wmlquaternion.inl

Wild Math Library数值计算库

// Magic Software, Inc.
// http://www.magic-software.com
// http://www.wild-magic.com
// Copyright (c) 2004.  All Rights Reserved
//
// The Wild Magic Library (WML) source code is supplied under the terms of
// the license agreement http://www.magic-software.com/License/WildMagic.pdf
// and may not be copied or disclosed except in accordance with the terms of
// that agreement.

//----------------------------------------------------------------------------
template <class Real>
Quaternion<Real>::Quaternion ()
{
    // the object is uninitialized
}
//----------------------------------------------------------------------------
template <class Real>
Quaternion<Real>::Quaternion (Real fW, Real fX, Real fY, Real fZ)
{
    m_afTuple[0] = fW;
    m_afTuple[1] = fX;
    m_afTuple[2] = fY;
    m_afTuple[3] = fZ;
}
//----------------------------------------------------------------------------
template <class Real>
Quaternion<Real>::Quaternion (const Quaternion& rkQ)
{
    memcpy(m_afTuple,rkQ.m_afTuple,4*sizeof(Real));
}
//----------------------------------------------------------------------------
template <class Real>
Quaternion<Real>::Quaternion (const Matrix3<Real>& rkRot)
{
    FromRotationMatrix(rkRot);
}
//----------------------------------------------------------------------------
template <class Real>
Quaternion<Real>::Quaternion (const Vector3<Real>& rkAxis, Real fAngle)
{
    FromAxisAngle(rkAxis,fAngle);
}
//----------------------------------------------------------------------------
template <class Real>
Quaternion<Real>::Quaternion (const Vector3<Real> akRotColumn[3])
{
    FromRotationMatrix(akRotColumn);
}
//----------------------------------------------------------------------------
template <class Real>
Quaternion<Real>::operator const Real* () const
{
    return m_afTuple;
}
//----------------------------------------------------------------------------
template <class Real>
Quaternion<Real>::operator Real* ()
{
    return m_afTuple;
}
//----------------------------------------------------------------------------
template <class Real>
Real Quaternion<Real>::operator[] (int i) const
{
    assert( 0 <= i && i < 4 );
    return m_afTuple[i];
}
//----------------------------------------------------------------------------
template <class Real>
Real& Quaternion<Real>::operator[] (int i)
{
    assert( 0 <= i && i < 4 );
    return m_afTuple[i];
}
//----------------------------------------------------------------------------
template <class Real>
Real Quaternion<Real>::W () const
{
    return m_afTuple[0];
}
//----------------------------------------------------------------------------
template <class Real>
Real& Quaternion<Real>::W ()
{
    return m_afTuple[0];
}
//----------------------------------------------------------------------------
template <class Real>
Real Quaternion<Real>::X () const
{
    return m_afTuple[1];
}
//----------------------------------------------------------------------------
template <class Real>
Real& Quaternion<Real>::X ()
{
    return m_afTuple[1];
}
//----------------------------------------------------------------------------
template <class Real>
Real Quaternion<Real>::Y () const
{
    return m_afTuple[2];
}
//----------------------------------------------------------------------------
template <class Real>
Real& Quaternion<Real>::Y ()
{
    return m_afTuple[2];
}
//----------------------------------------------------------------------------
template <class Real>
Real Quaternion<Real>::Z () const
{
    return m_afTuple[3];
}
//----------------------------------------------------------------------------
template <class Real>
Real& Quaternion<Real>::Z ()
{
    return m_afTuple[3];
}
//----------------------------------------------------------------------------
template <class Real>
Quaternion<Real>& Quaternion<Real>::operator= (const Quaternion& rkQ)
{
    memcpy(m_afTuple,rkQ.m_afTuple,4*sizeof(Real));
    return *this;
}
//----------------------------------------------------------------------------
template <class Real>
bool Quaternion<Real>::operator== (const Quaternion& rkQ) const
{
    for (int i = 0; i < 4; i++)
    {
        if ( m_afTuple[i] != rkQ.m_afTuple[i] )
            return false;
    }
    return true;
}
//----------------------------------------------------------------------------
template <class Real>
bool Quaternion<Real>::operator!= (const Quaternion& rkQ) const
{
    return !operator==(rkQ);
}
//----------------------------------------------------------------------------
template <class Real>
int Quaternion<Real>::CompareArrays (const Quaternion& rkQ) const
{
    return memcmp(m_afTuple,rkQ.m_afTuple,4*sizeof(Real));
}
//----------------------------------------------------------------------------
template <class Real>
bool Quaternion<Real>::operator< (const Quaternion& rkQ) const
{
    return CompareArrays(rkQ) < 0;
}
//----------------------------------------------------------------------------
template <class Real>
bool Quaternion<Real>::operator<= (const Quaternion& rkQ) const
{
    return CompareArrays(rkQ) <= 0;
}
//----------------------------------------------------------------------------
template <class Real>
bool Quaternion<Real>::operator> (const Quaternion& rkQ) const
{
    return CompareArrays(rkQ) > 0;
}
//----------------------------------------------------------------------------
template <class Real>
bool Quaternion<Real>::operator>= (const Quaternion& rkQ) const
{
    return CompareArrays(rkQ) >= 0;
}
//----------------------------------------------------------------------------
template <class Real>
Quaternion<Real> Quaternion<Real>::operator+ (const Quaternion& rkQ) const
{
    Quaternion<Real> kSum;
    for (int i = 0; i < 4; i++)
        kSum.m_afTuple[i] = m_afTuple[i] + rkQ.m_afTuple[i];
    return kSum;
}
//----------------------------------------------------------------------------
template <class Real>
Quaternion<Real> Quaternion<Real>::operator- (const Quaternion& rkQ) const
{
    Quaternion<Real> kDiff;
    for (int i = 0; i < 4; i++)
        kDiff.m_afTuple[i] = m_afTuple[i] - rkQ.m_afTuple[i];
    return kDiff;
}
//----------------------------------------------------------------------------
template <class Real>
Quaternion<Real> Quaternion<Real>::operator* (const Quaternion& rkQ) const
{
    // NOTE:  Multiplication is not generally commutative, so in most
    // cases p*q != q*p.

