moMathVector3.h

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/*******************************************************************************

                                moMathVector.h

  ****************************************************************************
  *                                                                          *
  *   This source is free software; you can redistribute it and/or modify    *
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  *   obtain it by writing to the Free Software Foundation,                  *
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  ****************************************************************************

  Copyright(C) 2006 Fabricio Costa

  Authors:
  Fabricio Costa
  Andrés Colubri

  Portions taken from
  Wild Magic Source Code
  David Eberly
  http://www.geometrictools.com
  Copyright (c) 1998-2007

*******************************************************************************/

#include "moMath.h"

#ifndef __MO_MATH_VECTOR3_H__
#define __MO_MATH_VECTOR3_H__

// moVector3 class ------------------------------------------------------------

template <class Real>
class LIBMOLDEO_API moVector3 : public moAbstract
{
public:
    // construction
    moVector3 () {} // uninitialized
    moVector3 (Real fX, Real fY, Real fZ) {
        m_afTuple[0] = fX;
        m_afTuple[1] = fY;
        m_afTuple[2] = fZ;
    }
    moVector3 (const Real* afTuple) {
        m_afTuple[0] = afTuple[0];
        m_afTuple[1] = afTuple[1];
        m_afTuple[2] = afTuple[2];
    }
    moVector3 (const moVector3& rkV) : moAbstract(rkV) {
        m_afTuple[0] = rkV.m_afTuple[0];
        m_afTuple[1] = rkV.m_afTuple[1];
        m_afTuple[2] = rkV.m_afTuple[2];
    }

    // coordinate access
    inline operator const Real* () const { return m_afTuple; }
    inline operator Real* () { return m_afTuple; }

    inline Real operator[] (int i) const { return m_afTuple[i]; }
    inline Real& operator[] (int i) { return m_afTuple[i]; }
    inline Real X () const { return m_afTuple[0]; }
    inline Real& X () { return m_afTuple[0]; }
    inline Real Y () const { return m_afTuple[1]; }
    inline Real& Y () { return m_afTuple[1]; }
    inline Real Z () const { return m_afTuple[2]; }
    inline Real& Z () { return m_afTuple[2]; }

    // assignment
    inline moVector3& operator= (const moVector3& rkV)
    {
        m_afTuple[0] = rkV.m_afTuple[0];
        m_afTuple[1] = rkV.m_afTuple[1];
        m_afTuple[2] = rkV.m_afTuple[2];
        return *this;
    }

    // comparison
    bool operator== (const moVector3& rkV) const { return CompareArrays(rkV) == 0; }
    bool operator!= (const moVector3& rkV) const { return CompareArrays(rkV) != 0; }
    bool operator<  (const moVector3& rkV) const { return CompareArrays(rkV) < 0; }
    bool operator<= (const moVector3& rkV) const { return CompareArrays(rkV) <= 0; }
    bool operator>  (const moVector3& rkV) const { return CompareArrays(rkV) > 0; }
    bool operator>= (const moVector3& rkV) const { return CompareArrays(rkV) >= 0; }

    // arithmetic operations

    moVector3 operator+ (const moVector3& rkV) const  {
          moVector3<Real> ret(m_afTuple[0]+rkV.m_afTuple[0], m_afTuple[1]+rkV.m_afTuple[1], m_afTuple[2]+rkV.m_afTuple[2]);
        return ret;
    }
    moVector3 operator- (const moVector3& rkV) const {
        return moVector3<Real>(m_afTuple[0]-rkV.m_afTuple[0],m_afTuple[1]-rkV.m_afTuple[1],m_afTuple[2]-rkV.m_afTuple[2]);
    }
    moVector3 operator* (Real fScalar) const {
        return moVector3<Real>(
            fScalar*m_afTuple[0],
            fScalar*m_afTuple[1],
            fScalar*m_afTuple[2]);
    }
    moVector3 operator/ (Real fScalar) const {
        moVector3<Real> kQuot;

        if (fScalar != (Real)0.0)
        {
            Real fInvScalar = ((Real)1.0)/fScalar;
            kQuot.m_afTuple[0] = fInvScalar*m_afTuple[0];
            kQuot.m_afTuple[1] = fInvScalar*m_afTuple[1];
            kQuot.m_afTuple[2] = fInvScalar*m_afTuple[2];
        }
        else
        {
            kQuot.m_afTuple[0] = moMath<Real>::MAX_REAL;
            kQuot.m_afTuple[1] = moMath<Real>::MAX_REAL;
            kQuot.m_afTuple[2] = moMath<Real>::MAX_REAL;
        }

        return kQuot;
    }

    moVector3 operator- () const {
        return moVector3<Real>(-m_afTuple[0], -m_afTuple[1], -m_afTuple[2]);
    }

