A 2x3 affine matrix class for 2D transformations. More...

#include <afmatrix.h>

Collaboration diagram for a2dAffineMatrix:

Public Member Functions
	a2dAffineMatrix (double xt, double yt, double scalex=1, double scaley=1, double degrees=0)
	constructor More...

	a2dAffineMatrix (double sx, double shx, double shy, double sy, double tx, double ty)

	a2dAffineMatrix (void)
	constructor (makes an identity matrix)

	a2dAffineMatrix (const a2dAffineMatrix &mat)
	constructor using other matrix

double	GetValue (int col, int row) const
	get the value in the matrix at col,row More...

void	SetValue (int col, int row, double value)
	set the value in the matrix at col,row More...

void	operator= (const a2dAffineMatrix &mat)
	make the same

bool	operator== (const a2dAffineMatrix &a)
	are they eqaul

bool	operator!= (const a2dAffineMatrix &a)
	are they NOT eqaul

a2dAffineMatrix &	operator*= (const a2dAffineMatrix &m)
	multiply matrix m with this

a2dAffineMatrix	operator* (const a2dAffineMatrix &m) const
	multiply this by matrix m and return result

a2dAffineMatrix	operator- (const a2dAffineMatrix &a)
	subtract two matrices More...

double &	operator() (int col, int row)

double	operator() (int col, int row) const

bool	Invert (void)
	Invert matrix.

bool	Identity (void)
	Make into identity matrix.

bool	IsIdentity (void) const
	Is the matrix the identity matrix? More...

bool	IsIdentity1 (void) const
	This does an actual check. More...

bool	IsTranslate (void) const
	Is the matrix only a translation? More...

bool	IsTranslateScaleIso (void) const

bool	Scale (double scale)
	Scale by scale (isotropic scaling i.e. the same in x and y): More...

bool	RemoveScale ()
	Remove Scale: More...

a2dAffineMatrix &	Scale (const double &xs, const double &ys, const double &xc, const double &yc)
	Scale with center point and x/y scale. More...

a2dAffineMatrix &	Mirror (bool y=true, bool x=false)
	mirror a matrix in x, y More...

bool	Translate (double x, double y)
	Translate by dx, dy: More...

bool	Rotate (double angle)
	Rotate clockwise by the given number of degrees: More...

bool	SkewX (double degrees)
	Skew Xaxis: More...

bool	SkewY (double degrees)
	Skew Yaxis: More...

a2dAffineMatrix &	Rotate (const double &r, const double &x, const double &y)
	Rotate counter clockwise with point of rotation. More...

void	TransformPoint (double x, double y, double &tx, double &ty) const
	Transform a point.

void	TransformPoint (double &tx, double &ty) const
	Transform a point.

void	TransformPoint (a2dPoint2D *point) const
	Transform a point.

void	TransformPoint (const a2dPoint2D &src, a2dPoint2D *dest) const
	Transform a point.

void	TransformVector (double dx, double dy, double &tdx, double &tdy) const
	Transform a vector. More...

double	TransformDistance (double distance) const
	Transform a distance. More...

void	TransformDistance (double &dx, double &dy) const
	Transform a distance.

double	Get_scaleX () const
	return scaling in X

double	Get_scaleY () const
	return scaling in Y

double	GetRotation () const
	return rotation More...

void	SetRotation (double rotation)
	set rotation More...

a2dPoint2D	GetTranslation () const
	get the translation vector as a point

double	GetDeterminant () const
	Calculate the determinat of the linear transformation.

double	GetDeterminant1 () const
	Calculate the determinat of the shift vector and the transformed y-axis vector.

double	GetDeterminant2 () const
	Calculate the determinat of the transformed x-axis vector and the shift vector.

double	GetMaximum () const
	Calculate the maximum absolute of the elemnts entering GetDeterminant.

double	GetMaximum1 () const
	Calculate the maximum absolute of the elemnts entering GetDeterminant1.

double	GetMaximum2 () const
	Calculate the maximum absolute of the elemnts entering GetDeterminant2.

void	DebugDump (const wxChar *text, double w, double h) const
	Dump the Matrix to a debug window.

Static Public Member Functions
static a2dAffineMatrix	Mul (const a2dAffineMatrix &m1, const a2dAffineMatrix &m2)

static const a2dAffineMatrix &	GetIdentityMatrix ()
	Return a static identity matrix as reference.

