MgcMatrix3.h

// Magic Software, Inc.
// http://www.magic-software.com
// Copyright (c) 2000-2002.  All Rights Reserved
//
// Source code from Magic Software is supplied under the terms of a license
// agreement and may not be copied or disclosed except in accordance with the
// terms of that agreement.  The various license agreements may be found at
// the Magic Software web site.  This file is subject to the license
//
// FREE SOURCE CODE
// http://www.magic-software.com/License/free.pdf

#ifndef MGCMATRIX3_H
#define MGCMATRIX3_H

#include "MgcVector3.h"

namespace Mgc {

// 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.


class UTILITIES_API MAGICFM Matrix3
{
public:
    // construction
    Matrix3 ();
    Matrix3 (const Real aafEntry[3][3]);
    Matrix3 (const Matrix3& rkMatrix);
    Matrix3 (Real fEntry00, Real fEntry01, Real fEntry02,
             Real fEntry10, Real fEntry11, Real fEntry12,
             Real fEntry20, Real fEntry21, Real fEntry22);

    // member access, allows use of construct mat[r][c]
    Real* operator[] (int iRow) const;
    operator Real* ();
    Vector3 GetColumn (int iCol) const;

    // assignment and comparison
    Matrix3& operator= (const Matrix3& rkMatrix);
    bool operator== (const Matrix3& rkMatrix) const;
    bool operator!= (const Matrix3& rkMatrix) const;

    // 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]
    MAGICFM friend Vector3 operator* (const Vector3& rkVector,
        const Matrix3& rkMatrix);

    // matrix * scalar
    Matrix3 operator* (Real fScalar) const;

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

    // M0.TransposeTimes(M1) = M0^t*M1 where M0^t is the transpose of M0
    Matrix3 TransposeTimes (const Matrix3& rkM) const;

    // M0.TimesTranspose(M1) = M0*M1^t where M1^t is the transpose of M1
    Matrix3 TimesTranspose (const Matrix3& rkM) const;

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

    // SLERP (spherical linear interpolation) without quaternions.  Computes
    // R(t) = R0*(Transpose(R0)*R1)^t.  If Q is a rotation matrix with
    // unit-length axis U and angle A, then Q^t is a rotation matrix with
    // unit-length axis U and rotation angle t*A.
    static Matrix3 Slerp (Real fT, const Matrix3& rkR0, const Matrix3& rkR1);

    // 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& rfRadians) const;
    void FromAxisAngle (const Vector3& rkAxis, Real 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 (Real& rfYAngle, Real& rfPAngle,
        Real& rfRAngle) const;
    bool ToEulerAnglesXZY (Real& rfYAngle, Real& rfPAngle,
        Real& rfRAngle) const;
    bool ToEulerAnglesYXZ (Real& rfYAngle, Real& rfPAngle,
        Real& rfRAngle) const;
    bool ToEulerAnglesYZX (Real& rfYAngle, Real& rfPAngle,
        Real& rfRAngle) const;
    bool ToEulerAnglesZXY (Real& rfYAngle, Real& rfPAngle,
        Real& rfRAngle) const;
    bool ToEulerAnglesZYX (Real& rfYAngle, Real& rfPAngle,
        Real& rfRAngle) const;
    void FromEulerAnglesXYZ (Real fYAngle, Real fPAngle, Real fRAngle);
    void FromEulerAnglesXZY (Real fYAngle, Real fPAngle, Real fRAngle);
    void FromEulerAnglesYXZ (Real fYAngle, Real fPAngle, Real fRAngle);
    void FromEulerAnglesYZX (Real fYAngle, Real fPAngle, Real fRAngle);
    void FromEulerAnglesZXY (Real fYAngle, Real fPAngle, Real fRAngle);
    void FromEulerAnglesZYX (Real fYAngle, Real fPAngle, Real fRAngle);

    // 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 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_aafEntry[3][3];
};

#include "MgcMatrix3.inl"

} // namespace Mgc

#endif

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