    // arithmetic updates

    moVector3& operator+= (const moVector3& rkV)
    {
        m_afTuple[0] += rkV.m_afTuple[0];
        m_afTuple[1] += rkV.m_afTuple[1];
        m_afTuple[2] += rkV.m_afTuple[2];
        return *this;
    }

    moVector3& operator-= (const moVector3& rkV)
    {
        m_afTuple[0] -= rkV.m_afTuple[0];
        m_afTuple[1] -= rkV.m_afTuple[1];
        m_afTuple[2] -= rkV.m_afTuple[2];
        return *this;
    }

    moVector3<Real>& operator*= (const Real fScalar)
    {
        m_afTuple[0] *= fScalar;
        m_afTuple[1] *= fScalar;
        m_afTuple[2] *= fScalar;
        return *this;
    }

    moVector3<Real>& operator/= (const Real fScalar)
    {
        if (fScalar != (Real)0.0)
        {
            Real fInvScalar = ((Real)1.0)/fScalar;
            m_afTuple[0] *= fInvScalar;
            m_afTuple[1] *= fInvScalar;
            m_afTuple[2] *= fInvScalar;
        }
        else
        {
            m_afTuple[0] = moMath<Real>::MAX_REAL;
            m_afTuple[1] = moMath<Real>::MAX_REAL;
            m_afTuple[2] = moMath<Real>::MAX_REAL;
        }

        return *this;
    }


    // vector operations
    Real Length () const {
        return moMath<Real>::Sqrt(
        m_afTuple[0]*m_afTuple[0] +
        m_afTuple[1]*m_afTuple[1] +
        m_afTuple[2]*m_afTuple[2]);
    }

    Real SquaredLength () const
    {
        return
            m_afTuple[0]*m_afTuple[0] +
            m_afTuple[1]*m_afTuple[1] +
            m_afTuple[2]*m_afTuple[2];
    }

    Real Dot (const moVector3& rkV) const
    {
        return
            m_afTuple[0]*rkV.m_afTuple[0] +
            m_afTuple[1]*rkV.m_afTuple[1] +
            m_afTuple[2]*rkV.m_afTuple[2];
    }
    Real Normalize () {
        Real fLength = Length();

        if (fLength > moMath<Real>::ZERO_TOLERANCE)
        {
            Real fInvLength = ((Real)1.0)/fLength;
            m_afTuple[0] *= fInvLength;
            m_afTuple[1] *= fInvLength;
            m_afTuple[2] *= fInvLength;
        }
        else
        {
            fLength = (Real)0.0;
            m_afTuple[0] = (Real)0.0;
            m_afTuple[1] = (Real)0.0;
            m_afTuple[2] = (Real)0.0;
        }

        return fLength;
    }

    // The cross products are computed using the right-handed rule.  Be aware
    // that some graphics APIs use a left-handed rule.  If you have to compute
    // a cross product with these functions and send the result to the API
    // that expects left-handed, you will need to change sign on the vector
    // (replace each component value c by -c).
    moVector3 Cross (const moVector3& rkV) const {
        moVector3<Real> kCross(
        m_afTuple[1]*rkV.m_afTuple[2] - m_afTuple[2]*rkV.m_afTuple[1],
        m_afTuple[2]*rkV.m_afTuple[0] - m_afTuple[0]*rkV.m_afTuple[2],
        m_afTuple[0]*rkV.m_afTuple[1] - m_afTuple[1]*rkV.m_afTuple[0]);
        return kCross;
    }
    moVector3 UnitCross (const moVector3& rkV) const {
        moVector3<Real> kCross(
                m_afTuple[1]*rkV.m_afTuple[2] - m_afTuple[2]*rkV.m_afTuple[1],
                m_afTuple[2]*rkV.m_afTuple[0] - m_afTuple[0]*rkV.m_afTuple[2],
                m_afTuple[0]*rkV.m_afTuple[1] - m_afTuple[1]*rkV.m_afTuple[0]);
         kCross.Normalize();
         return kCross;
    }


