source: downloads/ogreode/src/OgreOdeEigenSolver.cpp @ 45

#include "OgreOdePrecompiledHeaders.h"

#include "OgreOdeEigenSolver.h"

using namespace OgreOde;
using namespace Ogre;

void EigenSolver::DecrSortEigenStuff3 ()
{
        Tridiagonal3();
        QLAlgorithm();
        DecreasingSort();
        GuaranteeRotation();
}

void EigenSolver::Tridiagonal3 ()
{
        const Ogre::Real fM00 = m_kMat[0][0];
   Ogre::Real fM01 = m_kMat[0][1];
        Real fM02 = m_kMat[0][2];
        const Ogre::Real fM11 = m_kMat[1][1];
        const Ogre::Real fM12 = m_kMat[1][2];
        const Ogre::Real fM22 = m_kMat[2][2];

        m_afDiag[0] = fM00;
        m_afSubd[2] = (Real)0.0;
        if ( fM02 != (Real)0.0 )
        {
                const Ogre::Real fLength = sqrtf(fM01*fM01+fM02*fM02);
                const Ogre::Real fInvLength = ((Real)1.0)/fLength;
                fM01 *= fInvLength;
                fM02 *= fInvLength;
                const Ogre::Real fQ = ((Real)2.0)*fM01*fM12+fM02*(fM22-fM11);
                m_afDiag[1] = fM11+fM02*fQ;
                m_afDiag[2] = fM22-fM02*fQ;
                m_afSubd[0] = fLength;
                m_afSubd[1] = fM12-fM01*fQ;
                m_kMat[0][0] = (Real)1.0;
                m_kMat[0][1] = (Real)0.0;
                m_kMat[0][2] = (Real)0.0;
                m_kMat[1][0] = (Real)0.0;
                m_kMat[1][1] = fM01;
                m_kMat[1][2] = fM02;
                m_kMat[2][0] = (Real)0.0;
                m_kMat[2][1] = fM02;
                m_kMat[2][2] = -fM01;
        }
        else
        {
                m_afDiag[1] = fM11;
                m_afDiag[2] = fM22;
                m_afSubd[0] = fM01;
                m_afSubd[1] = fM12;
                m_kMat[0][0] = (Real)1.0;
                m_kMat[0][1] = (Real)0.0;
                m_kMat[0][2] = (Real)0.0;
                m_kMat[1][0] = (Real)0.0;
                m_kMat[1][1] = (Real)1.0;
                m_kMat[1][2] = (Real)0.0;
                m_kMat[2][0] = (Real)0.0;
                m_kMat[2][1] = (Real)0.0;
                m_kMat[2][2] = (Real)1.0;
        }
}

bool EigenSolver::QLAlgorithm ()
{
        const int iMaxIter = 32;

        for (int i0 = 0; i0 < m_iSize; i0++)
        {
                int i1;
                for (i1 = 0; i1 < iMaxIter; i1++)
                {
                        int i2;
                        for (i2 = i0; i2 <= m_iSize-2; i2++)
                        {
                                Real fTmp = fabs(m_afDiag[i2]) + fabs(m_afDiag[i2+1]);
                                if ( fabs(m_afSubd[i2]) + fTmp == fTmp ) break;
                        }
                        if ( i2 == i0 ) break;

                        Real fG = (m_afDiag[i0+1] - m_afDiag[i0])/(((Real)2.0) * m_afSubd[i0]);
                        Real fR = sqrtf(fG*fG+(Real)1.0);
                        if ( fG < (Real)0.0 ) fG = m_afDiag[i2]-m_afDiag[i0]+m_afSubd[i0]/(fG-fR);
                        else fG = m_afDiag[i2]-m_afDiag[i0]+m_afSubd[i0]/(fG+fR);
                        Real fSin = (Real)1.0, fCos = (Real)1.0, fP = (Real)0.0;
                        for (int i3 = i2-1; i3 >= i0; i3--)
                        {
                                Real fF = fSin*m_afSubd[i3];
               Ogre::Real fB = fCos*m_afSubd[i3];
                    if ( fabs(fF) >= fabs(fG) )
                        {
                                fCos = fG/fF;
                                    fR = sqrtf(fCos*fCos+(Real)1.0);
                                        m_afSubd[i3+1] = fF*fR;
                    fSin = ((Real)1.0)/fR;
                        fCos *= fSin;
                        }
                            else
                                {
                                        fSin = fF/fG;
                                        fR = sqrtf(fSin*fSin+(Real)1.0);
                                        m_afSubd[i3+1] = fG*fR;
                                        fCos = ((Real)1.0)/fR;
                                        fSin *= fCos;
                                }
                                fG = m_afDiag[i3+1]-fP;
                fR = (m_afDiag[i3]-fG)*fSin+((Real)2.0)*fB*fCos;
                    fP = fSin*fR;
                        m_afDiag[i3+1] = fG+fP;
                            fG = fCos*fR-fB;

