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//-----------------------------------------------------------------------------
// BSPLIB MODULE: Transform2.cpp
//
// Copyright (c) 1997-1998 by Markus Hadwiger
// All Rights Reserved.
//-----------------------------------------------------------------------------
// bsplib headers
#include "Transform2.h"
BSPLIB_NAMESPACE_BEGIN
// multiply two 3x3 matrices --------------------------------------------------
//
PRIVATE
void mat3x3_mul( double dest_matrix[][3], const double matrix1[][3], const double matrix2[][3] )
{
//NOTE:
// full homogeneous multiplication is performed. (that is, all 9
// elements are calculated.) normally this isn't necessary as
// most matrices are affine. but since this is no real-time
// application more flexibility seems better.
/*
for ( int i = 0; i < 3; i++ ) {
for ( int j = 0; j < 3; j++ ) {
dest_matrix[ i ][ j ] = 0.0;
for ( int k = 0; k < 3; k++ )
dest_matrix[ i ][ j ] += matrix1[ i ][ k ] * matrix2[ k ][ j ];
}
}
*/
dest_matrix[ 0 ][ 0 ] = matrix1[ 0 ][ 0 ] * matrix2[ 0 ][ 0 ] +
matrix1[ 0 ][ 1 ] * matrix2[ 1 ][ 0 ] +
matrix1[ 0 ][ 2 ] * matrix2[ 2 ][ 0 ];
dest_matrix[ 0 ][ 1 ] = matrix1[ 0 ][ 0 ] * matrix2[ 0 ][ 1 ] +
matrix1[ 0 ][ 1 ] * matrix2[ 1 ][ 1 ] +
matrix1[ 0 ][ 2 ] * matrix2[ 2 ][ 1 ];
dest_matrix[ 0 ][ 2 ] = matrix1[ 0 ][ 0 ] * matrix2[ 0 ][ 2 ] +
matrix1[ 0 ][ 1 ] * matrix2[ 1 ][ 2 ] +
matrix1[ 0 ][ 2 ] * matrix2[ 2 ][ 2 ];
dest_matrix[ 1 ][ 0 ] = matrix1[ 1 ][ 0 ] * matrix2[ 0 ][ 0 ] +
matrix1[ 1 ][ 1 ] * matrix2[ 1 ][ 0 ] +
matrix1[ 1 ][ 2 ] * matrix2[ 2 ][ 0 ];
dest_matrix[ 1 ][ 1 ] = matrix1[ 1 ][ 0 ] * matrix2[ 0 ][ 1 ] +
matrix1[ 1 ][ 1 ] * matrix2[ 1 ][ 1 ] +
matrix1[ 1 ][ 2 ] * matrix2[ 2 ][ 1 ];
dest_matrix[ 1 ][ 2 ] = matrix1[ 1 ][ 0 ] * matrix2[ 0 ][ 2 ] +
matrix1[ 1 ][ 1 ] * matrix2[ 1 ][ 2 ] +
matrix1[ 1 ][ 2 ] * matrix2[ 2 ][ 2 ];
dest_matrix[ 2 ][ 0 ] = matrix1[ 2 ][ 0 ] * matrix2[ 0 ][ 0 ] +
matrix1[ 2 ][ 1 ] * matrix2[ 1 ][ 0 ] +
matrix1[ 2 ][ 2 ] * matrix2[ 2 ][ 0 ];
dest_matrix[ 2 ][ 1 ] = matrix1[ 2 ][ 0 ] * matrix2[ 0 ][ 1 ] +
matrix1[ 2 ][ 1 ] * matrix2[ 1 ][ 1 ] +
matrix1[ 2 ][ 2 ] * matrix2[ 2 ][ 1 ];
dest_matrix[ 2 ][ 2 ] = matrix1[ 2 ][ 0 ] * matrix2[ 0 ][ 2 ] +
matrix1[ 2 ][ 1 ] * matrix2[ 1 ][ 2 ] +
matrix1[ 2 ][ 2 ] * matrix2[ 2 ][ 2 ];
}
// calculate concatenation; don't overwrite object matrix ---------------------
//
Transform2 operator *( const Transform2& trafo1, const Transform2& trafo2 )
{
Transform2 temp;
mat3x3_mul( temp.m_matrix, trafo1.m_matrix, trafo2.m_matrix );
return temp;
}
// calculate concatenation as new object matrix -------------------------------
//
Transform2& Transform2::Concat( const Transform2& cattrafo )
{
Transform2 temp;
mat3x3_mul( temp.m_matrix, (const double(*)[3]) m_matrix, cattrafo.m_matrix );
memcpy( m_matrix, temp.m_matrix, sizeof( m_matrix ) );