    Quaternion kProd;

    kProd.m_afTuple[0] =
        m_afTuple[0]*rkQ.m_afTuple[0] -
        m_afTuple[1]*rkQ.m_afTuple[1] -
        m_afTuple[2]*rkQ.m_afTuple[2] -
        m_afTuple[3]*rkQ.m_afTuple[3];

    kProd.m_afTuple[1] =
        m_afTuple[0]*rkQ.m_afTuple[1] +
        m_afTuple[1]*rkQ.m_afTuple[0] +
        m_afTuple[2]*rkQ.m_afTuple[3] -
        m_afTuple[3]*rkQ.m_afTuple[2];

    kProd.m_afTuple[2] =
        m_afTuple[0]*rkQ.m_afTuple[2] +
        m_afTuple[2]*rkQ.m_afTuple[0] +
        m_afTuple[3]*rkQ.m_afTuple[1] -
        m_afTuple[1]*rkQ.m_afTuple[3];

    kProd.m_afTuple[3] =
        m_afTuple[0]*rkQ.m_afTuple[3] +
        m_afTuple[3]*rkQ.m_afTuple[0] +
        m_afTuple[1]*rkQ.m_afTuple[2] -
        m_afTuple[2]*rkQ.m_afTuple[1];

    return kProd;
}
//----------------------------------------------------------------------------
template <class Real>
Quaternion<Real> Quaternion<Real>::operator* (Real fScalar) const
{
    Quaternion<Real> kProd;
    for (int i = 0; i < 4; i++)
        kProd.m_afTuple[i] = fScalar*m_afTuple[i];
    return kProd;
}
//----------------------------------------------------------------------------
template <class Real>
Quaternion<Real> Quaternion<Real>::operator/ (Real fScalar) const
{
    Quaternion<Real> kQuot;
    int i;

    if ( fScalar != (Real)0.0 )
    {
        Real fInvScalar = ((Real)1.0)/fScalar;
        for (i = 0; i < 4; i++)
            kQuot.m_afTuple[i] = fInvScalar*m_afTuple[i];
    }
    else
    {
        for (i = 0; i < 4; i++)
            kQuot.m_afTuple[i] = Math<Real>::MAX_REAL;
    }