    // Compute the barycentric coordinates of the point with respect to the
    // tetrahedron <V0,V1,V2,V3>, P = b0*V0 + b1*V1 + b2*V2 + b3*V3, where
    // b0 + b1 + b2 + b3 = 1.
    void GetBarycentrics (const moVector3<Real>& rkV0,
        const moVector3<Real>& rkV1, const moVector3<Real>& rkV2,
        const moVector3<Real>& rkV3, Real afBary[4]) const
    {
        // compute the vectors relative to V3 of the tetrahedron
        moVector3<Real> akDiff[4] =
        {
            rkV0 - rkV3,
            rkV1 - rkV3,
            rkV2 - rkV3,
            *this - rkV3
        };

        // If the vertices have large magnitude, the linear system of
        // equations for computing barycentric coordinates can be
        // ill-conditioned.  To avoid this, uniformly scale the tetrahedron
        // edges to be of order 1.  The scaling of all differences does not
        // change the barycentric coordinates.
        Real fMax = (Real)0.0;
        int i;
        for (i = 0; i < 3; i++)
        {
            for (int j = 0; j < 3; j++)
            {
                Real fValue = moMath<Real>::FAbs(akDiff[i][j]);
                if (fValue > fMax)
                {
                    fMax = fValue;
                }
            }
        }

        // scale down only large data
        if (fMax > (Real)1.0)
        {
            Real fInvMax = ((Real)1.0)/fMax;
            for (i = 0; i < 4; i++)
            {
                akDiff[i] *= fInvMax;
            }
        }

        Real fDet = akDiff[0].Dot(akDiff[1].Cross(akDiff[2]));
        moVector3<Real> kE1cE2 = akDiff[1].Cross(akDiff[2]);
        moVector3<Real> kE2cE0 = akDiff[2].Cross(akDiff[0]);
        moVector3<Real> kE0cE1 = akDiff[0].Cross(akDiff[1]);
        if (moMath<Real>::FAbs(fDet) > moMath<Real>::ZERO_TOLERANCE)
        {
            Real fInvDet = ((Real)1.0)/fDet;
            afBary[0] = akDiff[3].Dot(kE1cE2)*fInvDet;
            afBary[1] = akDiff[3].Dot(kE2cE0)*fInvDet;
            afBary[2] = akDiff[3].Dot(kE0cE1)*fInvDet;
            afBary[3] = (Real)1.0 - afBary[0] - afBary[1] - afBary[2];
        }
        else
        {
            // The tetrahedron is potentially flat.  Determine the face of
            // maximum area and compute barycentric coordinates with respect
            // to that face.
            moVector3<Real> kE02 = rkV0 - rkV2;
            moVector3<Real> kE12 = rkV1 - rkV2;
            moVector3<Real> kE02cE12 = kE02.Cross(kE12);
            Real fMaxSqrArea = kE02cE12.SquaredLength();
            int iMaxIndex = 3;
            Real fSqrArea = kE0cE1.SquaredLength();
            if (fSqrArea > fMaxSqrArea)
            {
                iMaxIndex = 0;
                fMaxSqrArea = fSqrArea;
            }
            fSqrArea = kE1cE2.SquaredLength();
            if (fSqrArea > fMaxSqrArea)
            {
                iMaxIndex = 1;
                fMaxSqrArea = fSqrArea;
            }
            fSqrArea = kE2cE0.SquaredLength();
            if (fSqrArea > fMaxSqrArea)
            {
                iMaxIndex = 2;
                fMaxSqrArea = fSqrArea;
            }

