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// Geometric Tools, LLC
// Copyright (c) 1998-2014
// Distributed under the Boost Software License, Version 1.0.
// http://www.boost.org/LICENSE_1_0.txt
// http://www.geometrictools.com/License/Boost/LICENSE_1_0.txt
//
// File Version: 5.0.1 (2010/10/01)
#include "Wm5MathematicsPCH.h"
#include "Wm5ApprGaussPointsFit3.h"
#include "Wm5EigenDecomposition.h"
namespace Wm5
{
//----------------------------------------------------------------------------
template <typename Real>
Box3<Real> GaussPointsFit3 (int numPoints, const Vector3<Real>* points)
{
Box3<Real> box(Vector3<Real>::ZERO,Vector3<Real>::UNIT_X,
Vector3<Real>::UNIT_Y,Vector3<Real>::UNIT_Z,(Real)1.0,(Real)1.0,
(Real)1.0);
// Compute the mean of the points.
box.Center = points[0];
int i;
for (i = 1; i < numPoints; ++i)
{
box.Center += points[i];
}
Real invNumPoints = ((Real)1.0)/numPoints;
box.Center *= invNumPoints;
// Compute the covariance matrix of the points.
Real sumXX = (Real)0, sumXY = (Real)0, sumXZ = (Real)0;
Real sumYY = (Real)0, sumYZ = (Real)0, sumZZ = (Real)0;
for (i = 0; i < numPoints; ++i)
{
Vector3<Real> diff = points[i] - box.Center;
sumXX += diff[0]*diff[0];
sumXY += diff[0]*diff[1];
sumXZ += diff[0]*diff[2];
sumYY += diff[1]*diff[1];
sumYZ += diff[1]*diff[2];
sumZZ += diff[2]*diff[2];
}
sumXX *= invNumPoints;
sumXY *= invNumPoints;
sumXZ *= invNumPoints;
sumYY *= invNumPoints;
sumYZ *= invNumPoints;
sumZZ *= invNumPoints;
// Setup the eigensolver.
EigenDecomposition<Real> esystem(3);
esystem(0,0) = sumXX;
esystem(0,1) = sumXY;
esystem(0,2) = sumXZ;
esystem(1,0) = sumXY;
esystem(1,1) = sumYY;
esystem(1,2) = sumYZ;
esystem(2,0) = sumXZ;
esystem(2,1) = sumYZ;
esystem(2,2) = sumZZ;
esystem.Solve(true);
for (i = 0; i < 3; ++i)
{
box.Extent[i] = esystem.GetEigenvalue(i);
box.Axis[i] = esystem.GetEigenvector3(i);
}
return box;
}
//----------------------------------------------------------------------------
//----------------------------------------------------------------------------
// Explicit instantiation.
//----------------------------------------------------------------------------
template WM5_MATHEMATICS_ITEM
Box3<float> GaussPointsFit3<float> (int, const Vector3<float>*);
template WM5_MATHEMATICS_ITEM
Box3<double> GaussPointsFit3<double> (int, const Vector3<double>*);
//----------------------------------------------------------------------------
}
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