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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 "Wm5ApprGaussPointsFit2.h"
#include "Wm5EigenDecomposition.h"
namespace Wm5
{
//----------------------------------------------------------------------------
template <typename Real>
Box2<Real> GaussPointsFit2 (int numPoints, const Vector2<Real>* points)
{
Box2<Real> box(Vector2<Real>::ZERO, Vector2<Real>::UNIT_X,
Vector2<Real>::UNIT_Y, (Real)1, (Real)1);
// 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)/numPoints;
box.Center *= invNumPoints;
// Compute the covariance matrix of the points.
Real sumXX = (Real)0, sumXY = (Real)0, sumYY = (Real)0;
for (i = 0; i < numPoints; ++i)
{
Vector2<Real> diff = points[i] - box.Center;
sumXX += diff[0]*diff[0];
sumXY += diff[0]*diff[1];
sumYY += diff[1]*diff[1];
}
sumXX *= invNumPoints;
sumXY *= invNumPoints;
sumYY *= invNumPoints;
// Setup the eigensolver.
EigenDecomposition<Real> esystem(2);
esystem(0,0) = sumXX;
esystem(0,1) = sumXY;
esystem(1,0) = sumXY;
esystem(1,1) = sumYY;
esystem.Solve(true);
for (i = 0; i < 2; ++i)
{
box.Extent[i] = esystem.GetEigenvalue(i);
box.Axis[i] = esystem.GetEigenvector2(i);
}
return box;
}
//----------------------------------------------------------------------------
//----------------------------------------------------------------------------
// Explicit instantiation.
//----------------------------------------------------------------------------
template WM5_MATHEMATICS_ITEM
Box2<float> GaussPointsFit2<float> (int, const Vector2<float>*);
template WM5_MATHEMATICS_ITEM
Box2<double> GaussPointsFit2<double> (int, const Vector2<double>*);
//----------------------------------------------------------------------------
}
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