            if (fMaxSqrArea > moMath<Real>::ZERO_TOLERANCE)
            {
                Real fInvSqrArea = ((Real)1.0)/fMaxSqrArea;
                moVector3<Real> kTmp;
                if (iMaxIndex == 0)
                {
                    kTmp = akDiff[3].Cross(akDiff[1]);
                    afBary[0] = kE0cE1.Dot(kTmp)*fInvSqrArea;
                    kTmp = akDiff[0].Cross(akDiff[3]);
                    afBary[1] = kE0cE1.Dot(kTmp)*fInvSqrArea;
                    afBary[2] = (Real)0.0;
                    afBary[3] = (Real)1.0 - afBary[0] - afBary[1];
                }
                else if (iMaxIndex == 1)
                {
                    afBary[0] = (Real)0.0;
                    kTmp = akDiff[3].Cross(akDiff[2]);
                    afBary[1] = kE1cE2.Dot(kTmp)*fInvSqrArea;
                    kTmp = akDiff[1].Cross(akDiff[3]);
                    afBary[2] = kE1cE2.Dot(kTmp)*fInvSqrArea;
                    afBary[3] = (Real)1.0 - afBary[1] - afBary[2];
                }
                else if (iMaxIndex == 2)
                {
                    kTmp = akDiff[2].Cross(akDiff[3]);
                    afBary[0] = kE2cE0.Dot(kTmp)*fInvSqrArea;
                    afBary[1] = (Real)0.0;
                    kTmp = akDiff[3].Cross(akDiff[0]);
                    afBary[2] = kE2cE0.Dot(kTmp)*fInvSqrArea;
                    afBary[3] = (Real)1.0 - afBary[0] - afBary[2];
                }
                else
                {
                    akDiff[3] = *this - rkV2;
                    kTmp = akDiff[3].Cross(kE12);
                    afBary[0] = kE02cE12.Dot(kTmp)*fInvSqrArea;
                    kTmp = kE02.Cross(akDiff[3]);
                    afBary[1] = kE02cE12.Dot(kTmp)*fInvSqrArea;
                    afBary[2] = (Real)1.0 - afBary[0] - afBary[1];
                    afBary[3] = (Real)0.0;
                }
            }
            else
            {
                // The tetrahedron is potentially a sliver.  Determine the edge of
                // maximum length and compute barycentric coordinates with respect
                // to that edge.
                Real fMaxSqrLength = akDiff[0].SquaredLength();
                iMaxIndex = 0;  // <V0,V3>
                Real fSqrLength = akDiff[1].SquaredLength();
                if (fSqrLength > fMaxSqrLength)
                {
                    iMaxIndex = 1;  // <V1,V3>
                    fMaxSqrLength = fSqrLength;
                }
                fSqrLength = akDiff[2].SquaredLength();
                if (fSqrLength > fMaxSqrLength)
                {
                    iMaxIndex = 2;  // <V2,V3>
                    fMaxSqrLength = fSqrLength;
                }
                fSqrLength = kE02.SquaredLength();
                if (fSqrLength > fMaxSqrLength)
                {
                    iMaxIndex = 3;  // <V0,V2>
                    fMaxSqrLength = fSqrLength;
                }
                fSqrLength = kE12.SquaredLength();
                if (fSqrLength > fMaxSqrLength)
                {
                    iMaxIndex = 4;  // <V1,V2>
                    fMaxSqrLength = fSqrLength;
                }
                moVector3<Real> kE01 = rkV0 - rkV1;
                fSqrLength = kE01.SquaredLength();
                if (fSqrLength > fMaxSqrLength)
                {
                    iMaxIndex = 5;  // <V0,V1>
                    fMaxSqrLength = fSqrLength;
                }