    return kQuot;
}
//----------------------------------------------------------------------------
template <class Real>
Quaternion<Real> Quaternion<Real>::operator- () const
{
    Quaternion<Real> kNeg;
    for (int i = 0; i < 4; i++)
        kNeg.m_afTuple[i] = -m_afTuple[i];
    return kNeg;
}
//----------------------------------------------------------------------------
template <class Real>
Quaternion<Real> operator* (Real fScalar, const Quaternion<Real>& rkQ)
{
    Quaternion<Real> kProd;
    for (int i = 0; i < 4; i++)
        kProd[i] = fScalar*rkQ[i];
    return kProd;
}
//----------------------------------------------------------------------------
template <class Real>
Quaternion<Real>& Quaternion<Real>::operator+= (const Quaternion& rkQ)
{
    for (int i = 0; i < 4; i++)
        m_afTuple[i] += rkQ.m_afTuple[i];
    return *this;
}
//----------------------------------------------------------------------------
template <class Real>
Quaternion<Real>& Quaternion<Real>::operator-= (const Quaternion& rkQ)
{
    for (int i = 0; i < 4; i++)
        m_afTuple[i] -= rkQ.m_afTuple[i];
    return *this;
}
//----------------------------------------------------------------------------
template <class Real>
Quaternion<Real>& Quaternion<Real>::operator*= (Real fScalar)
{
    for (int i = 0; i < 4; i++)
        m_afTuple[i] *= fScalar;
    return *this;
}
//----------------------------------------------------------------------------
template <class Real>
Quaternion<Real>& Quaternion<Real>::operator/= (Real fScalar)
{
    int i;

    if ( fScalar != (Real)0.0 )
    {
        Real fInvScalar = ((Real)1.0)/fScalar;
        for (i = 0; i < 4; i++)
            m_afTuple[i] *= fInvScalar;
    }
    else
    {
        for (i = 0; i < 4; i++)
            m_afTuple[i] = Math<Real>::MAX_REAL;
    }

    return *this;
}
//----------------------------------------------------------------------------
template <class Real>
void Quaternion<Real>::FromRotationMatrix (const Matrix3<Real>& rkRot)
{
    // Algorithm in Ken Shoemake's article in 1987 SIGGRAPH course notes
    // article "Quaternion Calculus and Fast Animation".

    Real fTrace = rkRot(0,0) + rkRot(1,1) + rkRot(2,2);
    Real fRoot;

    if ( fTrace > (Real)0.0 )
    {
        // |w| > 1/2, may as well choose w > 1/2
        fRoot = Math<Real>::Sqrt(fTrace + (Real)1.0);  // 2w
        m_afTuple[0] = ((Real)0.5)*fRoot;
        fRoot = ((Real)0.5)/fRoot;  // 1/(4w)
        m_afTuple[1] = (rkRot(2,1)-rkRot(1,2))*fRoot;
        m_afTuple[2] = (rkRot(0,2)-rkRot(2,0))*fRoot;
        m_afTuple[3] = (rkRot(1,0)-rkRot(0,1))*fRoot;
    }
    else
    {
        // |w| <= 1/2
        int i = 0;
        if ( rkRot(1,1) > rkRot(0,0) )
            i = 1;
        if ( rkRot(2,2) > rkRot(i,i) )
            i = 2;
        int j = ms_iNext[i];
        int k = ms_iNext[j];

        fRoot = Math<Real>::Sqrt(rkRot(i,i)-rkRot(j,j)-rkRot(k,k)+(Real)1.0);
        Real* apfQuat[3] = { &m_afTuple[1], &m_afTuple[2], &m_afTuple[3] };
        *apfQuat[i] = ((Real)0.5)*fRoot;
        fRoot = ((Real)0.5)/fRoot;
        m_afTuple[0] = (rkRot(k,j)-rkRot(j,k))*fRoot;
        *apfQuat[j] = (rkRot(j,i)+rkRot(i,j))*fRoot;
        *apfQuat[k] = (rkRot(k,i)+rkRot(i,k))*fRoot;
    }
}
//----------------------------------------------------------------------------
template <class Real>
void Quaternion<Real>::ToRotationMatrix (Matrix3<Real>& rkRot) const
{
    Real fTx  = ((Real)2.0)*m_afTuple[1];
    Real fTy  = ((Real)2.0)*m_afTuple[2];
    Real fTz  = ((Real)2.0)*m_afTuple[3];
    Real fTwx = fTx*m_afTuple[0];
    Real fTwy = fTy*m_afTuple[0];