Public Attributes
double	m_matrix [3][2]
	array store the six double for the affine matrix

bool	m_isIdentity
	true if identity matrix

Static Protected Attributes
static const a2dAffineMatrix	sm_Identity
	A static identity matrix in case an identity matrix is to be returned as reference.

Friends
bool	operator== (const a2dAffineMatrix &a, const a2dAffineMatrix &b)
	are they eqaul

bool	operator!= (const a2dAffineMatrix &a, const a2dAffineMatrix &b)
	are they NOT eqaul

a2dAffineMatrix	operator- (const a2dAffineMatrix &a, const a2dAffineMatrix &b)
	subtract two matrices

Detailed Description

A 2x3 affine matrix class for 2D transformations.

A 2x3 matrix to do 2D transformations.

It follows a 'column vector' convention, more or less. A point P=(x,y) is treated as the transpose of [x, y, 1], and transformation is accomplished by pre-multiplication by the transformation matrix M:

                [ sx  shx  tx ]   [x]
     [x',y'] =  [ shy  sy  ty ] * [y] = [sx*x+shx*y+tx, shy*x+sy*y+ty]
                                  [1]

It is only "more-or-less" so because accessors of this class use a convention of (col,row), which is backwards from normal mathematical notation. The actual memory layout is double[3][2], which means it's stored column-major: {sx, shy, shx, sy, tx, ty}.

It can be used to map data to window coordinates. But also for manipulating your own 2D data. Because this class is specialy designed to do 2D transformations a lot of things could be optimized for this particlular purpose. For example drawing a picture (composed of several primitives) at a certain coordinate and angle within another parent picture. At all times m_isIdentity is set if the matrix itself is an Identity matrix. m_isIdentity is used where possible to optimize calculations.

Definition at line 53 of file afmatrix.h.

Constructor & Destructor Documentation

a2dAffineMatrix::a2dAffineMatrix	(	double	xt,
		double	yt,
		double	scalex = `1`,
		double	scaley = `1`,
		double	degrees = `0`
	)

constructor

Initialize matrix.

First a translation is proceed after this a scalling at that position followed by a rotation at that position.

Parameters

xt	translation in x
yt	translation in y
scalex	scaling in x
scaley	scaling in y
degrees	rotation clockwise

Definition at line 53 of file afmatrix.cpp.

Member Function Documentation

double a2dAffineMatrix::GetRotation ( ) const

return rotation

Returns the absolute rotation in the range �179.999... to 180 degrees

See Also: SetRotation

Definition at line 799 of file afmatrix.cpp.

double a2dAffineMatrix::GetValue	(	int	col,
		int	row
	)		const

get the value in the matrix at col,row

rows are horizontal (second index of m_matrix member) columns are vertical (first index of m_matrix member)

Definition at line 106 of file afmatrix.cpp.

bool a2dAffineMatrix::IsIdentity ( void ) const

inline

Is the matrix the identity matrix?

Only returns a flag, which is set whenever an operation

is done.

Definition at line 147 of file afmatrix.h.

bool a2dAffineMatrix::IsIdentity1 ( void ) const

inline

This does an actual check.

Is the matrix the identity matrix? Each operation checks whether the result is still the identity matrix and sets a flag.

Definition at line 347 of file afmatrix.h.

bool a2dAffineMatrix::IsTranslate ( void ) const

inline

Is the matrix only a translation?

checks the matrix to see if it only does a traslation.

Definition at line 359 of file afmatrix.h.

a2dAffineMatrix & a2dAffineMatrix::Mirror	(	bool	y = `true`,
		bool	x = `false`
	)

mirror a matrix in x, y

ex:

           | -1     0      0 |
 matrix' = |  0    -1      0 | x matrix
           |  0     0      1 |

Definition at line 396 of file afmatrix.cpp.

double & a2dAffineMatrix::operator()	(	int	col,
		int	row
	)

rows are horizontal (second index of m_matrix member) columns are vertical (first index of m_matrix member)

Definition at line 174 of file afmatrix.cpp.

double a2dAffineMatrix::operator()	(	int	col,
		int	row
	)		const

rows are horizontal (second index of m_matrix member) columns are vertical (first index of m_matrix member)

