Wm4Matrix4.inl

// Wild Magic Source Code
// David Eberly
// http://www.geometrictools.com
// Copyright (c) 1998-2007
//
// This library 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 2.1 of the License, or (at
// your option) any later version.  The license is available for reading at
// either of the locations:
//     http://www.gnu.org/copyleft/lgpl.html
//     http://www.geometrictools.com/License/WildMagicLicense.pdf
// The license applies to versions 0 through 4 of Wild Magic.
//
// Version: 4.0.1 (2006/08/19)

namespace Wm4
{
//----------------------------------------------------------------------------
template <class Real>
Matrix4<Real>::Matrix4 (bool bZero)
{
    if (bZero)
    {
        MakeZero();
    }
    else
    {
        MakeIdentity();
    }
}
//----------------------------------------------------------------------------
template <class Real>
Matrix4<Real>::Matrix4 (const Matrix4& rkM)
{
    m_afEntry[ 0] = rkM.m_afEntry[ 0];
    m_afEntry[ 1] = rkM.m_afEntry[ 1];
    m_afEntry[ 2] = rkM.m_afEntry[ 2];
    m_afEntry[ 3] = rkM.m_afEntry[ 3];
    m_afEntry[ 4] = rkM.m_afEntry[ 4];
    m_afEntry[ 5] = rkM.m_afEntry[ 5];
    m_afEntry[ 6] = rkM.m_afEntry[ 6];
    m_afEntry[ 7] = rkM.m_afEntry[ 7];
    m_afEntry[ 8] = rkM.m_afEntry[ 8];
    m_afEntry[ 9] = rkM.m_afEntry[ 9];
    m_afEntry[10] = rkM.m_afEntry[10];
    m_afEntry[11] = rkM.m_afEntry[11];
    m_afEntry[12] = rkM.m_afEntry[12];
    m_afEntry[13] = rkM.m_afEntry[13];
    m_afEntry[14] = rkM.m_afEntry[14];
    m_afEntry[15] = rkM.m_afEntry[15];
}
//----------------------------------------------------------------------------
template <class Real>
Matrix4<Real>::Matrix4 (Real fM00, Real fM01, Real fM02, Real fM03,
    Real fM10, Real fM11, Real fM12, Real fM13, Real fM20, Real fM21,
    Real fM22, Real fM23, Real fM30, Real fM31, Real fM32, Real fM33)
{
    m_afEntry[ 0] = fM00;
    m_afEntry[ 1] = fM01;
    m_afEntry[ 2] = fM02;
    m_afEntry[ 3] = fM03;
    m_afEntry[ 4] = fM10;
    m_afEntry[ 5] = fM11;
    m_afEntry[ 6] = fM12;
    m_afEntry[ 7] = fM13;
    m_afEntry[ 8] = fM20;
    m_afEntry[ 9] = fM21;
    m_afEntry[10] = fM22;
    m_afEntry[11] = fM23;
    m_afEntry[12] = fM30;
    m_afEntry[13] = fM31;
    m_afEntry[14] = fM32;
    m_afEntry[15] = fM33;
}
//----------------------------------------------------------------------------
template <class Real>
Matrix4<Real>::Matrix4 (const Real afEntry[16], bool bRowMajor)
{
    if (bRowMajor)
    {
        m_afEntry[ 0] = afEntry[ 0];
        m_afEntry[ 1] = afEntry[ 1];
        m_afEntry[ 2] = afEntry[ 2];
        m_afEntry[ 3] = afEntry[ 3];
        m_afEntry[ 4] = afEntry[ 4];
        m_afEntry[ 5] = afEntry[ 5];
        m_afEntry[ 6] = afEntry[ 6];
        m_afEntry[ 7] = afEntry[ 7];
        m_afEntry[ 8] = afEntry[ 8];
        m_afEntry[ 9] = afEntry[ 9];
        m_afEntry[10] = afEntry[10];
        m_afEntry[11] = afEntry[11];
        m_afEntry[12] = afEntry[12];
        m_afEntry[13] = afEntry[13];
        m_afEntry[14] = afEntry[14];
        m_afEntry[15] = afEntry[15];
    }
    else
    {
        m_afEntry[ 0] = afEntry[ 0];
        m_afEntry[ 1] = afEntry[ 4];
        m_afEntry[ 2] = afEntry[ 8];
        m_afEntry[ 3] = afEntry[12];
        m_afEntry[ 4] = afEntry[ 1];
        m_afEntry[ 5] = afEntry[ 5];
        m_afEntry[ 6] = afEntry[ 9];
        m_afEntry[ 7] = afEntry[13];
        m_afEntry[ 8] = afEntry[ 2];
        m_afEntry[ 9] = afEntry[ 6];
        m_afEntry[10] = afEntry[10];
        m_afEntry[11] = afEntry[14];
        m_afEntry[12] = afEntry[ 3];
        m_afEntry[13] = afEntry[ 7];
        m_afEntry[14] = afEntry[11];
        m_afEntry[15] = afEntry[15];
    }
}
//----------------------------------------------------------------------------
template <class Real>
Matrix4<Real>::operator const Real* () const
{
    return m_afEntry;
}
//----------------------------------------------------------------------------
template <class Real>
Matrix4<Real>::operator Real* ()
{
    return m_afEntry;
}
//----------------------------------------------------------------------------
template <class Real>
const Real* Matrix4<Real>::operator[] (int iRow) const
{
    return &m_afEntry[4*iRow];
}
//----------------------------------------------------------------------------
template <class Real>
Real* Matrix4<Real>::operator[] (int iRow)
{
    return &m_afEntry[4*iRow];
}
//----------------------------------------------------------------------------
template <class Real>
Real Matrix4<Real>::operator() (int iRow, int iCol) const
{
    return m_afEntry[iCol+4*iRow];
}
//----------------------------------------------------------------------------
template <class Real>
Real& Matrix4<Real>::operator() (int iRow, int iCol)
{
    return m_afEntry[iCol+4*iRow];
}
//----------------------------------------------------------------------------
template <class Real>
void Matrix4<Real>::MakeZero ()
{
    m_afEntry[ 0] = (Real)0.0;
    m_afEntry[ 1] = (Real)0.0;
    m_afEntry[ 2] = (Real)0.0;
    m_afEntry[ 3] = (Real)0.0;
    m_afEntry[ 4] = (Real)0.0;
    m_afEntry[ 5] = (Real)0.0;
    m_afEntry[ 6] = (Real)0.0;
    m_afEntry[ 7] = (Real)0.0;
    m_afEntry[ 8] = (Real)0.0;
    m_afEntry[ 9] = (Real)0.0;
    m_afEntry[10] = (Real)0.0;
    m_afEntry[11] = (Real)0.0;
    m_afEntry[12] = (Real)0.0;
    m_afEntry[13] = (Real)0.0;
    m_afEntry[14] = (Real)0.0;
    m_afEntry[15] = (Real)0.0;
}
//----------------------------------------------------------------------------
template <class Real>
void Matrix4<Real>::MakeIdentity ()
{
    m_afEntry[ 0] = (Real)1.0;
    m_afEntry[ 1] = (Real)0.0;
    m_afEntry[ 2] = (Real)0.0;
    m_afEntry[ 3] = (Real)0.0;
    m_afEntry[ 4] = (Real)0.0;
    m_afEntry[ 5] = (Real)1.0;
    m_afEntry[ 6] = (Real)0.0;
    m_afEntry[ 7] = (Real)0.0;
    m_afEntry[ 8] = (Real)0.0;
    m_afEntry[ 9] = (Real)0.0;
    m_afEntry[10] = (Real)1.0;
    m_afEntry[11] = (Real)0.0;
    m_afEntry[12] = (Real)0.0;
    m_afEntry[13] = (Real)0.0;
    m_afEntry[14] = (Real)0.0;
    m_afEntry[15] = (Real)1.0;
}
//----------------------------------------------------------------------------
template <class Real>
