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MATRIX3x3< T > Class Template Reference

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

#include <matrix3x3.h>

Public Member Functions

 MATRIX3x3 ()
 Initialize all matrix members to zero. More...
 
 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. More...
 

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.

Definition at line 55 of file matrix3x3.h.

Constructor & Destructor Documentation

◆ MATRIX3x3() [1/2]

template<class T >
MATRIX3x3< T >::MATRIX3x3 ( )

Initialize all matrix members to zero.

Definition at line 180 of file matrix3x3.h.

181 {
182  for( int j = 0; j < 3; j++ )
183  {
184  for( int i = 0; i < 3; i++ )
185  {
186  m_data[i][j] = 0.0;
187  }
188  }
189 }
MATRIX3x3::m_data
T m_data[3][3]
Definition: matrix3x3.h:64

◆ MATRIX3x3() [2/2]

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
a00is the component [0,0].
a01is the component [0,1].
a02is the component [0,2].
a10is the component [1,0].
a11is the component [1,1].
a12is the component [1,2].
a20is the component [2,0].
a21is the component [2,1].
a22is the component [2,2].

Definition at line 193 of file matrix3x3.h.

194 {
195  m_data[0][0] = a00;
196  m_data[0][1] = a01;
197  m_data[0][2] = a02;
198 
199  m_data[1][0] = a10;
200  m_data[1][1] = a11;
201  m_data[1][2] = a12;
202 
203  m_data[2][0] = a20;
204  m_data[2][1] = a21;
205  m_data[2][2] = a22;
206 }
MATRIX3x3::m_data
T m_data[3][3]
Definition: matrix3x3.h:64

Member Function Documentation

◆ Determinant()

template<class T >
T MATRIX3x3< T >::Determinant ( ) const

Compute the determinant of the matrix.

Returns
the determinant value.

Definition at line 306 of file matrix3x3.h.

307 {
308  return m_data[0][0] * ( m_data[1][1] * m_data[2][2] - m_data[1][2] * m_data[2][1] )
309  - m_data[0][1] * ( m_data[1][0] * m_data[2][2] - m_data[1][2] * m_data[2][0] )
310  + m_data[0][2] * ( m_data[1][0] * m_data[2][1] - m_data[1][1] * m_data[2][0] );
311 }
MATRIX3x3::m_data
T m_data[3][3]
Definition: matrix3x3.h:64

◆ GetScale()

template<class T >
VECTOR2< T > MATRIX3x3< T >::GetScale ( ) const

Get the scale components of the matrix.

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

Definition at line 265 of file matrix3x3.h.

266 {
267  VECTOR2<T> result( m_data[0][0], m_data[1][1] );
268 
269  return result;
270 }
VECTOR2
Define a general 2D-vector/point.
Definition: vector2d.h:61
MATRIX3x3::m_data
T m_data[3][3]
Definition: matrix3x3.h:64

Referenced by KIGFX::PCB_PAINTER::draw(), KIGFX::SCH_PAINTER::getShadowWidth(), KIGFX::GAL::GetVisibleWorldExtents(), KIGFX::OPENGL_GAL::getWorldPixelSize(), KIGFX::VIEW::ToScreen(), and KIGFX::VIEW::ToWorld().

◆ GetTranslation()

template<class T >
VECTOR2< T > MATRIX3x3< T >::GetTranslation ( ) const

Get the translation components of the matrix.

Returns
is the translation (2D-vector).

Definition at line 234 of file matrix3x3.h.

235 {
236  VECTOR2<T> result;
237  result.x = m_data[0][2];
238  result.y = m_data[1][2];
239 
240  return result;
241 }
VECTOR2
Define a general 2D-vector/point.
Definition: vector2d.h:61
MATRIX3x3::m_data
T m_data[3][3]
Definition: matrix3x3.h:64

◆ Inverse()

template<class T >
MATRIX3x3< T > MATRIX3x3< T >::Inverse ( ) const

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.

Definition at line 339 of file matrix3x3.h.

340 {
341  MATRIX3x3<T> result;
342 
343  result.m_data[0][0] = m_data[1][1] * m_data[2][2] - m_data[2][1] * m_data[1][2];
344  result.m_data[0][1] = m_data[0][2] * m_data[2][1] - m_data[2][2] * m_data[0][1];
345  result.m_data[0][2] = m_data[0][1] * m_data[1][2] - m_data[1][1] * m_data[0][2];
346 
347  result.m_data[1][0] = m_data[1][2] * m_data[2][0] - m_data[2][2] * m_data[1][0];
348  result.m_data[1][1] = m_data[0][0] * m_data[2][2] - m_data[2][0] * m_data[0][2];
349  result.m_data[1][2] = m_data[0][2] * m_data[1][0] - m_data[1][2] * m_data[0][0];
350 
351  result.m_data[2][0] = m_data[1][0] * m_data[2][1] - m_data[2][0] * m_data[1][1];
352  result.m_data[2][1] = m_data[0][1] * m_data[2][0] - m_data[2][1] * m_data[0][0];
353  result.m_data[2][2] = m_data[0][0] * m_data[1][1] - m_data[1][0] * m_data[0][1];
354 
355  return result * ( 1.0 / Determinant() );
356 }
MATRIX3x3::m_data
T m_data[3][3]
Definition: matrix3x3.h:64
MATRIX3x3::Determinant
T Determinant() const
Compute the determinant of the matrix.
Definition: matrix3x3.h:306
MATRIX3x3
MATRIX3x3 describes a general 3x3 matrix.
Definition: matrix3x3.h:55