                                for (int i4 = 0; i4 < m_iSize; i4++)
                                {
                                        fF = m_kMat[i4][i3+1];
                    m_kMat[i4][i3+1] = fSin*m_kMat[i4][i3]+fCos*fF;
                        m_kMat[i4][i3] = fCos*m_kMat[i4][i3]-fSin*fF;
                        }
                        }
                        m_afDiag[i0] -= fP;
                        m_afSubd[i0] = fG;
                        m_afSubd[i2] = (Real)0.0;
                }
                if ( i1 == iMaxIter ) return false;
        }
        return true;
}

void EigenSolver::DecreasingSort ()
{
        // sort eigenvalues in decreasing order, e[0] >= ... >= e[iSize-1]
        for (int i0 = 0, i1; i0 <= m_iSize-2; i0++)
        {
                // locate maximum eigenvalue
                i1 = i0;
                Real fMax = m_afDiag[i1];
                int i2;
                for (i2 = i0+1; i2 < m_iSize; i2++)
                {
                        if ( m_afDiag[i2] > fMax )
                        {
                                i1 = i2;
                                fMax = m_afDiag[i1];
                        }
                }

                if ( i1 != i0 )
                {
                        // swap eigenvalues
                        m_afDiag[i1] = m_afDiag[i0];
                        m_afDiag[i0] = fMax;

                        // swap eigenvectors
                        for (i2 = 0; i2 < m_iSize; i2++)
                        {
                                Real fTmp = m_kMat[i2][i0];
                                m_kMat[i2][i0] = m_kMat[i2][i1];
                                m_kMat[i2][i1] = fTmp;
                                m_bIsRotation = !m_bIsRotation;
                        }
                }
        }
}

void EigenSolver::GuaranteeRotation ()
{
        if ( !m_bIsRotation )
        {
                // change sign on the first column
                for (int iRow = 0; iRow < m_iSize; iRow++) 
            m_kMat[iRow][0] = -m_kMat[iRow][0];
        }
}

void EigenSolver::orthogonalLineFit(unsigned int vertex_count, const Ogre::Vector3* vertices,Vector3& origin,Vector3& direction)
{
        unsigned int i;

    // compute average of points
        origin = vertices[0];
    for(i = 1; i < vertex_count; ++i) 
        origin += vertices[i];

        const Ogre::Real fInvQuantity = 1.0 / vertex_count;
        origin *= fInvQuantity;

        // compute sums of products
        Real fSumXX = 0.0, fSumXY = 0.0, fSumXZ = 0.0;
   Ogre::Real fSumYY = 0.0, fSumYZ = 0.0, fSumZZ = 0.0;
        for (i = 0; i < vertex_count; i++) 
        {
                const Ogre::Vector3 kDiff (vertices[i] - origin);
            fSumXX += kDiff.x*kDiff.x;
        fSumXY += kDiff.x*kDiff.y;
                fSumXZ += kDiff.x*kDiff.z;
            fSumYY += kDiff.y*kDiff.y;
        fSumYZ += kDiff.y*kDiff.z;
                fSumZZ += kDiff.z*kDiff.z;
        }
        fSumXX *= fInvQuantity;
        fSumXY *= fInvQuantity;
        fSumXZ *= fInvQuantity;
        fSumYY *= fInvQuantity;
        fSumYZ *= fInvQuantity;
        fSumZZ *= fInvQuantity;

        // setup the eigensolver
        EigenSolver kES(3);
        kES(0,0) = fSumYY+fSumZZ;
        kES(0,1) = -fSumXY;
        kES(0,2) = -fSumXZ;
        kES(1,0) = kES(0,1);
        kES(1,1) = fSumXX+fSumZZ;
        kES(1,2) = -fSumYZ;
        kES(2,0) = kES(0,2);
        kES(2,1) = kES(1,2);
    kES(2,2) = fSumXX+fSumYY;

        // compute eigenstuff, smallest eigenvalue is in last position
        kES.DecrSortEigenStuff3();

    // unit-length direction for best-fit line
        kES.GetEigenvector(2,direction);
}

Real EigenSolver::SqrDistance(const Ogre::Vector3& rkPoint,const Ogre::Vector3& origin,const Ogre::Vector3& direction)
{
        Vector3 kDiff(rkPoint - origin);
    const Ogre::Real fSqrLen = direction.squaredLength();
        const Ogre::Real fT = kDiff.dotProduct(direction) / fSqrLen;

    kDiff -= fT*direction;

        return kDiff.squaredLength();
}

void EigenSolver::GenerateOrthonormalBasis (Vector3& rkU, Ogre::Vector3& rkV, Ogre::Vector3& rkW, bool bUnitLengthW)
{
        if ( !bUnitLengthW ) rkW.normalise();

