dxvector.h

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    for( i = 0;i < 4; i++ )
    {
        Pivot = 0;
        for( j = 0; j < 4; j++ )
        {
            if( fabs(m_Coeff[i][j]) > fabs(m_Coeff[i][Pivot]) ) Pivot = j;
        }

        if( m_Coeff[i][Pivot] == 0.0 )
        {
            ZeroMatrix();   /* Singular Matrix */
            return FALSE; 
        }

/* Normalize */
        PValue = m_Coeff[i][Pivot];
        for( j = 0; j < 4; j++ )
        {
            m_Coeff[i][j] /= PValue;
            Mx.m_Coeff[i][j] /= PValue;
        }

/* Zeroing */
        for( j = 0; j < 4; j++ )
        {
            if( j != i )
            {
                PValue = m_Coeff[j][Pivot];
                for( k = 0; k < 4; k++ )
                {
                    m_Coeff[j][k] -= PValue*m_Coeff[i][k];
                    Mx.m_Coeff[j][k] -= PValue*Mx.m_Coeff[i][k];
                }
            }
        }
    }

/* Reorder rows */
    for( i = 0; i < 4; i++ )
    {
        if( m_Coeff[i][i] != 1.0 )
        {
            for( j = i + 1; j < 4; j++ )
                if( m_Coeff[j][i] == 1.0 ) break;
            if( j >= 4 )
            {
                ZeroMatrix();
                return FALSE;
            }

            //--- swap rows i and j of original
            for( k = 0; k < 4; k++ )
            {
                m_Coeff[i][k] += m_Coeff[j][k];
                m_Coeff[j][k] = m_Coeff[i][k] - m_Coeff[j][k];
                m_Coeff[i][k] -= m_Coeff[j][k];
            }
            
            //--- swap rows i and j of result
            for( k = 0; k < 4; k++ )
            {
                Mx.m_Coeff[i][k] += Mx.m_Coeff[j][k];
                Mx.m_Coeff[j][k] = Mx.m_Coeff[i][k] - Mx.m_Coeff[j][k];
                Mx.m_Coeff[i][k] -= Mx.m_Coeff[j][k];
            }
        }
    }
    *this = Mx;
    return TRUE;
} /* CDXMatrix4x4F::Invert */

inline void CDXMatrix4x4F::Transpose()
{
    float temp;

    temp = m_Coeff[0][1];
    m_Coeff[0][1] = m_Coeff[1][0];
    m_Coeff[1][0] = temp;

    temp = m_Coeff[0][2];
    m_Coeff[0][2] = m_Coeff[2][0];
    m_Coeff[2][0] = temp;

    temp = m_Coeff[0][3];
    m_Coeff[0][3] = m_Coeff[3][0];
    m_Coeff[3][0] = temp;

    temp = m_Coeff[1][2];
    m_Coeff[1][2] = m_Coeff[2][1];
    m_Coeff[2][1] = temp;

    temp = m_Coeff[1][3];
    m_Coeff[1][3] = m_Coeff[3][1];
    m_Coeff[3][1] = temp;

    temp = m_Coeff[2][3];
    m_Coeff[2][3] = m_Coeff[3][2];
    m_Coeff[3][2] = temp;

} /* CDXMatrix4x4F::Transpose */

inline void CDXMatrix4x4F::GetTranspose( CDXMatrix4x4F *m )
{
    float temp;

    (*this) = *m;

    temp = m_Coeff[0][1];
    m_Coeff[0][1] = m_Coeff[1][0];
    m_Coeff[1][0] = temp;

    temp = m_Coeff[0][2];
    m_Coeff[0][2] = m_Coeff[2][0];
    m_Coeff[2][0] = temp;

    temp = m_Coeff[0][3];
    m_Coeff[0][3] = m_Coeff[3][0];
    m_Coeff[3][0] = temp;

    temp = m_Coeff[1][2];
    m_Coeff[1][2] = m_Coeff[2][1];
    m_Coeff[2][1] = temp;

    temp = m_Coeff[1][3];
    m_Coeff[1][3] = m_Coeff[3][1];
    m_Coeff[3][1] = temp;

    temp = m_Coeff[2][3];
    m_Coeff[2][3] = m_Coeff[3][2];
    m_Coeff[3][2] = temp;

} /* CDXMatrix4x4F::Transpose */


/*
Matrix Inversion
by Richard Carling
from "Graphics Gems", Academic Press, 1990
*/

#define SMALL_NUMBER    1.e-8
/* 
 *   inverse( original_matrix, inverse_matrix )
 * 
 *    calculate the inverse of a 4x4 matrix
 *
 *     -1     
 *     A  = ___1__ adjoint A
 *         det A
 */

inline BOOL CDXMatrix4x4F::GetInverse( CDXMatrix4x4F *pIn )
{
    int i, j;
    float det;

