Wm4ApprPlaneFit3.cpp

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// 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: 4.0.0 (2006/06/28)

#include "Wm4FoundationPCH.h"
#include "Wm4ApprPlaneFit3.h"
#include "Wm4Eigen.h"
#include "Wm4LinearSystem.h"

namespace Wm4
{
//----------------------------------------------------------------------------
template <class Real>
bool HeightPlaneFit3 (int iQuantity, const Vector3<Real>* akPoint, Real& rfA,
    Real& rfB, Real& rfC)
{
    // You need at least three points to determine the plane.  Even so, if
    // the points are on a vertical plane, there is no least-squares fit in
    // the 'height' sense.  This will be trapped by the determinant of the
    // coefficient matrix.

    // compute sums for linear system
    Real fSumX = (Real)0.0, fSumY = (Real)0.0, fSumZ = (Real)0.0;
    Real fSumXX = (Real)0.0, fSumXY = (Real)0.0, fSumXZ = (Real)0.0;
    Real fSumYY = (Real)0.0, fSumYZ = (Real)0.0;
    int i;
    for (i = 0; i < iQuantity; i++)
    {
        fSumX += akPoint[i].X();
        fSumY += akPoint[i].Y();
        fSumZ += akPoint[i].Z();
        fSumXX += akPoint[i].X()*akPoint[i].X();
        fSumXY += akPoint[i].X()*akPoint[i].Y();
        fSumXZ += akPoint[i].X()*akPoint[i].Z();
        fSumYY += akPoint[i].Y()*akPoint[i].Y();
        fSumYZ += akPoint[i].Y()*akPoint[i].Z();
    }

    Real aafA[3][3] =
    {
        {fSumXX, fSumXY, fSumX},
        {fSumXY, fSumYY, fSumY},
        {fSumX,  fSumY,  (Real)iQuantity}
    };

    Real afB[3] =
    {
        fSumXZ,
        fSumYZ,
        fSumZ
    };

    Real afX[3];

    bool bNonsingular = LinearSystem<Real>().Solve3(aafA,afB,afX);
    if (bNonsingular)
    {
        rfA = afX[0];
        rfB = afX[1];
        rfC = afX[2];
    }
    else
    {
        rfA = Math<Real>::MAX_REAL;
        rfB = Math<Real>::MAX_REAL;
        rfC = Math<Real>::MAX_REAL;
    }

    return bNonsingular;
}
//----------------------------------------------------------------------------
template <class Real>
Plane3<Real> OrthogonalPlaneFit3 (int iQuantity, const Vector3<Real>* akPoint)
{
    // compute the mean of the points
    Vector3<Real> kOrigin = Vector3<Real>::ZERO;
    int i;
    for (i = 0; i < iQuantity; i++)
    {
        kOrigin += akPoint[i];
    }
    Real fInvQuantity = ((Real)1.0)/iQuantity;
    kOrigin *= fInvQuantity;

    // compute sums of products
    Real fSumXX = (Real)0.0, fSumXY = (Real)0.0, fSumXZ = (Real)0.0;
    Real fSumYY = (Real)0.0, fSumYZ = (Real)0.0, fSumZZ = (Real)0.0;
    for (i = 0; i < iQuantity; i++) 
    {
        Vector3<Real> kDiff = akPoint[i] - kOrigin;
        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
    Eigen<Real> 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;

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

    // get plane normal
    Vector3<Real> kNormal;
    kES.GetEigenvector(2,kNormal);

    // the minimum energy
    return Plane3<Real>(kNormal,kOrigin);
}
//----------------------------------------------------------------------------

//----------------------------------------------------------------------------
// explicit instantiation
//----------------------------------------------------------------------------
template WM4_FOUNDATION_ITEM
bool HeightPlaneFit3<float> (int, const Vector3<float>*, float&, float&,
    float&);

template WM4_FOUNDATION_ITEM
Plane3<float> OrthogonalPlaneFit3<float> (int, const Vector3<float>*);

template WM4_FOUNDATION_ITEM
bool HeightPlaneFit3<double> (int, const Vector3<double>*, double&, double&,
    double&);

template WM4_FOUNDATION_ITEM
Plane3<double> OrthogonalPlaneFit3<double> (int, const Vector3<double>*);
//----------------------------------------------------------------------------
}