return *this;
}
// reversed concatenation -----------------------------------------------------
//
Transform2& Transform2::ConcatR( const Transform2& cattrafo )
{
Transform2 temp;
mat3x3_mul( temp.m_matrix, cattrafo.m_matrix, (const double(*)[3]) m_matrix );
memcpy( m_matrix, temp.m_matrix, sizeof( m_matrix ) );
return *this;
}
// transform Vector2 by matrix (homogeneous component is also evaluated!) -----
//
Vector2 Transform2::TransformVector2( const Vector2& vec ) const
{
Vector2 temp;
temp.setX( m_matrix[ 0 ][ 0 ] * vec.getX() + m_matrix[ 1 ][ 0 ] * vec.getY() + m_matrix[ 2 ][ 0 ] * vec.getW() );
temp.setY( m_matrix[ 0 ][ 1 ] * vec.getX() + m_matrix[ 1 ][ 1 ] * vec.getY() + m_matrix[ 2 ][ 1 ] * vec.getW() );
temp.setW( m_matrix[ 0 ][ 2 ] * vec.getX() + m_matrix[ 1 ][ 2 ] * vec.getY() + m_matrix[ 2 ][ 2 ] * vec.getW() );
return temp;
}
// calc determinant of matrix -------------------------------------------------
//
double Transform2::Determinant()
{
// calc determinant using rule of sarrus
double pos;
pos = m_matrix[ 0 ][ 0 ] * m_matrix[ 1 ][ 1 ] * m_matrix[ 2 ][ 2 ];
pos += m_matrix[ 0 ][ 1 ] * m_matrix[ 1 ][ 2 ] * m_matrix[ 2 ][ 0 ];
pos += m_matrix[ 0 ][ 2 ] * m_matrix[ 1 ][ 0 ] * m_matrix[ 2 ][ 1 ];
double neg;
neg = m_matrix[ 0 ][ 0 ] * m_matrix[ 1 ][ 2 ] * m_matrix[ 2 ][ 1 ];
neg += m_matrix[ 0 ][ 1 ] * m_matrix[ 1 ][ 0 ] * m_matrix[ 2 ][ 2 ];
neg += m_matrix[ 0 ][ 2 ] * m_matrix[ 1 ][ 1 ] * m_matrix[ 2 ][ 0 ];
return ( pos - neg );
}
// calc matrix inverse --------------------------------------------------------
//
int Transform2::Inverse( Transform2& inverse )
{
// calculate determinant
double det = Determinant();
// check for singularity
if ( fabs( det ) < EPS_DENOM_ZERO )
return 0;
// calculate inverse
double detinv = 1 / det;
inverse.m_matrix[ 0 ][ 0 ] = ( m_matrix[ 1 ][ 1 ] * m_matrix[ 2 ][ 2 ] - m_matrix[ 1 ][ 2 ] * m_matrix[ 2 ][ 1 ] ) * detinv;
inverse.m_matrix[ 0 ][ 1 ] = ( m_matrix[ 0 ][ 2 ] * m_matrix[ 2 ][ 1 ] - m_matrix[ 0 ][ 1 ] * m_matrix[ 2 ][ 2 ] ) * detinv;
inverse.m_matrix[ 0 ][ 2 ] = ( m_matrix[ 0 ][ 1 ] * m_matrix[ 1 ][ 2 ] - m_matrix[ 0 ][ 2 ] * m_matrix[ 1 ][ 1 ] ) * detinv;
inverse.m_matrix[ 1 ][ 0 ] = ( m_matrix[ 1 ][ 2 ] * m_matrix[ 2 ][ 0 ] - m_matrix[ 1 ][ 0 ] * m_matrix[ 2 ][ 2 ] ) * detinv;
inverse.m_matrix[ 1 ][ 1 ] = ( m_matrix[ 0 ][ 0 ] * m_matrix[ 2 ][ 2 ] - m_matrix[ 0 ][ 2 ] * m_matrix[ 2 ][ 0 ] ) * detinv;
inverse.m_matrix[ 1 ][ 2 ] = ( m_matrix[ 0 ][ 2 ] * m_matrix[ 1 ][ 0 ] - m_matrix[ 0 ][ 0 ] * m_matrix[ 1 ][ 2 ] ) * detinv;
inverse.m_matrix[ 2 ][ 0 ] = ( m_matrix[ 1 ][ 0 ] * m_matrix[ 2 ][ 1 ] - m_matrix[ 1 ][ 1 ] * m_matrix[ 2 ][ 0 ] ) * detinv;
inverse.m_matrix[ 2 ][ 1 ] = ( m_matrix[ 0 ][ 1 ] * m_matrix[ 2 ][ 0 ] - m_matrix[ 0 ][ 0 ] * m_matrix[ 2 ][ 1 ] ) * detinv;