void Matrix4<Real>::SetRow (int iRow, const Vector4<Real>& rkV)
{
    int i0 = 4*iRow, i1 = i0+1, i2 = i1+1, i3 = i2+1;
    m_afEntry[i0] = rkV[0];
    m_afEntry[i1] = rkV[1];
    m_afEntry[i2] = rkV[2];
    m_afEntry[i3] = rkV[3];
}
//----------------------------------------------------------------------------
template <class Real>
Vector4<Real> Matrix4<Real>::GetRow (int iRow) const
{
    int i0 = 4*iRow, i1 = i0+1, i2 = i1+1, i3 = i2+1;
    return Vector4<Real>(m_afEntry[i0],m_afEntry[i1],m_afEntry[i2],
        m_afEntry[i3]);
}
//----------------------------------------------------------------------------
template <class Real>
void Matrix4<Real>::SetColumn (int iCol, const Vector4<Real>& rkV)
{
    m_afEntry[iCol] = rkV[0];
    m_afEntry[iCol+4] = rkV[1];
    m_afEntry[iCol+8] = rkV[2];
    m_afEntry[iCol+12] = rkV[3];
}
//----------------------------------------------------------------------------
template <class Real>
Vector4<Real> Matrix4<Real>::GetColumn (int iCol) const
{
    return Vector4<Real>(m_afEntry[iCol],m_afEntry[iCol+4],m_afEntry[iCol+8],
        m_afEntry[iCol+12]);
}
//----------------------------------------------------------------------------
template <class Real>
void Matrix4<Real>::GetColumnMajor (Real* afCMajor) const
{
    afCMajor[ 0] = m_afEntry[ 0];
    afCMajor[ 1] = m_afEntry[ 4];
    afCMajor[ 2] = m_afEntry[ 8];
    afCMajor[ 3] = m_afEntry[12];
    afCMajor[ 4] = m_afEntry[ 1];
    afCMajor[ 5] = m_afEntry[ 5];
    afCMajor[ 6] = m_afEntry[ 9];
    afCMajor[ 7] = m_afEntry[13];
    afCMajor[ 8] = m_afEntry[ 2];
    afCMajor[ 9] = m_afEntry[ 6];
    afCMajor[10] = m_afEntry[10];
    afCMajor[11] = m_afEntry[14];
    afCMajor[12] = m_afEntry[ 3];
    afCMajor[13] = m_afEntry[ 7];
    afCMajor[14] = m_afEntry[11];
    afCMajor[15] = m_afEntry[15];
}
//----------------------------------------------------------------------------
template <class Real>
Matrix4<Real>& Matrix4<Real>::operator= (const Matrix4& rkM)
{
    m_afEntry[ 0] = rkM.m_afEntry[ 0];
    m_afEntry[ 1] = rkM.m_afEntry[ 1];
    m_afEntry[ 2] = rkM.m_afEntry[ 2];
    m_afEntry[ 3] = rkM.m_afEntry[ 3];
    m_afEntry[ 4] = rkM.m_afEntry[ 4];
    m_afEntry[ 5] = rkM.m_afEntry[ 5];
    m_afEntry[ 6] = rkM.m_afEntry[ 6];
    m_afEntry[ 7] = rkM.m_afEntry[ 7];
    m_afEntry[ 8] = rkM.m_afEntry[ 8];
    m_afEntry[ 9] = rkM.m_afEntry[ 9];
    m_afEntry[10] = rkM.m_afEntry[10];
    m_afEntry[11] = rkM.m_afEntry[11];
    m_afEntry[12] = rkM.m_afEntry[12];
    m_afEntry[13] = rkM.m_afEntry[13];
    m_afEntry[14] = rkM.m_afEntry[14];
    m_afEntry[15] = rkM.m_afEntry[15];
    return *this;
}
//----------------------------------------------------------------------------
template <class Real>
int Matrix4<Real>::CompareArrays (const Matrix4& rkM) const
{
    return memcmp(m_afEntry,rkM.m_afEntry,16*sizeof(Real));
}
//----------------------------------------------------------------------------
template <class Real>
bool Matrix4<Real>::operator== (const Matrix4& rkM) const
{
    return CompareArrays(rkM) == 0;
}
//----------------------------------------------------------------------------
template <class Real>
bool Matrix4<Real>::operator!= (const Matrix4& rkM) const
{
    return CompareArrays(rkM) != 0;
}
//----------------------------------------------------------------------------
template <class Real>
bool Matrix4<Real>::operator<  (const Matrix4& rkM) const
{
    return CompareArrays(rkM) < 0;
}
//----------------------------------------------------------------------------
template <class Real>
bool Matrix4<Real>::operator<= (const Matrix4& rkM) const
{
    return CompareArrays(rkM) <= 0;
}
//----------------------------------------------------------------------------
template <class Real>
bool Matrix4<Real>::operator>  (const Matrix4& rkM) const
{
    return CompareArrays(rkM) > 0;
}
//----------------------------------------------------------------------------
template <class Real>
bool Matrix4<Real>::operator>= (const Matrix4& rkM) const
{
    return CompareArrays(rkM) >= 0;
}
//----------------------------------------------------------------------------
template <class Real>
Matrix4<Real> Matrix4<Real>::operator+ (const Matrix4& rkM) const
{
    return Matrix4<Real>(
        m_afEntry[ 0] + rkM.m_afEntry[ 0],
        m_afEntry[ 1] + rkM.m_afEntry[ 1],
        m_afEntry[ 2] + rkM.m_afEntry[ 2],
        m_afEntry[ 3] + rkM.m_afEntry[ 3],
        m_afEntry[ 4] + rkM.m_afEntry[ 4],
        m_afEntry[ 5] + rkM.m_afEntry[ 5],
        m_afEntry[ 6] + rkM.m_afEntry[ 6],
        m_afEntry[ 7] + rkM.m_afEntry[ 7],
        m_afEntry[ 8] + rkM.m_afEntry[ 8],
        m_afEntry[ 9] + rkM.m_afEntry[ 9],
        m_afEntry[10] + rkM.m_afEntry[10],
        m_afEntry[11] + rkM.m_afEntry[11],
        m_afEntry[12] + rkM.m_afEntry[12],
        m_afEntry[13] + rkM.m_afEntry[13],
        m_afEntry[14] + rkM.m_afEntry[14],
        m_afEntry[15] + rkM.m_afEntry[15]);
}
//----------------------------------------------------------------------------
template <class Real>
Matrix4<Real> Matrix4<Real>::operator- (const Matrix4& rkM) const
{
    return Matrix4<Real>(
        m_afEntry[ 0] - rkM.m_afEntry[ 0],
        m_afEntry[ 1] - rkM.m_afEntry[ 1],
        m_afEntry[ 2] - rkM.m_afEntry[ 2],
        m_afEntry[ 3] - rkM.m_afEntry[ 3],
        m_afEntry[ 4] - rkM.m_afEntry[ 4],
        m_afEntry[ 5] - rkM.m_afEntry[ 5],
        m_afEntry[ 6] - rkM.m_afEntry[ 6],
        m_afEntry[ 7] - rkM.m_afEntry[ 7],
        m_afEntry[ 8] - rkM.m_afEntry[ 8],
        m_afEntry[ 9] - rkM.m_afEntry[ 9],
        m_afEntry[10] - rkM.m_afEntry[10],
        m_afEntry[11] - rkM.m_afEntry[11],
        m_afEntry[12] - rkM.m_afEntry[12],
        m_afEntry[13] - rkM.m_afEntry[13],
        m_afEntry[14] - rkM.m_afEntry[14],
        m_afEntry[15] - rkM.m_afEntry[15]);
}
//----------------------------------------------------------------------------
template <class Real>
Matrix4<Real> Matrix4<Real>::operator* (const Matrix4& rkM) const
{
    return Matrix4<Real>(
        m_afEntry[ 0]*rkM.m_afEntry[ 0] +
        m_afEntry[ 1]*rkM.m_afEntry[ 4] +
        m_afEntry[ 2]*rkM.m_afEntry[ 8] +
        m_afEntry[ 3]*rkM.m_afEntry[12],