                if (fMaxSqrLength > moMath<Real>::ZERO_TOLERANCE)
                {
                    Real fInvSqrLength = ((Real)1.0)/fMaxSqrLength;
                    if (iMaxIndex == 0)
                    {
                        // P-V3 = t*(V0-V3)
                        afBary[0] = akDiff[3].Dot(akDiff[0])*fInvSqrLength;
                        afBary[1] = (Real)0.0;
                        afBary[2] = (Real)0.0;
                        afBary[3] = (Real)1.0 - afBary[0];
                    }
                    else if (iMaxIndex == 1)
                    {
                        // P-V3 = t*(V1-V3)
                        afBary[0] = (Real)0.0;
                        afBary[1] = akDiff[3].Dot(akDiff[1])*fInvSqrLength;
                        afBary[2] = (Real)0.0;
                        afBary[3] = (Real)1.0 - afBary[1];
                    }
                    else if (iMaxIndex == 2)
                    {
                        // P-V3 = t*(V2-V3)
                        afBary[0] = (Real)0.0;
                        afBary[1] = (Real)0.0;
                        afBary[2] = akDiff[3].Dot(akDiff[2])*fInvSqrLength;
                        afBary[3] = (Real)1.0 - afBary[2];
                    }
                    else if (iMaxIndex == 3)
                    {
                        // P-V2 = t*(V0-V2)
                        akDiff[3] = *this - rkV2;
                        afBary[0] = akDiff[3].Dot(kE02)*fInvSqrLength;
                        afBary[1] = (Real)0.0;
                        afBary[2] = (Real)1.0 - afBary[0];
                        afBary[3] = (Real)0.0;
                    }
                    else if (iMaxIndex == 4)
                    {
                        // P-V2 = t*(V1-V2)
                        akDiff[3] = *this - rkV2;
                        afBary[0] = (Real)0.0;
                        afBary[1] = akDiff[3].Dot(kE12)*fInvSqrLength;
                        afBary[2] = (Real)1.0 - afBary[1];
                        afBary[3] = (Real)0.0;
                    }
                    else
                    {
                        // P-V1 = t*(V0-V1)
                        akDiff[3] = *this - rkV1;
                        afBary[0] = akDiff[3].Dot(kE01)*fInvSqrLength;
                        afBary[1] = (Real)1.0 - afBary[0];
                        afBary[2] = (Real)0.0;
                        afBary[3] = (Real)0.0;
                    }
                }
                else
                {
                    // tetrahedron is a nearly a point, just return equal weights
                    afBary[0] = (Real)0.25;
                    afBary[1] = afBary[0];
                    afBary[2] = afBary[0];
                    afBary[3] = afBary[0];
                }
            }
        }
    }

    // Gram-Schmidt orthonormalization.  Take linearly independent vectors
    // U, V, and W and compute an orthonormal set (unit length, mutually
    // perpendicular).
    static void Orthonormalize (moVector3& rkU, moVector3& rkV, moVector3& rkW)
    {
        // If the input vectors are v0, v1, and v2, then the Gram-Schmidt
        // orthonormalization produces vectors u0, u1, and u2 as follows,
        //
        //   u0 = v0/|v0|
        //   u1 = (v1-(u0*v1)u0)/|v1-(u0*v1)u0|
        //   u2 = (v2-(u0*v2)u0-(u1*v2)u1)/|v2-(u0*v2)u0-(u1*v2)u1|
        //
        // where |A| indicates length of vector A and A*B indicates dot
        // product of vectors A and B.

        // compute u0
        rkU.Normalize();

        // compute u1
        Real fDot0 = rkU.Dot(rkV);
        rkV -= fDot0*rkU;
        rkV.Normalize();

        // compute u2
        Real fDot1 = rkV.Dot(rkW);
        fDot0 = rkU.Dot(rkW);
        rkW -= fDot0*rkU + fDot1*rkV;
        rkW.Normalize();
    }


    static void Orthonormalize (moVector3* akV)
    {
        Orthonormalize(akV[0],akV[1],akV[2]);
    }

    // Input W must be a nonzero vector. The output is an orthonormal basis
    // {U,V,W}.  The input W is normalized by this function.  If you know
    // W is already unit length, use GenerateComplementBasis to compute U
    // and V.
    static void GenerateOrthonormalBasis (moVector3& rkU, moVector3& rkV,
        moVector3& rkW)
    {
        rkW.Normalize();
        GenerateComplementBasis(rkU,rkV,rkW);
    }

    // Input W must be a unit-length vector.  The output vectors {U,V} are
    // unit length and mutually perpendicular, and {U,V,W} is an orthonormal
    // basis.
    static void GenerateComplementBasis (moVector3& rkU, moVector3& rkV,
        const moVector3& rkW)
    {
        Real fInvLength;

