/usr/include/opencollada/COLLADABaseUtils/Math/COLLADABUMathMatrix3.h is in opencollada-dev 0.1.0~20140703.ddf8f47+dfsg1-2.
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Copyright (c) 2008-2009 NetAllied Systems GmbH
This file is part of COLLADABaseUtils.
Licensed under the MIT Open Source License,
for details please see LICENSE file or the website
http://www.opensource.org/licenses/mit-license.php
*/
#ifndef __COMMONBU_MATH_MATRIX3_H__
#define __COMMONBU_MATH_MATRIX3_H__
#include "COLLADABUMathPrerequisites.h"
#include "COLLADABUMathVector3.h"
#include <memory>
#include <string.h>
// NOTE. The (x,y,z) coordinate system is assumed to be right-handed.
// Coordinate axis rotation matrices are of the form
// RX = 1 0 0
// 0 cos(t) -sin(t)
// 0 sin(t) cos(t)
// where t > 0 indicates a counterclockwise rotation in the yz-plane
// RY = cos(t) 0 sin(t)
// 0 1 0
// -sin(t) 0 cos(t)
// where t > 0 indicates a counterclockwise rotation in the zx-plane
// RZ = cos(t) -sin(t) 0
// sin(t) cos(t) 0
// 0 0 1
// where t > 0 indicates a counterclockwise rotation in the xy-plane.
namespace COLLADABU
{
namespace Math
{
class Vector3;
/** A 3x3 matrix which can represent rotations around axes.
@note
<b>All the code is adapted from the Wild Magic 0.2 Matrix
library (http://www.magic-software.com).</b>
@par
The coordinate system is assumed to be <b>right-handed</b>.
*/
class Matrix3
{
public:
/** Default constructor.
@note
It does <b>NOT</b> initialize the matrix for efficiency.
*/
inline Matrix3 ()
{}
;
inline explicit Matrix3 ( const Real arr[ 3 ][ 3 ] )
{
memcpy( m, arr, 9 * sizeof( Real ) );
}
inline Matrix3 ( const Matrix3& rkMatrix )
{
memcpy( m, rkMatrix.m, 9 * sizeof( Real ) );
}
Matrix3 ( Real fEntry00, Real fEntry01, Real fEntry02,
Real fEntry10, Real fEntry11, Real fEntry12,
Real fEntry20, Real fEntry21, Real fEntry22 )
{
m[ 0 ][ 0 ] = fEntry00;
m[ 0 ][ 1 ] = fEntry01;
m[ 0 ][ 2 ] = fEntry02;
m[ 1 ][ 0 ] = fEntry10;
m[ 1 ][ 1 ] = fEntry11;
m[ 1 ][ 2 ] = fEntry12;
m[ 2 ][ 0 ] = fEntry20;
m[ 2 ][ 1 ] = fEntry21;
m[ 2 ][ 2 ] = fEntry22;
}
inline void setAllElements(
Real fEntry00, Real fEntry01, Real fEntry02,
Real fEntry10, Real fEntry11, Real fEntry12,
Real fEntry20, Real fEntry21, Real fEntry22 )
{
m[ 0 ][ 0 ] = fEntry00;
m[ 0 ][ 1 ] = fEntry01;
m[ 0 ][ 2 ] = fEntry02;
m[ 1 ][ 0 ] = fEntry10;
m[ 1 ][ 1 ] = fEntry11;
m[ 1 ][ 2 ] = fEntry12;
m[ 2 ][ 0 ] = fEntry20;
m[ 2 ][ 1 ] = fEntry21;
m[ 2 ][ 2 ] = fEntry22;
}
// member access, allows use of construct mat[r][c]
inline Real* operator[] ( size_t iRow ) const
{
return ( Real* ) m[ iRow ];
}
/*inline operator Real* ()
{
return (Real*)m[0];
}*/
Vector3 getColumn ( size_t iCol ) const;
void setColumn( size_t iCol, const Vector3& vec );
void fromAxes( const Vector3& xAxis, const Vector3& yAxis, const Vector3& zAxis );
// assignment and comparison
inline Matrix3& operator= ( const Matrix3& rkMatrix )
{
memcpy( m, rkMatrix.m, 9 * sizeof( Real ) );
return *this;
}
bool operator== ( const Matrix3& rkMatrix ) const;
inline bool operator!= ( const Matrix3& rkMatrix ) const
{
return !operator==( rkMatrix );
}
// arithmetic operations
Matrix3 operator+ ( const Matrix3& rkMatrix ) const;
Matrix3 operator- ( const Matrix3& rkMatrix ) const;
Matrix3 operator* ( const Matrix3& rkMatrix ) const;
Matrix3 operator- () const;
// matrix * vector [3x3 * 3x1 = 3x1]
Vector3 operator* ( const Vector3& rkVector ) const;
// vector * matrix [1x3 * 3x3 = 1x3]
friend Vector3 operator* ( const Vector3& rkVector,
const Matrix3& rkMatrix );
// matrix * scalar
Matrix3 operator* ( Real fScalar ) const;
// scalar * matrix
friend Matrix3 operator* ( Real fScalar, const Matrix3& rkMatrix );
// utilities
Matrix3 transpose () const;
bool inverse ( Matrix3& rkInverse, Real fTolerance = 1e-06 ) const;
Matrix3 inverse ( Real fTolerance = 1e-06 ) const;
Real determinant () const;
// singular value decomposition
void singularValueDecomposition ( Matrix3& rkL, Vector3& rkS,
Matrix3& rkR ) const;
void singularValueComposition ( const Matrix3& rkL,
const Vector3& rkS, const Matrix3& rkR );
// Gram-Schmidt orthonormalization (applied to columns of rotation matrix)
void orthonormalize ();
// orthogonal Q, diagonal D, upper triangular U stored as (u01,u02,u12)
void qDUDecomposition ( Matrix3& rkQ, Vector3& rkD,
Vector3& rkU ) const;
Real spectralNorm () const;
// matrix must be orthonormal
void toAxisAngle ( Vector3& rkAxis, Real& rfAngle_radian ) const;
void fromAxisAngle ( const Vector3& rkAxis, const Real& fRadians_radian );
// The matrix must be orthonormal. The decomposition is yaw*pitch*roll
// where yaw is rotation about the Up vector, pitch is rotation about the
// Right axis, and roll is rotation about the Direction axis.
bool toEulerAnglesXYZ ( Real& rfYAngle_radian, Real& rfPAngle_radian,
Real& rfRAngle_radian ) const;
bool toEulerAnglesXZY ( Real& rfYAngle_radian, Real& rfPAngle_radian,
Real& rfRAngle_radian ) const;
bool toEulerAnglesYXZ ( Real& rfYAngle_radian, Real& rfPAngle_radian,
Real& rfRAngle_radian ) const;
bool toEulerAnglesYZX ( Real& rfYAngle_radian, Real& rfPAngle_radian,
Real& rfRAngle_radian ) const;
bool toEulerAnglesZXY ( Real& rfYAngle_radian, Real& rfPAngle_radian,
Real& rfRAngle_radian ) const;
bool toEulerAnglesZYX ( Real& rfYAngle_radian, Real& rfPAngle_radian,
Real& rfRAngle_radian ) const;
void fromEulerAnglesXYZ ( const Real& fYAngle_radian, const Real& fPAngle_radian, const Real& fRAngle_radian );
void fromEulerAnglesXZY ( const Real& fYAngle_radian, const Real& fPAngle_radian, const Real& fRAngle_radian );
void fromEulerAnglesYXZ ( const Real& fYAngle_radian, const Real& fPAngle_radian, const Real& fRAngle_radian );
void fromEulerAnglesYZX ( const Real& fYAngle_radian, const Real& fPAngle_radian, const Real& fRAngle_radian );
void fromEulerAnglesZXY ( const Real& fYAngle_radian, const Real& fPAngle_radian, const Real& fRAngle_radian );
void fromEulerAnglesZYX ( const Real& fYAngle_radian, const Real& fPAngle_radian, const Real& fRAngle_radian );
// eigensolver, matrix must be symmetric
void eigenSolveSymmetric ( Real afEigenvalue[ 3 ],
Vector3 akEigenvector[ 3 ] ) const;
static void tensorProduct ( const Vector3& rkU, const Vector3& rkV,
Matrix3& rkProduct );
static const Real EPSILON;
static const Matrix3 ZERO;
static const Matrix3 IDENTITY;
protected:
// support for eigensolver
void tridiagonal ( Real afDiag[ 3 ], Real afSubDiag[ 3 ] );
bool qLAlgorithm ( Real afDiag[ 3 ], Real afSubDiag[ 3 ] );
// support for singular value decomposition
static const Real ms_fSvdEpsilon;
static const unsigned int ms_iSvdMaxIterations;
static void bidiagonalize ( Matrix3& kA, Matrix3& kL,
Matrix3& kR );
static void golubKahanStep ( Matrix3& kA, Matrix3& kL,
Matrix3& kR );
// support for spectral norm
static Real maxCubicRoot ( Real afCoeff[ 3 ] );
Real m[ 3 ][ 3 ];
// for faster access
friend class Matrix4;
public:
/* Returns a vector which represents the scale of the current matrix.
see http://www.ogre3d.org/phpBB2/viewtopic.php?t=18978
*/
inline Vector3 getScale();
};
}
}
#endif //__COMMONBU_MATH_MATRIX3_H__
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