        m_afEntry[ 0]*rkM.m_afEntry[ 1] +
        m_afEntry[ 1]*rkM.m_afEntry[ 5] +
        m_afEntry[ 2]*rkM.m_afEntry[ 9] +
        m_afEntry[ 3]*rkM.m_afEntry[13],

        m_afEntry[ 0]*rkM.m_afEntry[ 2] +
        m_afEntry[ 1]*rkM.m_afEntry[ 6] +
        m_afEntry[ 2]*rkM.m_afEntry[10] +
        m_afEntry[ 3]*rkM.m_afEntry[14],

        m_afEntry[ 0]*rkM.m_afEntry[ 3] +
        m_afEntry[ 1]*rkM.m_afEntry[ 7] +
        m_afEntry[ 2]*rkM.m_afEntry[11] +
        m_afEntry[ 3]*rkM.m_afEntry[15],

        m_afEntry[ 4]*rkM.m_afEntry[ 0] +
        m_afEntry[ 5]*rkM.m_afEntry[ 4] +
        m_afEntry[ 6]*rkM.m_afEntry[ 8] +
        m_afEntry[ 7]*rkM.m_afEntry[12],

        m_afEntry[ 4]*rkM.m_afEntry[ 1] +
        m_afEntry[ 5]*rkM.m_afEntry[ 5] +
        m_afEntry[ 6]*rkM.m_afEntry[ 9] +
        m_afEntry[ 7]*rkM.m_afEntry[13],

        m_afEntry[ 4]*rkM.m_afEntry[ 2] +
        m_afEntry[ 5]*rkM.m_afEntry[ 6] +
        m_afEntry[ 6]*rkM.m_afEntry[10] +
        m_afEntry[ 7]*rkM.m_afEntry[14],

        m_afEntry[ 4]*rkM.m_afEntry[ 3] +
        m_afEntry[ 5]*rkM.m_afEntry[ 7] +
        m_afEntry[ 6]*rkM.m_afEntry[11] +
        m_afEntry[ 7]*rkM.m_afEntry[15],

        m_afEntry[ 8]*rkM.m_afEntry[ 0] +
        m_afEntry[ 9]*rkM.m_afEntry[ 4] +
        m_afEntry[10]*rkM.m_afEntry[ 8] +
        m_afEntry[11]*rkM.m_afEntry[12],

        m_afEntry[ 8]*rkM.m_afEntry[ 1] +
        m_afEntry[ 9]*rkM.m_afEntry[ 5] +
        m_afEntry[10]*rkM.m_afEntry[ 9] +
        m_afEntry[11]*rkM.m_afEntry[13],

        m_afEntry[ 8]*rkM.m_afEntry[ 2] +
        m_afEntry[ 9]*rkM.m_afEntry[ 6] +
        m_afEntry[10]*rkM.m_afEntry[10] +
        m_afEntry[11]*rkM.m_afEntry[14],

        m_afEntry[ 8]*rkM.m_afEntry[ 3] +
        m_afEntry[ 9]*rkM.m_afEntry[ 7] +
        m_afEntry[10]*rkM.m_afEntry[11] +
        m_afEntry[11]*rkM.m_afEntry[15],

        m_afEntry[12]*rkM.m_afEntry[ 0] +
        m_afEntry[13]*rkM.m_afEntry[ 4] +
        m_afEntry[14]*rkM.m_afEntry[ 8] +
        m_afEntry[15]*rkM.m_afEntry[12],

        m_afEntry[12]*rkM.m_afEntry[ 1] +
        m_afEntry[13]*rkM.m_afEntry[ 5] +
        m_afEntry[14]*rkM.m_afEntry[ 9] +
        m_afEntry[15]*rkM.m_afEntry[13],

        m_afEntry[12]*rkM.m_afEntry[ 2] +
        m_afEntry[13]*rkM.m_afEntry[ 6] +
        m_afEntry[14]*rkM.m_afEntry[10] +
        m_afEntry[15]*rkM.m_afEntry[14],

        m_afEntry[12]*rkM.m_afEntry[ 3] +
        m_afEntry[13]*rkM.m_afEntry[ 7] +
        m_afEntry[14]*rkM.m_afEntry[11] +
        m_afEntry[15]*rkM.m_afEntry[15]);
}
//----------------------------------------------------------------------------
template <class Real>
Matrix4<Real> Matrix4<Real>::operator* (Real fScalar) const
{
    return Matrix4<Real>(
        fScalar*m_afEntry[ 0],
        fScalar*m_afEntry[ 1],
        fScalar*m_afEntry[ 2],
        fScalar*m_afEntry[ 3],
        fScalar*m_afEntry[ 4],
        fScalar*m_afEntry[ 5],
        fScalar*m_afEntry[ 6],
        fScalar*m_afEntry[ 7],
        fScalar*m_afEntry[ 8],
        fScalar*m_afEntry[ 9],
        fScalar*m_afEntry[10],
        fScalar*m_afEntry[11],
        fScalar*m_afEntry[12],
        fScalar*m_afEntry[13],
        fScalar*m_afEntry[14],
        fScalar*m_afEntry[15]);
}
//----------------------------------------------------------------------------
template <class Real>
Matrix4<Real> Matrix4<Real>::operator/ (Real fScalar) const
{
    if (fScalar != (Real)0.0)
    {
        Real fInvScalar = ((Real)1.0)/fScalar;
        return Matrix4<Real>(
            fInvScalar*m_afEntry[ 0],
            fInvScalar*m_afEntry[ 1],
            fInvScalar*m_afEntry[ 2],
            fInvScalar*m_afEntry[ 3],
            fInvScalar*m_afEntry[ 4],
            fInvScalar*m_afEntry[ 5],
            fInvScalar*m_afEntry[ 6],
            fInvScalar*m_afEntry[ 7],
            fInvScalar*m_afEntry[ 8],
            fInvScalar*m_afEntry[ 9],
            fInvScalar*m_afEntry[10],
            fInvScalar*m_afEntry[11],
            fInvScalar*m_afEntry[12],
            fInvScalar*m_afEntry[13],
            fInvScalar*m_afEntry[14],
            fInvScalar*m_afEntry[15]);
    }