        if (moMath<Real>::FAbs(rkW.m_afTuple[0]) >=
            moMath<Real>::FAbs(rkW.m_afTuple[1]) )
        {
            // W.x or W.z is the largest magnitude component, swap them
            fInvLength = moMath<Real>::InvSqrt(rkW.m_afTuple[0]*rkW.m_afTuple[0] +
                rkW.m_afTuple[2]*rkW.m_afTuple[2]);
            rkU.m_afTuple[0] = -rkW.m_afTuple[2]*fInvLength;
            rkU.m_afTuple[1] = (Real)0.0;
            rkU.m_afTuple[2] = +rkW.m_afTuple[0]*fInvLength;
            rkV.m_afTuple[0] = rkW.m_afTuple[1]*rkU.m_afTuple[2];
            rkV.m_afTuple[1] = rkW.m_afTuple[2]*rkU.m_afTuple[0] -
                rkW.m_afTuple[0]*rkU.m_afTuple[2];
            rkV.m_afTuple[2] = -rkW.m_afTuple[1]*rkU.m_afTuple[0];
        }
        else
        {
            // W.y or W.z is the largest magnitude component, swap them
            fInvLength = moMath<Real>::InvSqrt(rkW.m_afTuple[1]*rkW.m_afTuple[1] +
                rkW.m_afTuple[2]*rkW.m_afTuple[2]);
            rkU.m_afTuple[0] = (Real)0.0;
            rkU.m_afTuple[1] = +rkW.m_afTuple[2]*fInvLength;
            rkU.m_afTuple[2] = -rkW.m_afTuple[1]*fInvLength;
            rkV.m_afTuple[0] = rkW.m_afTuple[1]*rkU.m_afTuple[2] -
                rkW.m_afTuple[2]*rkU.m_afTuple[1];
            rkV.m_afTuple[1] = -rkW.m_afTuple[0]*rkU.m_afTuple[2];
            rkV.m_afTuple[2] = rkW.m_afTuple[0]*rkU.m_afTuple[1];
        }
    }


    // Compute the extreme values.
    static void ComputeExtremes (int iVQuantity, const moVector3* akPoint,
        moVector3& rkMin, moVector3& rkMax)
    {
        if (!(iVQuantity > 0 && akPoint)) return;

        rkMin = akPoint[0];
        rkMax = rkMin;
        for (int i = 1; i < iVQuantity; i++)
        {
            const moVector3<Real>& rkPoint = akPoint[i];
            for (int j = 0; j < 3; j++)
            {
                if (rkPoint[j] < rkMin[j])
                {
                    rkMin[j] = rkPoint[j];
                }
                else if (rkPoint[j] > rkMax[j])
                {
                    rkMax[j] = rkPoint[j];
                }
            }
        }
    }


    // Cosine between 'this' vector and rkV.
    Real Cosine (const moVector3<Real>& rkV) {
        Real l = Length();
        Real lv = rkV.Length();
        if ((0 < l) && (0 < lv)) return Dot(rkV) / (l * lv);
        else return 0;
    }
    // Angle between 'this' vector and rkV.
    Real Angle (const moVector3<Real>& rkV) {
        return moMath<Real>::ACos(Cosine(rkV));
    }

    // special vectors
    static const moVector3 ZERO;    // (0,0,0)
    static const moVector3 UNIT_X;  // (1,0,0)
    static const moVector3 UNIT_Y;  // (0,1,0)
    static const moVector3 UNIT_Z;  // (0,0,1)
    static const moVector3 ONE;     // (1,1,1)

private:
    // support for comparisons
    int CompareArrays (const moVector3& rkV) const {return memcmp(m_afTuple,rkV.m_afTuple,3*sizeof(Real));}

    Real m_afTuple[3];
};


// arithmetic operations
template <class Real>
inline moVector3<Real> operator* (Real fScalar, const moVector3<Real>& rkV)
{
    return moVector3<Real>(fScalar*rkV[0], fScalar*rkV[1], fScalar*rkV[2]);
}

#ifndef MO_MACOSX
#ifndef MO_RASPBIAN
template class LIBMOLDEO_API moVector3<MOlong>;
template class LIBMOLDEO_API moVector3<MOfloat>;
template class LIBMOLDEO_API moVector3<MOdouble>;
#endif
#endif

typedef moVector3<MOlong> moVector3i;
typedef moVector3<MOfloat> moVector3f;
typedef moVector3<MOdouble> moVector3d;
typedef moVector3i moVertex3i;
typedef moVector3f moVertex3f;
typedef moVector3d moVertex3d;

moDeclareExportedDynamicArray( moVector3i, moVector3iArray );
moDeclareExportedDynamicArray( moVector3f, moVector3fArray );
moDeclareExportedDynamicArray( moVector3d, moVector3dArray );

#endif