inverse.m_matrix[ 2 ][ 2 ] = ( m_matrix[ 0 ][ 0 ] * m_matrix[ 1 ][ 1 ] - m_matrix[ 0 ][ 1 ] * m_matrix[ 1 ][ 0 ] ) * detinv;
return 1;
}
// fetch translation part of matrix -------------------------------------------
//
Vector2 Transform2::FetchTranslation() const
{
// return translation vector
return Vector2( m_matrix[ 2 ][ 0 ], m_matrix[ 2 ][ 1 ] );
}
// extract translation part of matrix; set to NULL translation afterwards -----
//
Vector2 Transform2::ExtractTranslation()
{
// create translation vector
Vector2 temp( m_matrix[ 2 ][ 0 ], m_matrix[ 2 ][ 1 ] );
// zero translation part of matrix
m_matrix[ 2 ][ 0 ] = 0.0;
m_matrix[ 2 ][ 1 ] = 0.0;
return temp;
}
// create rotation matrix -----------------------------------------------------
//
Transform2& Transform2::LoadRotation( double angle )
{
// init matrix
LoadIdentity();
// set rotated basis
m_matrix[ 0 ][ 0 ] = cos( angle );
m_matrix[ 0 ][ 1 ] = sin( angle );
m_matrix[ 1 ][ 0 ] = -m_matrix[ 0 ][ 1 ];
m_matrix[ 1 ][ 1 ] = m_matrix[ 0 ][ 0 ];
return *this;
}
// create scale matrix --------------------------------------------------------
//
Transform2& Transform2::LoadScale( double x, double y )
{
LoadIdentity();
m_matrix[ 0 ][ 0 ] = x;
m_matrix[ 1 ][ 1 ] = y;
return *this;
}
// create translation matrix --------------------------------------------------
//
Transform2& Transform2::LoadTranslation( double x, double y )
{
LoadIdentity();
m_matrix[ 2 ][ 0 ] = x;
m_matrix[ 2 ][ 1 ] = y;
return *this;
}
// rotate around arbitrary axis -----------------------------------------------
//
Transform2& Transform2::Rotate( double angle )
{
Transform2 temp;
temp.LoadRotation( angle );
Concat( temp );
return *this;
}
// rotate around arbitrary axis (reversed) ------------------------------------
//
Transform2& Transform2::RotateR( double angle )
{
Transform2 temp;
temp.LoadRotation( angle );
ConcatR( temp );
return *this;
}
// apply scale factors --------------------------------------------------------
//
Transform2& Transform2::Scale( double x, double y )
{
Transform2 temp;
temp.LoadScale( x, y );
Concat( temp );
return *this;
}
// apply scale factors (reversed) ---------------------------------------------
//
Transform2& Transform2::ScaleR( double x, double y )
{
Transform2 temp;
temp.LoadScale( x, y );
ConcatR( temp );
return *this;
}
// apply translation ----------------------------------------------------------
//
Transform2& Transform2::Translate( double x, double y )
{
m_matrix[ 2 ][ 0 ] += x;
m_matrix[ 2 ][ 1 ] += y;
return *this;
}
// apply translation (reversed) -----------------------------------------------
//
Transform2& Transform2::TranslateR( double x, double y )
{
Transform2 temp;
temp.LoadTranslation( x, y );
ConcatR( temp );
return *this;
}
BSPLIB_NAMESPACE_END
//-----------------------------------------------------------------------------
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