    return Matrix4<Real>(
        Math<Real>::MAX_REAL,
        Math<Real>::MAX_REAL,
        Math<Real>::MAX_REAL,
        Math<Real>::MAX_REAL,
        Math<Real>::MAX_REAL,
        Math<Real>::MAX_REAL,
        Math<Real>::MAX_REAL,
        Math<Real>::MAX_REAL,
        Math<Real>::MAX_REAL,
        Math<Real>::MAX_REAL,
        Math<Real>::MAX_REAL,
        Math<Real>::MAX_REAL,
        Math<Real>::MAX_REAL,
        Math<Real>::MAX_REAL,
        Math<Real>::MAX_REAL,
        Math<Real>::MAX_REAL);
}
//----------------------------------------------------------------------------
template <class Real>
Matrix4<Real> Matrix4<Real>::operator- () const
{
    return Matrix4<Real>(
        -m_afEntry[ 0],
        -m_afEntry[ 1],
        -m_afEntry[ 2],
        -m_afEntry[ 3],
        -m_afEntry[ 4],
        -m_afEntry[ 5],
        -m_afEntry[ 6],
        -m_afEntry[ 7],
        -m_afEntry[ 8],
        -m_afEntry[ 9],
        -m_afEntry[10],
        -m_afEntry[11],
        -m_afEntry[12],
        -m_afEntry[13],
        -m_afEntry[14],
        -m_afEntry[15]);
}
//----------------------------------------------------------------------------
template <class Real>
Matrix4<Real>& Matrix4<Real>::operator+= (const Matrix4& rkM)
{
    m_afEntry[ 0] += rkM.m_afEntry[ 0];
    m_afEntry[ 1] += rkM.m_afEntry[ 1];
    m_afEntry[ 2] += rkM.m_afEntry[ 2];
    m_afEntry[ 3] += rkM.m_afEntry[ 3];
    m_afEntry[ 4] += rkM.m_afEntry[ 4];
    m_afEntry[ 5] += rkM.m_afEntry[ 5];
    m_afEntry[ 6] += rkM.m_afEntry[ 6];
    m_afEntry[ 7] += rkM.m_afEntry[ 7];
    m_afEntry[ 8] += rkM.m_afEntry[ 8];
    m_afEntry[ 9] += rkM.m_afEntry[ 9];
    m_afEntry[10] += rkM.m_afEntry[10];
    m_afEntry[11] += rkM.m_afEntry[11];
    m_afEntry[12] += rkM.m_afEntry[12];
    m_afEntry[13] += rkM.m_afEntry[13];
    m_afEntry[14] += rkM.m_afEntry[14];
    m_afEntry[15] += rkM.m_afEntry[15];
    return *this;
}
//----------------------------------------------------------------------------
template <class Real>
Matrix4<Real>& Matrix4<Real>::operator-= (const Matrix4& rkM)
{
    m_afEntry[ 0] -= rkM.m_afEntry[ 0];
    m_afEntry[ 1] -= rkM.m_afEntry[ 1];
    m_afEntry[ 2] -= rkM.m_afEntry[ 2];
    m_afEntry[ 3] -= rkM.m_afEntry[ 3];
    m_afEntry[ 4] -= rkM.m_afEntry[ 4];
    m_afEntry[ 5] -= rkM.m_afEntry[ 5];
    m_afEntry[ 6] -= rkM.m_afEntry[ 6];
    m_afEntry[ 7] -= rkM.m_afEntry[ 7];
    m_afEntry[ 8] -= rkM.m_afEntry[ 8];
    m_afEntry[ 9] -= rkM.m_afEntry[ 9];
    m_afEntry[10] -= rkM.m_afEntry[10];
    m_afEntry[11] -= rkM.m_afEntry[11];
    m_afEntry[12] -= rkM.m_afEntry[12];
    m_afEntry[13] -= rkM.m_afEntry[13];
    m_afEntry[14] -= rkM.m_afEntry[14];
    m_afEntry[15] -= rkM.m_afEntry[15];
    return *this;
}
//----------------------------------------------------------------------------
template <class Real>
Matrix4<Real>& Matrix4<Real>::operator*= (Real fScalar)
{
    m_afEntry[ 0] *= fScalar;
    m_afEntry[ 1] *= fScalar;
    m_afEntry[ 2] *= fScalar;
    m_afEntry[ 3] *= fScalar;
    m_afEntry[ 4] *= fScalar;
    m_afEntry[ 5] *= fScalar;
    m_afEntry[ 6] *= fScalar;
    m_afEntry[ 7] *= fScalar;
    m_afEntry[ 8] *= fScalar;
    m_afEntry[ 9] *= fScalar;
    m_afEntry[10] *= fScalar;
    m_afEntry[11] *= fScalar;
    m_afEntry[12] *= fScalar;
    m_afEntry[13] *= fScalar;
    m_afEntry[14] *= fScalar;
    m_afEntry[15] *= fScalar;
    return *this;
}
//----------------------------------------------------------------------------
template <class Real>
Matrix4<Real>& Matrix4<Real>::operator/= (Real fScalar)
{
    if (fScalar != (Real)0.0)
    {
        Real fInvScalar = ((Real)1.0)/fScalar;
        m_afEntry[ 0] *= fInvScalar;
        m_afEntry[ 1] *= fInvScalar;
        m_afEntry[ 2] *= fInvScalar;
        m_afEntry[ 3] *= fInvScalar;
        m_afEntry[ 4] *= fInvScalar;
        m_afEntry[ 5] *= fInvScalar;
        m_afEntry[ 6] *= fInvScalar;
        m_afEntry[ 7] *= fInvScalar;
        m_afEntry[ 8] *= fInvScalar;
        m_afEntry[ 9] *= fInvScalar;
        m_afEntry[10] *= fInvScalar;
        m_afEntry[11] *= fInvScalar;
        m_afEntry[12] *= fInvScalar;
        m_afEntry[13] *= fInvScalar;
        m_afEntry[14] *= fInvScalar;
        m_afEntry[15] *= fInvScalar;
    }
    else
    {
        m_afEntry[ 0] = Math<Real>::MAX_REAL;
        m_afEntry[ 1] = Math<Real>::MAX_REAL;
        m_afEntry[ 2] = Math<Real>::MAX_REAL;
        m_afEntry[ 3] = Math<Real>::MAX_REAL;
        m_afEntry[ 4] = Math<Real>::MAX_REAL;
        m_afEntry[ 5] = Math<Real>::MAX_REAL;
        m_afEntry[ 6] = Math<Real>::MAX_REAL;
        m_afEntry[ 7] = Math<Real>::MAX_REAL;
        m_afEntry[ 8] = Math<Real>::MAX_REAL;
        m_afEntry[ 9] = Math<Real>::MAX_REAL;
        m_afEntry[10] = Math<Real>::MAX_REAL;
        m_afEntry[11] = Math<Real>::MAX_REAL;
        m_afEntry[12] = Math<Real>::MAX_REAL;
        m_afEntry[13] = Math<Real>::MAX_REAL;
        m_afEntry[14] = Math<Real>::MAX_REAL;
        m_afEntry[15] = Math<Real>::MAX_REAL;
    }

    return *this;
}
//----------------------------------------------------------------------------
template <class Real>
Vector4<Real> Matrix4<Real>::operator* (const Vector4<Real>& rkV) const
{
    return Vector4<Real>(
        m_afEntry[ 0]*rkV[0] +
        m_afEntry[ 1]*rkV[1] +
        m_afEntry[ 2]*rkV[2] +
        m_afEntry[ 3]*rkV[3],

        m_afEntry[ 4]*rkV[0] +
        m_afEntry[ 5]*rkV[1] +
        m_afEntry[ 6]*rkV[2] +
        m_afEntry[ 7]*rkV[3],