Referenced by KIGFX::CAIRO_PRINT_GAL::ComputeWorldScreenMatrix(), and KIGFX::GAL::ComputeWorldScreenMatrix().

◆ 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.

Definition at line 210 of file matrix3x3.h.

211 {
212  for( int j = 0; j < 3; j++ )
213  {
214  for( int i = 0; i < 3; i++ )
215  {
216  if( i == j )
217  m_data[i][j] = 1.0;
218  else
219  m_data[i][j] = 0.0;
220  }
221  }
222 }
MATRIX3x3::m_data
T m_data[3][3]
Definition: matrix3x3.h:64

Referenced by KIGFX::CAIRO_PRINT_GAL::ComputeWorldScreenMatrix(), and KIGFX::GAL::ComputeWorldScreenMatrix().

◆ 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
aAngleis the rotation angle in [rad].

Definition at line 245 of file matrix3x3.h.

246 {
247  T cosValue = cos( aAngle );
248  T sinValue = sin( aAngle );
249  m_data[0][0] = cosValue;
250  m_data[0][1] = -sinValue;
251  m_data[1][0] = sinValue;
252  m_data[1][1] = cosValue;
253 }
MATRIX3x3::m_data
T m_data[3][3]
Definition: matrix3x3.h:64

Referenced by KIGFX::CAIRO_PRINT_GAL::ComputeWorldScreenMatrix(), and KIGFX::GAL::ComputeWorldScreenMatrix().

◆ SetScale()

template<class T>
void MATRIX3x3< T >::SetScale ( VECTOR2< T >  aScale)

Set the scale components of the matrix.

Parameters
aScalecontains the scale factors, specified as 2D-vector.

Definition at line 257 of file matrix3x3.h.

258 {
259  m_data[0][0] = aScale.x;
260  m_data[1][1] = aScale.y;
261 }
MATRIX3x3::m_data
T m_data[3][3]
Definition: matrix3x3.h:64

Referenced by KIGFX::CAIRO_PRINT_GAL::ComputeWorldScreenMatrix(), and KIGFX::GAL::ComputeWorldScreenMatrix().

◆ SetTranslation()

template<class T>
void MATRIX3x3< T >::SetTranslation ( VECTOR2< T >  aTranslation)

Set the translation components of the matrix.

Parameters
aTranslationis the translation, specified as 2D-vector.

Definition at line 226 of file matrix3x3.h.

227 {
228  m_data[0][2] = aTranslation.x;
229  m_data[1][2] = aTranslation.y;
230 }
MATRIX3x3::m_data
T m_data[3][3]
Definition: matrix3x3.h:64

Referenced by KIGFX::CAIRO_PRINT_GAL::ComputeWorldScreenMatrix(), and KIGFX::GAL::ComputeWorldScreenMatrix().

◆ Transpose()

template<class T >
MATRIX3x3< T > MATRIX3x3< T >::Transpose ( ) const

Get the transpose of the matrix.

Returns
the transpose matrix.

Definition at line 360 of file matrix3x3.h.

361 {
362  MATRIX3x3<T> result;
363 
364  for( int i = 0; i < 3; i++ )
365  {
366  for( int j = 0; j < 3; j++ )
367  {
368  result.m_data[j][i] = m_data[i][j];
369  }
370  }
371 
372  return result;
373 }
MATRIX3x3::m_data
T m_data[3][3]
Definition: matrix3x3.h:64
MATRIX3x3
MATRIX3x3 describes a general 3x3 matrix.
Definition: matrix3x3.h:55

Friends And Related Function Documentation

◆ operator

template<class T>
std::ostream& operator ( std::ostream &  aStream,
const MATRIX3x3< T > &  aMatrix 
)
friend

Output to a stream.

Member Data Documentation

◆ m_data

template<class T>
T MATRIX3x3< T >::m_data[3][3]

Definition at line 64 of file matrix3x3.h.

Referenced by KIGFX::OPENGL_GAL::beginDrawing(), MATRIX3x3< double >::Inverse(), operator *(), operator<<(), KIGFX::CAIRO_GAL_BASE::resetContext(), KIGFX::CAIRO_GAL_BASE::Transform(), KIGFX::OPENGL_GAL::Transform(), and MATRIX3x3< double >::Transpose().

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