        Real fInvLength;

        if ( fabs(rkW[0]) >= fabs(rkW[1]) )
        {
                // W.x or W.z is the largest magnitude component, swap them
                fInvLength = 1.0 / sqrtf(rkW[0]*rkW[0] + rkW[2]*rkW[2]);

            rkU[0] = -rkW[2]*fInvLength;
        rkU[1] = (Real)0.0;
                rkU[2] = +rkW[0]*fInvLength;
        }
    else
        {
        // W.y or W.z is the largest magnitude component, swap them
                fInvLength = 1.0 / sqrtf(rkW[1]*rkW[1] + rkW[2]*rkW[2]);

            rkU[0] = (Real)0.0;
        rkU[1] = +rkW[2]*fInvLength;
                rkU[2] = -rkW[1]*fInvLength;
        }

        rkV = rkW.crossProduct(rkU);
}

EigenSolver::EigenSolver(int iSize)
{
        assert( iSize >= 2 );
    m_iSize = iSize;
        m_afDiag = new Ogre::Real[m_iSize];
    m_afSubd = new Ogre::Real[m_iSize];

        // set according to the parity of the number of Householder reflections
        m_bIsRotation = ((iSize % 2) == 0);
}

Ogre::Real& EigenSolver::operator() (int iRow, int iCol)
{
        return m_kMat[iRow][iCol];
}

EigenSolver::~EigenSolver()
{
    delete[] m_afSubd;
        delete[] m_afDiag;
}

void EigenSolver::GetEigenvector (int i, Ogre::Vector3& rkV) const
{
        assert( m_iSize == 3 );
        if ( m_iSize == 3 )
        {
                for (int iRow = 0; iRow < m_iSize; iRow++) 
            rkV[iRow] = m_kMat[iRow][i];
        }
        else
        {
            rkV = Ogre::Vector3::ZERO;
    }
}

void EigenSolver::GaussPointsFit(unsigned int iQuantity,const Ogre::Vector3* akPoint,Vector3 &rkCenter,Vector3 akAxis[3],Real afExtent[3])
{
    // compute mean of points
    rkCenter = akPoint[0];
    unsigned int i;
    for (i = 1; i < iQuantity; i++)
        rkCenter += akPoint[i];
    const Ogre::Real fInvQuantity = ((Real)1.0)/iQuantity;
    rkCenter *= fInvQuantity;

    // compute covariances of points
   Ogre::Real fSumXX = (Real)0.0, fSumXY = (Real)0.0, fSumXZ = (Real)0.0;
   Ogre::Real fSumYY = (Real)0.0, fSumYZ = (Real)0.0, fSumZZ = (Real)0.0;
    for (i = 0; i < iQuantity; i++)
    {
        const Ogre::Vector3 kDiff (akPoint[i] - rkCenter);
        fSumXX += kDiff.x*kDiff.x;
        fSumXY += kDiff.x*kDiff.y;
        fSumXZ += kDiff.x*kDiff.z;
        fSumYY += kDiff.y*kDiff.y;
        fSumYZ += kDiff.y*kDiff.z;
        fSumZZ += kDiff.z*kDiff.z;
    }
    fSumXX *= fInvQuantity;
    fSumXY *= fInvQuantity;
    fSumXZ *= fInvQuantity;
    fSumYY *= fInvQuantity;
    fSumYZ *= fInvQuantity;
    fSumZZ *= fInvQuantity;

    // compute eigenvectors for covariance matrix
    EigenSolver kES(3);
    kES(0,0) = fSumXX;
    kES(0,1) = fSumXY;
    kES(0,2) = fSumXZ;
    kES(1,0) = fSumXY;
    kES(1,1) = fSumYY;
    kES(1,2) = fSumYZ;
    kES(2,0) = fSumXZ;
    kES(2,1) = fSumYZ;
    kES(2,2) = fSumZZ;
    kES.IncrSortEigenStuff3();

    for (i = 0; i < 3; i++)
    {
        afExtent[i] = kES.GetEigenvalue(i);
        kES.GetEigenvector(i,akAxis[i]);
    }
}

Real EigenSolver::GetEigenvalue (int i) const
{
    return m_afDiag[i];
}

void EigenSolver::IncrSortEigenStuff3 ()
{
    Tridiagonal3();
    QLAlgorithm();
    IncreasingSort();
    GuaranteeRotation();
}

void EigenSolver::IncreasingSort ()
{
    // sort eigenvalues in increasing order, e[0] <= ... <= e[iSize-1]
    for (int i0 = 0, i1; i0 <= m_iSize-2; i0++)
    {
        // locate minimum eigenvalue
        i1 = i0;
       Ogre::Real fMin = m_afDiag[i1];
        int i2;
        for (i2 = i0+1; i2 < m_iSize; i2++)
        {
            if ( m_afDiag[i2] < fMin )
            {
                i1 = i2;
                fMin = m_afDiag[i1];
            }
        }

        if ( i1 != i0 )
        {
            // swap eigenvalues
            m_afDiag[i1] = m_afDiag[i0];
            m_afDiag[i0] = fMin;

            // swap eigenvectors
            for (i2 = 0; i2 < m_iSize; i2++)
            {
               Ogre::Real fTmp = m_kMat[i2][i0];
                m_kMat[i2][i0] = m_kMat[i2][i1];
                m_kMat[i2][i1] = fTmp;
                m_bIsRotation = !m_bIsRotation;
            }
        }
    }
}