        m_afEntry[ 8]*rkV[0] +
        m_afEntry[ 9]*rkV[1] +
        m_afEntry[10]*rkV[2] +
        m_afEntry[11]*rkV[3],

        m_afEntry[12]*rkV[0] +
        m_afEntry[13]*rkV[1] +
        m_afEntry[14]*rkV[2] +
        m_afEntry[15]*rkV[3]);
}
//----------------------------------------------------------------------------
template <class Real>
Matrix4<Real> Matrix4<Real>::Transpose () const
{
    return Matrix4<Real>(
        m_afEntry[ 0],
        m_afEntry[ 4],
        m_afEntry[ 8],
        m_afEntry[12],
        m_afEntry[ 1],
        m_afEntry[ 5],
        m_afEntry[ 9],
        m_afEntry[13],
        m_afEntry[ 2],
        m_afEntry[ 6],
        m_afEntry[10],
        m_afEntry[14],
        m_afEntry[ 3],
        m_afEntry[ 7],
        m_afEntry[11],
        m_afEntry[15]);
}
//----------------------------------------------------------------------------
template <class Real>
Matrix4<Real> Matrix4<Real>::TransposeTimes (const Matrix4& rkM) const
{
    // P = A^T*B
    return Matrix4<Real>(
        m_afEntry[ 0]*rkM.m_afEntry[ 0] +
        m_afEntry[ 4]*rkM.m_afEntry[ 4] +
        m_afEntry[ 8]*rkM.m_afEntry[ 8] +
        m_afEntry[12]*rkM.m_afEntry[12],

        m_afEntry[ 0]*rkM.m_afEntry[ 1] +
        m_afEntry[ 4]*rkM.m_afEntry[ 5] +
        m_afEntry[ 8]*rkM.m_afEntry[ 9] +
        m_afEntry[12]*rkM.m_afEntry[13],

        m_afEntry[ 0]*rkM.m_afEntry[ 2] +
        m_afEntry[ 4]*rkM.m_afEntry[ 6] +
        m_afEntry[ 8]*rkM.m_afEntry[10] +
        m_afEntry[12]*rkM.m_afEntry[14],

        m_afEntry[ 0]*rkM.m_afEntry[ 3] +
        m_afEntry[ 4]*rkM.m_afEntry[ 7] +
        m_afEntry[ 8]*rkM.m_afEntry[11] +
        m_afEntry[12]*rkM.m_afEntry[15],

        m_afEntry[ 1]*rkM.m_afEntry[ 0] +
        m_afEntry[ 5]*rkM.m_afEntry[ 4] +
        m_afEntry[ 9]*rkM.m_afEntry[ 8] +
        m_afEntry[13]*rkM.m_afEntry[12],

        m_afEntry[ 1]*rkM.m_afEntry[ 1] +
        m_afEntry[ 5]*rkM.m_afEntry[ 5] +
        m_afEntry[ 9]*rkM.m_afEntry[ 9] +
        m_afEntry[13]*rkM.m_afEntry[13],

        m_afEntry[ 1]*rkM.m_afEntry[ 2] +
        m_afEntry[ 5]*rkM.m_afEntry[ 6] +
        m_afEntry[ 9]*rkM.m_afEntry[10] +
        m_afEntry[13]*rkM.m_afEntry[14],

        m_afEntry[ 1]*rkM.m_afEntry[ 3] +
        m_afEntry[ 5]*rkM.m_afEntry[ 7] +
        m_afEntry[ 9]*rkM.m_afEntry[11] +
        m_afEntry[13]*rkM.m_afEntry[15],

        m_afEntry[ 2]*rkM.m_afEntry[ 0] +
        m_afEntry[ 6]*rkM.m_afEntry[ 4] +
        m_afEntry[10]*rkM.m_afEntry[ 8] +
        m_afEntry[14]*rkM.m_afEntry[12],

        m_afEntry[ 2]*rkM.m_afEntry[ 1] +
        m_afEntry[ 6]*rkM.m_afEntry[ 5] +
        m_afEntry[10]*rkM.m_afEntry[ 9] +
        m_afEntry[14]*rkM.m_afEntry[13],

        m_afEntry[ 2]*rkM.m_afEntry[ 2] +
        m_afEntry[ 6]*rkM.m_afEntry[ 6] +
        m_afEntry[10]*rkM.m_afEntry[10] +
        m_afEntry[14]*rkM.m_afEntry[14],

        m_afEntry[ 2]*rkM.m_afEntry[ 3] +
        m_afEntry[ 6]*rkM.m_afEntry[ 7] +
        m_afEntry[10]*rkM.m_afEntry[11] +
        m_afEntry[14]*rkM.m_afEntry[15],

        m_afEntry[ 3]*rkM.m_afEntry[ 0] +
        m_afEntry[ 7]*rkM.m_afEntry[ 4] +
        m_afEntry[11]*rkM.m_afEntry[ 8] +
        m_afEntry[15]*rkM.m_afEntry[12],

        m_afEntry[ 3]*rkM.m_afEntry[ 1] +
        m_afEntry[ 7]*rkM.m_afEntry[ 5] +
        m_afEntry[11]*rkM.m_afEntry[ 9] +
        m_afEntry[15]*rkM.m_afEntry[13],

        m_afEntry[ 3]*rkM.m_afEntry[ 2] +
        m_afEntry[ 7]*rkM.m_afEntry[ 6] +
        m_afEntry[11]*rkM.m_afEntry[10] +
        m_afEntry[15]*rkM.m_afEntry[14],

        m_afEntry[ 3]*rkM.m_afEntry[ 3] +
        m_afEntry[ 7]*rkM.m_afEntry[ 7] +
        m_afEntry[11]*rkM.m_afEntry[11] +
        m_afEntry[15]*rkM.m_afEntry[15]);
}
//----------------------------------------------------------------------------
template <class Real>
Matrix4<Real> Matrix4<Real>::TimesTranspose (const Matrix4& rkM) const
{
    // P = A*B^T
    return Matrix4<Real>(
        m_afEntry[ 0]*rkM.m_afEntry[ 0] +
        m_afEntry[ 1]*rkM.m_afEntry[ 1] +
        m_afEntry[ 2]*rkM.m_afEntry[ 2] +
        m_afEntry[ 3]*rkM.m_afEntry[ 3],

        m_afEntry[ 0]*rkM.m_afEntry[ 4] +
        m_afEntry[ 1]*rkM.m_afEntry[ 5] +
        m_afEntry[ 2]*rkM.m_afEntry[ 6] +
        m_afEntry[ 3]*rkM.m_afEntry[ 7],

        m_afEntry[ 0]*rkM.m_afEntry[ 8] +
        m_afEntry[ 1]*rkM.m_afEntry[ 9] +
        m_afEntry[ 2]*rkM.m_afEntry[10] +
        m_afEntry[ 3]*rkM.m_afEntry[11],

        m_afEntry[ 0]*rkM.m_afEntry[12] +
        m_afEntry[ 1]*rkM.m_afEntry[13] +
        m_afEntry[ 2]*rkM.m_afEntry[14] +
        m_afEntry[ 3]*rkM.m_afEntry[15],

        m_afEntry[ 4]*rkM.m_afEntry[ 0] +
        m_afEntry[ 5]*rkM.m_afEntry[ 1] +
        m_afEntry[ 6]*rkM.m_afEntry[ 2] +
        m_afEntry[ 7]*rkM.m_afEntry[ 3],