    /* calculate the adjoint matrix */

    GetAdjoint( pIn );

    /*  calculate the 4x4 determinant
     *  if the determinant is zero, 
     *  then the inverse matrix is not unique.
     */

    det = det4x4( pIn );

    if( fabs( det ) < SMALL_NUMBER )
    {
        //  Non-singular matrix, no inverse!
        return FALSE;;
    }

    /* scale the adjoint matrix to get the inverse */

    for( i = 0; i < 4; i++ )
        for( j = 0; j < 4; j++ )
            m_Coeff[i][j] = m_Coeff[i][j] / det;

    return TRUE;
}


/* 
 *   adjoint( original_matrix, inverse_matrix )
 * 
 *     calculate the adjoint of a 4x4 matrix
 *
 *      Let  a   denote the minor determinant of matrix A obtained by
 *           ij
 *
 *      deleting the ith row and jth column from A.
 *
 *                    i+j
 *     Let  b   = (-1)    a
 *          ij            ji
 *
 *    The matrix B = (b  ) is the adjoint of A
 *                     ij
 */
inline void CDXMatrix4x4F::GetAdjoint( CDXMatrix4x4F *pIn )
{
    float a1, a2, a3, a4, b1, b2, b3, b4;
    float c1, c2, c3, c4, d1, d2, d3, d4;

    /* assign to individual variable names to aid  */
    /* selecting correct values  */

    a1 = pIn->m_Coeff[0][0]; b1 = pIn->m_Coeff[0][1]; 
    c1 = pIn->m_Coeff[0][2]; d1 = pIn->m_Coeff[0][3];

    a2 = pIn->m_Coeff[1][0]; b2 = pIn->m_Coeff[1][1]; 
    c2 = pIn->m_Coeff[1][2]; d2 = pIn->m_Coeff[1][3];

    a3 = pIn->m_Coeff[2][0]; b3 = pIn->m_Coeff[2][1];
    c3 = pIn->m_Coeff[2][2]; d3 = pIn->m_Coeff[2][3];

    a4 = pIn->m_Coeff[3][0]; b4 = pIn->m_Coeff[3][1]; 
    c4 = pIn->m_Coeff[3][2]; d4 = pIn->m_Coeff[3][3];


    /* row column labeling reversed since we transpose rows & columns */

    m_Coeff[0][0]  =   det3x3( b2, b3, b4, c2, c3, c4, d2, d3, d4);
    m_Coeff[1][0]  = - det3x3( a2, a3, a4, c2, c3, c4, d2, d3, d4);
    m_Coeff[2][0]  =   det3x3( a2, a3, a4, b2, b3, b4, d2, d3, d4);
    m_Coeff[3][0]  = - det3x3( a2, a3, a4, b2, b3, b4, c2, c3, c4);
        
    m_Coeff[0][1]  = - det3x3( b1, b3, b4, c1, c3, c4, d1, d3, d4);
    m_Coeff[1][1]  =   det3x3( a1, a3, a4, c1, c3, c4, d1, d3, d4);
    m_Coeff[2][1]  = - det3x3( a1, a3, a4, b1, b3, b4, d1, d3, d4);
    m_Coeff[3][1]  =   det3x3( a1, a3, a4, b1, b3, b4, c1, c3, c4);
        
    m_Coeff[0][2]  =   det3x3( b1, b2, b4, c1, c2, c4, d1, d2, d4);
    m_Coeff[1][2]  = - det3x3( a1, a2, a4, c1, c2, c4, d1, d2, d4);
    m_Coeff[2][2]  =   det3x3( a1, a2, a4, b1, b2, b4, d1, d2, d4);
    m_Coeff[3][2]  = - det3x3( a1, a2, a4, b1, b2, b4, c1, c2, c4);
        
    m_Coeff[0][3]  = - det3x3( b1, b2, b3, c1, c2, c3, d1, d2, d3);
    m_Coeff[1][3]  =   det3x3( a1, a2, a3, c1, c2, c3, d1, d2, d3);
    m_Coeff[2][3]  = - det3x3( a1, a2, a3, b1, b2, b3, d1, d2, d3);
    m_Coeff[3][3]  =   det3x3( a1, a2, a3, b1, b2, b3, c1, c2, c3);
}
/*
 * float = det4x4( matrix )
 * 
 * calculate the determinant of a 4x4 matrix.
 */
inline float det4x4( CDXMatrix4x4F *pIn )
{
    float ans;
    float a1, a2, a3, a4, b1, b2, b3, b4, c1, c2, c3, c4, d1, d2, d3, d4;

