance()

void Cairo::Matrix::transform_distance	(	double &	dx,
		double &	dy
	)		const

Transforms the distance vector (dx,dy) by matrix.

This is similar to transform_point() except that the translation components of the transformation are ignored. The calculation of the returned vector is as follows:

dx2 = dx1 * a + dy1 * c;

dy2 = dx1 * b + dy1 * d;

Affine transformations are position invariant, so the same vector always transforms to the same vector. If (x1,y1) transforms to (x2,y2) then (x1+dx1,y1+dy1) will transform to (x1+dx2,y1+dy2) for all values of x1 and x2.

Parameters

dx	X component of a distance vector. An in/out parameter
dy	Y component of a distance vector. An in/out parameter

◆ transform_point()

void Cairo::Matrix::transform_point	(	double &	x,
		double &	y
	)		const

Transforms the point (x, y) by this matrix.

Parameters

x	X position. An in/out parameter
y	Y position. An in/out parameter

◆ translate()

void Cairo::Matrix::translate	(	double	tx,
		double	ty
	)

Applies a translation by tx, ty to the transformation in matrix.

The effect of the new transformation is to first translate the coordinates by tx and ty, then apply the original transformation to the coordinates.

Parameters

tx	amount to translate in the X direction
ty	amount to translate in the Y direction

Friends And Related Function Documentation

◆ identity_matrix()

Matrix identity_matrix ( )

◆ operator*()

Matrix operator*	(	const Matrix &	a,
		const Matrix &	b
	)

The effect of the resulting transformation is to first apply the transformation in a to the coordinates and then apply the transformation in b to the coordinates.

It is allowable for result to be identical to either a or b.

Parameters

a	a Matrix
b	a Matrix

◆ rotation_matrix()

Matrix rotation_matrix ( double radians )

Parameters

radians angle of rotation, in radians. The direction of rotation is defined such that positive angles rotate in the direction from the positive X axis toward the positive Y axis. With the default axis orientation of cairo, positive angles rotate in a clockwise direction.

◆ scaling_matrix()

Matrix scaling_matrix	(	double	sx,
		double	sy
	)

Parameters

sx	scale factor in the X direction
sy	scale factor in the Y direction

◆ translation_matrix()

Matrix translation_matrix	(	double	tx,
		double	ty
	)

Parameters

tx	amount to translate in the X direction
ty	amount to translate in the Y direction

The documentation for this class was generated from the following file:

cairomm/matrix.h

Public Member Functions

Related Functions

Detailed Description

Constructor & Destructor Documentation

◆ Matrix() [1/2]

◆ Matrix() [2/2]

Member Function Documentation

◆ invert()

◆ multiply()

◆ rotate()

◆ scale()

◆ transform_distance()

◆ transform_point()

◆ translate()

Friends And Related Function Documentation

◆ identity_matrix()

◆ operator*()

◆ rotation_matrix()

◆ scaling_matrix()

◆ translation_matrix()