        m_afEntry[ 4]*rkM.m_afEntry[ 4] +
        m_afEntry[ 5]*rkM.m_afEntry[ 5] +
        m_afEntry[ 6]*rkM.m_afEntry[ 6] +
        m_afEntry[ 7]*rkM.m_afEntry[ 7],

        m_afEntry[ 4]*rkM.m_afEntry[ 8] +
        m_afEntry[ 5]*rkM.m_afEntry[ 9] +
        m_afEntry[ 6]*rkM.m_afEntry[10] +
        m_afEntry[ 7]*rkM.m_afEntry[11],

        m_afEntry[ 4]*rkM.m_afEntry[12] +
        m_afEntry[ 5]*rkM.m_afEntry[13] +
        m_afEntry[ 6]*rkM.m_afEntry[14] +
        m_afEntry[ 7]*rkM.m_afEntry[15],

        m_afEntry[ 8]*rkM.m_afEntry[ 0] +
        m_afEntry[ 9]*rkM.m_afEntry[ 1] +
        m_afEntry[10]*rkM.m_afEntry[ 2] +
        m_afEntry[11]*rkM.m_afEntry[ 3],

        m_afEntry[ 8]*rkM.m_afEntry[ 4] +
        m_afEntry[ 9]*rkM.m_afEntry[ 5] +
        m_afEntry[10]*rkM.m_afEntry[ 6] +
        m_afEntry[11]*rkM.m_afEntry[ 7],

        m_afEntry[ 8]*rkM.m_afEntry[ 8] +
        m_afEntry[ 9]*rkM.m_afEntry[ 9] +
        m_afEntry[10]*rkM.m_afEntry[10] +
        m_afEntry[11]*rkM.m_afEntry[11],

        m_afEntry[ 8]*rkM.m_afEntry[12] +
        m_afEntry[ 9]*rkM.m_afEntry[13] +
        m_afEntry[10]*rkM.m_afEntry[14] +
        m_afEntry[11]*rkM.m_afEntry[15],

        m_afEntry[12]*rkM.m_afEntry[ 0] +
        m_afEntry[13]*rkM.m_afEntry[ 1] +
        m_afEntry[14]*rkM.m_afEntry[ 2] +
        m_afEntry[15]*rkM.m_afEntry[ 3],

        m_afEntry[12]*rkM.m_afEntry[ 4] +
        m_afEntry[13]*rkM.m_afEntry[ 5] +
        m_afEntry[14]*rkM.m_afEntry[ 6] +
        m_afEntry[15]*rkM.m_afEntry[ 7],

        m_afEntry[12]*rkM.m_afEntry[ 8] +
        m_afEntry[13]*rkM.m_afEntry[ 9] +
        m_afEntry[14]*rkM.m_afEntry[10] +
        m_afEntry[15]*rkM.m_afEntry[11],

        m_afEntry[12]*rkM.m_afEntry[12] +
        m_afEntry[13]*rkM.m_afEntry[13] +
        m_afEntry[14]*rkM.m_afEntry[14] +
        m_afEntry[15]*rkM.m_afEntry[15]);
}
//----------------------------------------------------------------------------
template <class Real>
Matrix4<Real> Matrix4<Real>::Inverse () const
{
    Real fA0 = m_afEntry[ 0]*m_afEntry[ 5] - m_afEntry[ 1]*m_afEntry[ 4];
    Real fA1 = m_afEntry[ 0]*m_afEntry[ 6] - m_afEntry[ 2]*m_afEntry[ 4];
    Real fA2 = m_afEntry[ 0]*m_afEntry[ 7] - m_afEntry[ 3]*m_afEntry[ 4];
    Real fA3 = m_afEntry[ 1]*m_afEntry[ 6] - m_afEntry[ 2]*m_afEntry[ 5];
    Real fA4 = m_afEntry[ 1]*m_afEntry[ 7] - m_afEntry[ 3]*m_afEntry[ 5];
    Real fA5 = m_afEntry[ 2]*m_afEntry[ 7] - m_afEntry[ 3]*m_afEntry[ 6];
    Real fB0 = m_afEntry[ 8]*m_afEntry[13] - m_afEntry[ 9]*m_afEntry[12];
    Real fB1 = m_afEntry[ 8]*m_afEntry[14] - m_afEntry[10]*m_afEntry[12];
    Real fB2 = m_afEntry[ 8]*m_afEntry[15] - m_afEntry[11]*m_afEntry[12];
    Real fB3 = m_afEntry[ 9]*m_afEntry[14] - m_afEntry[10]*m_afEntry[13];
    Real fB4 = m_afEntry[ 9]*m_afEntry[15] - m_afEntry[11]*m_afEntry[13];
    Real fB5 = m_afEntry[10]*m_afEntry[15] - m_afEntry[11]*m_afEntry[14];

    Real fDet = fA0*fB5-fA1*fB4+fA2*fB3+fA3*fB2-fA4*fB1+fA5*fB0;
    if (Math<Real>::FAbs(fDet) <= Math<Real>::ZERO_TOLERANCE)
    {
        return Matrix4<Real>::ZERO;
    }

    Matrix4 kInv;
    kInv.m_afEntry[ 0] =
        + m_afEntry[ 5]*fB5 - m_afEntry[ 6]*fB4 + m_afEntry[ 7]*fB3;
    kInv.m_afEntry[ 4] =
        - m_afEntry[ 4]*fB5 + m_afEntry[ 6]*fB2 - m_afEntry[ 7]*fB1;
    kInv.m_afEntry[ 8] =
        + m_afEntry[ 4]*fB4 - m_afEntry[ 5]*fB2 + m_afEntry[ 7]*fB0;
    kInv.m_afEntry[12] =
        - m_afEntry[ 4]*fB3 + m_afEntry[ 5]*fB1 - m_afEntry[ 6]*fB0;
    kInv.m_afEntry[ 1] =
        - m_afEntry[ 1]*fB5 + m_afEntry[ 2]*fB4 - m_afEntry[ 3]*fB3;
    kInv.m_afEntry[ 5] =
        + m_afEntry[ 0]*fB5 - m_afEntry[ 2]*fB2 + m_afEntry[ 3]*fB1;
    kInv.m_afEntry[ 9] =
        - m_afEntry[ 0]*fB4 + m_afEntry[ 1]*fB2 - m_afEntry[ 3]*fB0;
    kInv.m_afEntry[13] =
        + m_afEntry[ 0]*fB3 - m_afEntry[ 1]*fB1 + m_afEntry[ 2]*fB0;
    kInv.m_afEntry[ 2] =
        + m_afEntry[13]*fA5 - m_afEntry[14]*fA4 + m_afEntry[15]*fA3;
    kInv.m_afEntry[ 6] =
        - m_afEntry[12]*fA5 + m_afEntry[14]*fA2 - m_afEntry[15]*fA1;
    kInv.m_afEntry[10] =
        + m_afEntry[12]*fA4 - m_afEntry[13]*fA2 + m_afEntry[15]*fA0;
    kInv.m_afEntry[14] =
        - m_afEntry[12]*fA3 + m_afEntry[13]*fA1 - m_afEntry[14]*fA0;
    kInv.m_afEntry[ 3] =
        - m_afEntry[ 9]*fA5 + m_afEntry[10]*fA4 - m_afEntry[11]*fA3;
    kInv.m_afEntry[ 7] =
        + m_afEntry[ 8]*fA5 - m_afEntry[10]*fA2 + m_afEntry[11]*fA1;
    kInv.m_afEntry[11] =
        - m_afEntry[ 8]*fA4 + m_afEntry[ 9]*fA2 - m_afEntry[11]*fA0;
    kInv.m_afEntry[15] =
        + m_afEntry[ 8]*fA3 - m_afEntry[ 9]*fA1 + m_afEntry[10]*fA0;

