MATRIX3x3< T > Class Template Reference

MATRIX3x3 describes a general 3x3 matrix. More...

Public Member Functions
	MATRIX3x3 ()
	Initialize all matrix members to zero.
	MATRIX3x3 (T a00, T a01, T a02, T a10, T a11, T a12, T a20, T a21, T a22)
	Initialize with given matrix members. More...
void	SetIdentity ()
	Set the matrix to the identity matrix. More...
void	SetTranslation (VECTOR2< T > aTranslation)
	Set the translation components of the matrix. More...
VECTOR2< T >	GetTranslation () const
	Get the translation components of the matrix. More...
void	SetRotation (T aAngle)
	Set the rotation components of the matrix. More...
void	SetScale (VECTOR2< T > aScale)
	Set the scale components of the matrix. More...
VECTOR2< T >	GetScale () const
	Get the scale components of the matrix. More...
T	Determinant () const
	Compute the determinant of the matrix. More...
MATRIX3x3	Inverse () const
	Determine the inverse of the matrix. More...
MATRIX3x3	Transpose () const
	Get the transpose of the matrix. More...

Public Attributes
T	m_data [3][3]

Friends
std::ostream &	operator (std::ostream &aStream, const MATRIX3x3< T > &aMatrix)
	Output to a stream.

Detailed Description

template<class T>
class MATRIX3x3< T >

MATRIX3x3 describes a general 3x3 matrix.

Any linear transformation in 2D can be represented by a homogeneous 3x3 transformation matrix. Given a vector x, the linear transformation with the transformation matrix M is given as

x' = M * x

To represent an affine transformation, homogeneous coordinates have to be used. That means the 2D-vector (x, y) has to be extended to a 3D-vector by a third component (x, y, 1).

Transformations can be easily combined by matrix multiplication.

A * (B * x ) = (A * B) * x ( A, B: transformation matrices, x: vector )

This class was implemented using templates, so flexible type combinations are possible.

Constructor & Destructor Documentation

MATRIX3x3()

template<class T >

MATRIX3x3< T >::MATRIX3x3	(	T	a00,
		T	a01,
		T	a02,
		T	a10,
		T	a11,
		T	a12,
		T	a20,
		T	a21,
		T	a22
	)

Initialize with given matrix members.

Parameters

a00	is the component [0,0].
a01	is the component [0,1].
a02	is the component [0,2].
a10	is the component [1,0].
a11	is the component [1,1].
a12	is the component [1,2].
a20	is the component [2,0].
a21	is the component [2,1].
a22	is the component [2,2].

Member Function Documentation

Determinant()

template<class T >

T MATRIX3x3< T >::Determinant

Compute the determinant of the matrix.

Returns

the determinant value.

GetScale()

template<class T >

VECTOR2< T > MATRIX3x3< T >::GetScale

Get the scale components of the matrix.

Returns

the scale factors, specified as 2D-vector.

GetTranslation()

template<class T >

VECTOR2< T > MATRIX3x3< T >::GetTranslation

Get the translation components of the matrix.

Returns

is the translation (2D-vector).

Inverse()

template<class T >

MATRIX3x3< T > MATRIX3x3< T >::Inverse

Determine the inverse of the matrix.

The inverse of a transformation matrix can be used to revert a transformation.

x = Minv * ( M * x ) ( M: transformation matrix, Minv: inverse transformation matrix, x: vector)

Returns

the inverse matrix.

SetIdentity()

template<class T >

void MATRIX3x3< T >::SetIdentity

(

void

)

Set the matrix to the identity matrix.

The diagonal components of the matrix are set to 1.

SetRotation()

template<class T >

void MATRIX3x3< T >::SetRotation

(

T

aAngle

)

Set the rotation components of the matrix.

The angle needs to have a positive value for an anti-clockwise rotation.

Parameters

aAngle

is the rotation angle in [rad].

SetScale()

template<class T >

void MATRIX3x3< T >::SetScale

(

VECTOR2< T >

aScale

)

Set the scale components of the matrix.

Parameters

aScale

contains the scale factors, specified as 2D-vector.

SetTranslation()

template<class T >

void MATRIX3x3< T >::SetTranslation

(

VECTOR2< T >

aTranslation

)

Set the translation components of the matrix.

Parameters

aTranslation

is the translation, specified as 2D-vector.

Transpose()

template<class T >

MATRIX3x3< T > MATRIX3x3< T >::Transpose

Get the transpose of the matrix.

Returns

the transpose matrix.

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

• 3rd_party/router/kimath/include/math/matrix3x3.h