    /* assign to individual variable names to aid selecting */
    /*  correct elements */

    a1 = pIn->m_Coeff[0][0]; b1 = pIn->m_Coeff[0][1]; 
    c1 = pIn->m_Coeff[0][2]; d1 = pIn->m_Coeff[0][3];

    a2 = pIn->m_Coeff[1][0]; b2 = pIn->m_Coeff[1][1]; 
    c2 = pIn->m_Coeff[1][2]; d2 = pIn->m_Coeff[1][3];

    a3 = pIn->m_Coeff[2][0]; b3 = pIn->m_Coeff[2][1]; 
    c3 = pIn->m_Coeff[2][2]; d3 = pIn->m_Coeff[2][3];

    a4 = pIn->m_Coeff[3][0]; b4 = pIn->m_Coeff[3][1]; 
    c4 = pIn->m_Coeff[3][2]; d4 = pIn->m_Coeff[3][3];

    ans = a1 * det3x3( b2, b3, b4, c2, c3, c4, d2, d3, d4 )
        - b1 * det3x3( a2, a3, a4, c2, c3, c4, d2, d3, d4 )
        + c1 * det3x3( a2, a3, a4, b2, b3, b4, d2, d3, d4 )
        - d1 * det3x3( a2, a3, a4, b2, b3, b4, c2, c3, c4 );
    return ans;
}

/*
 * float = det3x3(  a1, a2, a3, b1, b2, b3, c1, c2, c3 )
 * 
 * calculate the determinant of a 3x3 matrix
 * in the form
 *
 *     | a1,  b1,  c1 |
 *     | a2,  b2,  c2 |
 *     | a3,  b3,  c3 |
 */

inline float det3x3( float a1, float a2, float a3, 
                     float b1, float b2, float b3, 
                     float c1, float c2, float c3 )
{
    float ans;

    ans = a1 * det2x2( b2, b3, c2, c3 )
        - b1 * det2x2( a2, a3, c2, c3 )
        + c1 * det2x2( a2, a3, b2, b3 );
    return ans;
}

/*
 * float = det2x2( float a, float b, float c, float d )
 * 
 * calculate the determinant of a 2x2 matrix.
 */
inline float det2x2( float a, float b, float c, float d )
{
    float ans = a * d - b * c;
    return ans;
}

inline HRESULT CDXMatrix4x4F::InitFromSafeArray( SAFEARRAY * /*pSA*/ )
{
    HRESULT hr = S_OK;
#if 0
    long *pData;

    if( !pSA || ( pSA->cDims != 1 ) ||
         ( pSA->cbElements != sizeof(float) ) ||
         ( pSA->rgsabound->lLbound   != 1 ) ||
         ( pSA->rgsabound->cElements != 8 ) 
      )
    {
        hr = E_INVALIDARG;
    }
    else
    {
        hr = SafeArrayAccessData(pSA, (void **)&pData);

        if( SUCCEEDED( hr ) )
        {
            for( int i = 0; i < 4; ++i )
            {
                m_Bounds[i].Min = pData[i];
                m_Bounds[i].Max = pData[i+4];
                m_Bounds[i].SampleRate = SampleRate;
            }

            hr = SafeArrayUnaccessData( pSA );
        }
    }
#endif
    return hr;
} /* CDXMatrix4x4F::InitFromSafeArray */

inline HRESULT CDXMatrix4x4F::GetSafeArray( SAFEARRAY ** /*ppSA*/ ) const
{
    HRESULT hr = S_OK;
#if 0
    SAFEARRAY *pSA;

    if( !ppSA )
    {
        hr = E_POINTER;
    }
    else
    {
        SAFEARRAYBOUND rgsabound;
        rgsabound.lLbound   = 1;
        rgsabound.cElements = 16;

        if( !(pSA = SafeArrayCreate( VT_I4, 1, &rgsabound ) ) )
        {
            hr = E_OUTOFMEMORY;
        }
        else
        {
            long *pData;
            hr = SafeArrayAccessData( pSA, (void **)&pData );

            if( SUCCEEDED( hr ) )
            {
                for( int i = 0; i < 4; ++i )
                {
                    pData[i]   = m_Bounds[i].Min;
                    pData[i+4] = m_Bounds[i].Max;
                }

                hr = SafeArrayUnaccessData( pSA );
            }
        }

        if( SUCCEEDED( hr ) )
        {
            *ppSA = pSA;
        }
    }
#endif
    return hr;
} /* CDXMatrix4x4F::GetSafeArray */

inline void CDXMatrix4x4F::TransformBounds( DXBNDS& /*Bnds*/, DXBNDS& /*ResultBnds*/ )
{

} /* CDXMatrix4x4F::TransformBounds */

#pragma option pop /*P_O_Pop*/
#endif  // DXVector_h