    Real fInvDet = ((Real)1.0)/fDet;
    kInv.m_afEntry[ 0] *= fInvDet;
    kInv.m_afEntry[ 1] *= fInvDet;
    kInv.m_afEntry[ 2] *= fInvDet;
    kInv.m_afEntry[ 3] *= fInvDet;
    kInv.m_afEntry[ 4] *= fInvDet;
    kInv.m_afEntry[ 5] *= fInvDet;
    kInv.m_afEntry[ 6] *= fInvDet;
    kInv.m_afEntry[ 7] *= fInvDet;
    kInv.m_afEntry[ 8] *= fInvDet;
    kInv.m_afEntry[ 9] *= fInvDet;
    kInv.m_afEntry[10] *= fInvDet;
    kInv.m_afEntry[11] *= fInvDet;
    kInv.m_afEntry[12] *= fInvDet;
    kInv.m_afEntry[13] *= fInvDet;
    kInv.m_afEntry[14] *= fInvDet;
    kInv.m_afEntry[15] *= fInvDet;

    return kInv;
}
//----------------------------------------------------------------------------
template <class Real>
Matrix4<Real> Matrix4<Real>::Adjoint () const
{
    Real fA0 = m_afEntry[ 0]*m_afEntry[ 5] - m_afEntry[ 1]*m_afEntry[ 4];
    Real fA1 = m_afEntry[ 0]*m_afEntry[ 6] - m_afEntry[ 2]*m_afEntry[ 4];
    Real fA2 = m_afEntry[ 0]*m_afEntry[ 7] - m_afEntry[ 3]*m_afEntry[ 4];
    Real fA3 = m_afEntry[ 1]*m_afEntry[ 6] - m_afEntry[ 2]*m_afEntry[ 5];
    Real fA4 = m_afEntry[ 1]*m_afEntry[ 7] - m_afEntry[ 3]*m_afEntry[ 5];
    Real fA5 = m_afEntry[ 2]*m_afEntry[ 7] - m_afEntry[ 3]*m_afEntry[ 6];
    Real fB0 = m_afEntry[ 8]*m_afEntry[13] - m_afEntry[ 9]*m_afEntry[12];
    Real fB1 = m_afEntry[ 8]*m_afEntry[14] - m_afEntry[10]*m_afEntry[12];
    Real fB2 = m_afEntry[ 8]*m_afEntry[15] - m_afEntry[11]*m_afEntry[12];
    Real fB3 = m_afEntry[ 9]*m_afEntry[14] - m_afEntry[10]*m_afEntry[13];
    Real fB4 = m_afEntry[ 9]*m_afEntry[15] - m_afEntry[11]*m_afEntry[13];
    Real fB5 = m_afEntry[10]*m_afEntry[15] - m_afEntry[11]*m_afEntry[14];

    return Matrix4<Real>(
        + m_afEntry[ 5]*fB5 - m_afEntry[ 6]*fB4 + m_afEntry[ 7]*fB3,
        - m_afEntry[ 1]*fB5 + m_afEntry[ 2]*fB4 - m_afEntry[ 3]*fB3,
        + m_afEntry[13]*fA5 - m_afEntry[14]*fA4 + m_afEntry[15]*fA3,
        - m_afEntry[ 9]*fA5 + m_afEntry[10]*fA4 - m_afEntry[11]*fA3,
        - m_afEntry[ 4]*fB5 + m_afEntry[ 6]*fB2 - m_afEntry[ 7]*fB1,
        + m_afEntry[ 0]*fB5 - m_afEntry[ 2]*fB2 + m_afEntry[ 3]*fB1,
        - m_afEntry[12]*fA5 + m_afEntry[14]*fA2 - m_afEntry[15]*fA1,
        + m_afEntry[ 8]*fA5 - m_afEntry[10]*fA2 + m_afEntry[11]*fA1,
        + m_afEntry[ 4]*fB4 - m_afEntry[ 5]*fB2 + m_afEntry[ 7]*fB0,
        - m_afEntry[ 0]*fB4 + m_afEntry[ 1]*fB2 - m_afEntry[ 3]*fB0,
        + m_afEntry[12]*fA4 - m_afEntry[13]*fA2 + m_afEntry[15]*fA0,
        - m_afEntry[ 8]*fA4 + m_afEntry[ 9]*fA2 - m_afEntry[11]*fA0,
        - m_afEntry[ 4]*fB3 + m_afEntry[ 5]*fB1 - m_afEntry[ 6]*fB0,
        + m_afEntry[ 0]*fB3 - m_afEntry[ 1]*fB1 + m_afEntry[ 2]*fB0,
        - m_afEntry[12]*fA3 + m_afEntry[13]*fA1 - m_afEntry[14]*fA0,
        + m_afEntry[ 8]*fA3 - m_afEntry[ 9]*fA1 + m_afEntry[10]*fA0);
}
//----------------------------------------------------------------------------
template <class Real>
Real Matrix4<Real>::Determinant () const
{
    Real fA0 = m_afEntry[ 0]*m_afEntry[ 5] - m_afEntry[ 1]*m_afEntry[ 4];
    Real fA1 = m_afEntry[ 0]*m_afEntry[ 6] - m_afEntry[ 2]*m_afEntry[ 4];
    Real fA2 = m_afEntry[ 0]*m_afEntry[ 7] - m_afEntry[ 3]*m_afEntry[ 4];
    Real fA3 = m_afEntry[ 1]*m_afEntry[ 6] - m_afEntry[ 2]*m_afEntry[ 5];
    Real fA4 = m_afEntry[ 1]*m_afEntry[ 7] - m_afEntry[ 3]*m_afEntry[ 5];
    Real fA5 = m_afEntry[ 2]*m_afEntry[ 7] - m_afEntry[ 3]*m_afEntry[ 6];
    Real fB0 = m_afEntry[ 8]*m_afEntry[13] - m_afEntry[ 9]*m_afEntry[12];
    Real fB1 = m_afEntry[ 8]*m_afEntry[14] - m_afEntry[10]*m_afEntry[12];
    Real fB2 = m_afEntry[ 8]*m_afEntry[15] - m_afEntry[11]*m_afEntry[12];
    Real fB3 = m_afEntry[ 9]*m_afEntry[14] - m_afEntry[10]*m_afEntry[13];
    Real fB4 = m_afEntry[ 9]*m_afEntry[15] - m_afEntry[11]*m_afEntry[13];
    Real fB5 = m_afEntry[10]*m_afEntry[15] - m_afEntry[11]*m_afEntry[14];
    Real fDet = fA0*fB5-fA1*fB4+fA2*fB3+fA3*fB2-fA4*fB1+fA5*fB0;
    return fDet;
}
//----------------------------------------------------------------------------
template <class Real>
Real Matrix4<Real>::QForm (const Vector4<Real>& rkU,
    const Vector4<Real>& rkV) const
{
    return rkU.Dot((*this)*rkV);
}
//----------------------------------------------------------------------------
template <class Real>
void Matrix4<Real>::MakeObliqueProjection (const Vector3<Real>& rkNormal,
    const Vector3<Real>& rkPoint, const Vector3<Real>& rkDirection)
{
    // The projection plane is Dot(N,X-P) = 0 where N is a 3-by-1 unit-length
    // normal vector and P is a 3-by-1 point on the plane.  The projection
    // is oblique to the plane, in the direction of the 3-by-1 vector D.
    // Necessarily Dot(N,D) is not zero for this projection to make sense.
    // Given a 3-by-1 point U, compute the intersection of the line U+t*D
    // with the plane to obtain t = -Dot(N,U-P)/Dot(N,D).  Then
    //
    //   projection(U) = P + [I - D*N^T/Dot(N,D)]*(U-P)
    //
    // A 4-by-4 homogeneous transformation representing the projection is
    //
    //       +-                               -+
    //   M = | D*N^T - Dot(N,D)*I   -Dot(N,P)D |
    //       |          0^T          -Dot(N,D) |
    //       +-                               -+
    //
    // where M applies to [U^T 1]^T by M*[U^T 1]^T.  The matrix is chosen so
    // that M[3][3] > 0 whenever Dot(N,D) < 0 (projection is onto the
    // "positive side" of the plane).