Definition at line 182 of file afmatrix.cpp.

a2dAffineMatrix a2dAffineMatrix::operator- ( const a2dAffineMatrix & a )

subtract two matrices

matrixes subtract

Definition at line 726 of file afmatrix.cpp.

bool a2dAffineMatrix::RemoveScale ( )

Remove Scale:

ex:

          | 1/sqrt(det) 0           0      |
matrix' = | 0           1/sqrt(det) 0      | x matrix
          | 0           0           1      |

Definition at line 290 of file afmatrix.cpp.

bool a2dAffineMatrix::Rotate ( double angle )

Rotate clockwise by the given number of degrees:

Rotates clockwise: If you call Rotate(20); Rotate(10); the absolute rotation is 30 degrees (if the initially rotation was 0)

See Also: SetRotation

:

           |  cos sin 0 |
 matrix' = | -sin cos 0 | x matrix
           |   0   0  1 |

Definition at line 432 of file afmatrix.cpp.

a2dAffineMatrix & a2dAffineMatrix::Rotate	(	const double &	r,
		const double &	x,
		const double &	y
	)

Rotate counter clockwise with point of rotation.

ex:

           |  cos(r) -sin(r)    x(1-cos(r))+y(sin(r)|
 matrix' = |  sin(r)  cos(r)    y(1-cos(r))-x(sin(r)| x matrix
           |   0          0                       1 |

Definition at line 484 of file afmatrix.cpp.

bool a2dAffineMatrix::Scale ( double scale )

Scale by scale (isotropic scaling i.e. the same in x and y):

ex:

           | scale  0      0      |
 matrix' = |  0     scale  0      | x matrix
           |  0     0      scale  |

Definition at line 270 of file afmatrix.cpp.

a2dAffineMatrix & a2dAffineMatrix::Scale	(	const double &	xs,
		const double &	ys,
		const double &	xc,
		const double &	yc
	)

Scale with center point and x/y scale.

ex:

           |  xs    0      xc(1-xs) |
 matrix' = |  0    ys      yc(1-ys) | x matrix
           |  0     0      1        |

Definition at line 327 of file afmatrix.cpp.

void a2dAffineMatrix::SetRotation ( double rotation )

set rotation

In opposite to Rotate this method sets an absolute rotation.

See Also: Rotate

Definition at line 815 of file afmatrix.cpp.

void a2dAffineMatrix::SetValue	(	int	col,
		int	row,
		double	value
	)

set the value in the matrix at col,row

rows are horizontal (second index of m_matrix member) columns are vertical (first index of m_matrix member)

Definition at line 114 of file afmatrix.cpp.

bool a2dAffineMatrix::SkewX ( double degrees )

Skew Xaxis:

ex:

           |   1   tan(a) 0 |
 matrix' = |   0   1      0 | x matrix
           |   0   0      1 |

Definition at line 441 of file afmatrix.cpp.

bool a2dAffineMatrix::SkewY ( double degrees )

Skew Yaxis:

ex:

           |     1    0      0 |
 matrix' = | tan(a)   1      0 | x matrix
           |     0    0      1 |

Definition at line 460 of file afmatrix.cpp.

double a2dAffineMatrix::TransformDistance ( double distance ) const

Transform a distance.

This transforms a relative distance. A horizontal and vertical line starting at the origin, and distance long, is transformed. The length of the line with the minimum distance in the transformed space is returned.

Parameters

distance distance to transform

Returns: transformed distance

Definition at line 616 of file afmatrix.cpp.

void a2dAffineMatrix::TransformVector	(	double	dx,
		double	dy,
		double &	tdx,
		double &	tdy
	)		const

Transform a vector.

This transforms a free vector. It is equivalent to transforming the two points (px,py) and (px+dx,py+dy) and then subtracting the former from the latter. In effect this means it ignores the translation portion of the matrix, and just multiplies by the core 2x2 linear transform.

Definition at line 602 of file afmatrix.cpp.

bool a2dAffineMatrix::Translate	(	double	x,
		double	y
	)

Translate by dx, dy:

ex:

           | 1  0 dx |
 matrix' = | 0  1 dy | x matrix
           | 0  0  1 |

Definition at line 420 of file afmatrix.cpp.

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

Public Member Functions

Static Public Member Functions

Public Attributes

Static Protected Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation