ParaMatrix3.h

/*
-----------------------------------------------------------------------------
This source file is part of OGRE
    (Object-oriented Graphics Rendering Engine)
For the latest info, see http://www.ogre3d.org/

Copyright (c) 2000-2006 Torus Knot Software Ltd
Also see acknowledgements in Readme.html

This program is free software; you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License as published by the Free Software
Foundation; either version 2 of the License, or (at your option) any later
version.

This program is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details.

You should have received a copy of the GNU Lesser General Public License along with
this program; if not, write to the Free Software Foundation, Inc., 59 Temple
Place - Suite 330, Boston, MA 02111-1307, USA, or go to
http://www.gnu.org/copyleft/lesser.txt.

You may alternatively use this source under the terms of a specific version of
the OGRE Unrestricted License provided you have obtained such a license from
Torus Knot Software Ltd.
-----------------------------------------------------------------------------
*/
#ifndef __Matrix3_H__
#define __Matrix3_H__



#include "ParaVector3.h"

// NB All code adapted from Wild Magic 0.2 Matrix math (free source code)
// http://www.geometrictools.com/

// 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 ParaEngine
{
    class Matrix3
    {
    public:
        union {
            struct {
                float        _11, _12, _13;
                float        _21, _22, _23;
                float        _31, _32, _33;
            };
            float m[3][3];
        };

    public:
        inline Matrix3 () {};
        inline explicit Matrix3 (const float arr[3][3])
        {
            memcpy(m,arr,9*sizeof(float));
        }
        inline Matrix3 (const Matrix3& rkMatrix)
        {
            memcpy(m,rkMatrix.m,9*sizeof(float));
        }
        Matrix3(const Matrix4& rkMatrix);
        Matrix3 (float fEntry00, float fEntry01, float fEntry02,
                    float fEntry10, float fEntry11, float fEntry12,
                    float fEntry20, float fEntry21, float 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 float* operator[] (size_t iRow) const
        {
            return (float*)m[iRow];
        }
        /*inline operator float* ()
        {
            return (float*)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(float));
            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* (float fScalar) const;

        // scalar * matrix
        friend Matrix3 operator* (float fScalar, const Matrix3& rkMatrix);

        // utilities
        Matrix3 Transpose () const;
        bool Inverse (Matrix3& rkInverse, float fTolerance = 1e-06) const;
        Matrix3 Inverse (float fTolerance = 1e-06) const;
        float 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;

        float SpectralNorm () const;

        // matrix must be orthonormal
        void ToAxisAngle (Vector3& rkAxis, Radian& rfAngle) const;
        inline void ToAxisAngle (Vector3& rkAxis, Degree& rfAngle) const {
            Radian r;
            ToAxisAngle ( rkAxis, r );
            rfAngle = r;
        }
        void FromAxisAngle (const Vector3& rkAxis, const Radian& fRadians);

        // 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 (Radian& rfYAngle, Radian& rfPAngle,
            Radian& rfRAngle) const;
        bool ToEulerAnglesXZY (Radian& rfYAngle, Radian& rfPAngle,
            Radian& rfRAngle) const;
        bool ToEulerAnglesYXZ (Radian& rfYAngle, Radian& rfPAngle,
            Radian& rfRAngle) const;
        bool ToEulerAnglesYZX (Radian& rfYAngle, Radian& rfPAngle,
            Radian& rfRAngle) const;
        bool ToEulerAnglesZXY (Radian& rfYAngle, Radian& rfPAngle,
            Radian& rfRAngle) const;
        bool ToEulerAnglesZYX (Radian& rfYAngle, Radian& rfPAngle,
            Radian& rfRAngle) const;
        void FromEulerAnglesXYZ (const Radian& fYAngle, const Radian& fPAngle, const Radian& fRAngle);
        void FromEulerAnglesXZY (const Radian& fYAngle, const Radian& fPAngle, const Radian& fRAngle);
        void FromEulerAnglesYXZ (const Radian& fYAngle, const Radian& fPAngle, const Radian& fRAngle);
        void FromEulerAnglesYZX (const Radian& fYAngle, const Radian& fPAngle, const Radian& fRAngle);
        void FromEulerAnglesZXY (const Radian& fYAngle, const Radian& fPAngle, const Radian& fRAngle);
        void FromEulerAnglesZYX (const Radian& fYAngle, const Radian& fPAngle, const Radian& fRAngle);
        // eigensolver, matrix must be symmetric
        void EigenSolveSymmetric (float afEigenvalue[3],
            Vector3 akEigenvector[3]) const;

        static void TensorProduct (const Vector3& rkU, const Vector3& rkV,
            Matrix3& rkProduct);

        inline bool hasScale() const
        {
            // check magnitude of column vectors (==local axes)
            float t = m[0][0] * m[0][0] + m[1][0] * m[1][0] + m[2][0] * m[2][0];
            if (!Math::RealEqual(t, 1.0f, 1e-04f))
                return true;
            t = m[0][1] * m[0][1] + m[1][1] * m[1][1] + m[2][1] * m[2][1];
            if (!Math::RealEqual(t, 1.0f, 1e-04f))
                return true;
            t = m[0][2] * m[0][2] + m[1][2] * m[1][2] + m[2][2] * m[2][2];
            if (!Math::RealEqual(t, 1.0f, 1e-04f))
                return true;

            return false;
        }
        void                RotX(float angle);

        void                RotY(float angle);

        void                RotZ(float angle);

        static const float EPSILON;
        static const Matrix3 ZERO;
        static const Matrix3 IDENTITY;

    protected:
        // support for eigensolver
        void Tridiagonal (float afDiag[3], float afSubDiag[3]);
        bool QLAlgorithm (float afDiag[3], float afSubDiag[3]);

        // support for singular value decomposition
        static const float 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 float MaxCubicRoot (float afCoeff[3]);

        // for faster access
        friend class Matrix4;
    };
}
#endif