    Real fNdD = rkNormal.Dot(rkDirection);
    Real fNdP = rkNormal.Dot(rkPoint);
    m_afEntry[ 0] = rkDirection[0]*rkNormal[0] - fNdD;
    m_afEntry[ 1] = rkDirection[0]*rkNormal[1];
    m_afEntry[ 2] = rkDirection[0]*rkNormal[2];
    m_afEntry[ 3] = -fNdP*rkDirection[0];
    m_afEntry[ 4] = rkDirection[1]*rkNormal[0];
    m_afEntry[ 5] = rkDirection[1]*rkNormal[1] - fNdD;
    m_afEntry[ 6] = rkDirection[1]*rkNormal[2];
    m_afEntry[ 7] = -fNdP*rkDirection[1];
    m_afEntry[ 8] = rkDirection[2]*rkNormal[0];
    m_afEntry[ 9] = rkDirection[2]*rkNormal[1];
    m_afEntry[10] = rkDirection[2]*rkNormal[2] - fNdD;
    m_afEntry[11] = -fNdP*rkDirection[2];
    m_afEntry[12] = 0.0f;
    m_afEntry[13] = 0.0f;
    m_afEntry[14] = 0.0f;
    m_afEntry[15] = -fNdD;
}
//----------------------------------------------------------------------------
template <class Real>
void Matrix4<Real>::MakePerspectiveProjection (const Vector3<Real>& rkNormal,
    const Vector3<Real>& rkPoint, const Vector3<Real>& rkEye)
{
    //     +-                                                 -+
    // M = | Dot(N,E-P)*I - E*N^T    -(Dot(N,E-P)*I - E*N^T)*E |
    //     |        -N^t                      Dot(N,E)         |
    //     +-                                                 -+
    //
    // where E is the eye point, P is a point on the plane, and N is a
    // unit-length plane normal.

    Real fNdEmP = rkNormal.Dot(rkEye-rkPoint);

    m_afEntry[ 0] = fNdEmP - rkEye[0]*rkNormal[0];
    m_afEntry[ 1] = -rkEye[0]*rkNormal[1];
    m_afEntry[ 2] = -rkEye[0]*rkNormal[2];
    m_afEntry[ 3] = -(m_afEntry[0]*rkEye[0] + m_afEntry[1]*rkEye[1] +
        m_afEntry[2]*rkEye[2]);
    m_afEntry[ 4] = -rkEye[1]*rkNormal[0];
    m_afEntry[ 5] = fNdEmP - rkEye[1]*rkNormal[1];
    m_afEntry[ 6] = -rkEye[1]*rkNormal[2];
    m_afEntry[ 7] = -(m_afEntry[4]*rkEye[0] + m_afEntry[5]*rkEye[1] +
        m_afEntry[6]*rkEye[2]);
    m_afEntry[ 8] = -rkEye[2]*rkNormal[0];
    m_afEntry[ 9] = -rkEye[2]*rkNormal[1];
    m_afEntry[10] = fNdEmP- rkEye[2]*rkNormal[2];
    m_afEntry[11] = -(m_afEntry[8]*rkEye[0] + m_afEntry[9]*rkEye[1] +
        m_afEntry[10]*rkEye[2]);
    m_afEntry[12] = -rkNormal[0];
    m_afEntry[13] = -rkNormal[1];
    m_afEntry[14] = -rkNormal[2];
    m_afEntry[15] = rkNormal.Dot(rkEye);
}
//----------------------------------------------------------------------------
template <class Real>
void Matrix4<Real>::MakeReflection (const Vector3<Real>& rkNormal,
    const Vector3<Real>& rkPoint)
{
    //     +-                         -+
    // M = | I-2*N*N^T    2*Dot(N,P)*N |
    //     |     0^T            1      |
    //     +-                         -+
    //
    // where P is a point on the plane and N is a unit-length plane normal.

    Real fTwoNdP = ((Real)2.0)*(rkNormal.Dot(rkPoint));

    m_afEntry[ 0] = (Real)1.0 - ((Real)2.0)*rkNormal[0]*rkNormal[0];
    m_afEntry[ 1] = -((Real)2.0)*rkNormal[0]*rkNormal[1];
    m_afEntry[ 2] = -((Real)2.0)*rkNormal[0]*rkNormal[2];
    m_afEntry[ 3] = fTwoNdP*rkNormal[0];
    m_afEntry[ 4] = -((Real)2.0)*rkNormal[1]*rkNormal[0];
    m_afEntry[ 5] = (Real)1.0 - ((Real)2.0)*rkNormal[1]*rkNormal[1];
    m_afEntry[ 6] = -((Real)2.0)*rkNormal[1]*rkNormal[2];
    m_afEntry[ 7] = fTwoNdP*rkNormal[1];
    m_afEntry[ 8] = -((Real)2.0)*rkNormal[2]*rkNormal[0];
    m_afEntry[ 9] = -((Real)2.0)*rkNormal[2]*rkNormal[1];
    m_afEntry[10] = (Real)1.0 - ((Real)2.0)*rkNormal[2]*rkNormal[2];
    m_afEntry[11] = fTwoNdP*rkNormal[2];
    m_afEntry[12] = (Real)0.0;
    m_afEntry[13] = (Real)0.0;
    m_afEntry[14] = (Real)0.0;
    m_afEntry[15] = (Real)1.0;
}
//----------------------------------------------------------------------------
template <class Real>
Matrix4<Real> operator* (Real fScalar, const Matrix4<Real>& rkM)
{
    return rkM*fScalar;
}
//----------------------------------------------------------------------------
template <class Real>
Vector4<Real> operator* (const Vector4<Real>& rkV, const Matrix4<Real>& rkM)
{
    return Vector4<Real>(
        rkV[0]*rkM[0][0]+rkV[1]*rkM[1][0]+rkV[2]*rkM[2][0]+rkV[3]*rkM[3][0],
        rkV[0]*rkM[0][1]+rkV[1]*rkM[1][1]+rkV[2]*rkM[2][1]+rkV[3]*rkM[3][1],
        rkV[0]*rkM[0][2]+rkV[1]*rkM[1][2]+rkV[2]*rkM[2][2]+rkV[3]*rkM[3][2],
        rkV[0]*rkM[0][3]+rkV[1]*rkM[1][3]+rkV[2]*rkM[2][3]+rkV[3]*rkM[3][3]);
}
//----------------------------------------------------------------------------
} //namespace Wm4