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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 "Wm5ApprLineFit2.h"
#include "Wm5EigenDecomposition.h"
#include "Wm5LinearSystem.h"
namespace Wm5
{
//----------------------------------------------------------------------------
template <typename Real>
bool HeightLineFit2 (int numPoints, const Vector2<Real>* points, Real& a,
Real& b)
{
// You need at least two points to determine the line. Even so, if
// the points are on a vertical line, there is no least-squares fit in
// the 'height' sense. This will be trapped by the determinant of the
// coefficient matrix being (nearly) zero.
// Compute sums for linear system.
Real sumX = (Real)0, sumY = (Real)0;
Real sumXX = (Real)0, sumXY = (Real)0;
int i;
for (i = 0; i < numPoints; ++i)
{
sumX += points[i].X();
sumY += points[i].Y();
sumXX += points[i].X()*points[i].X();
sumXY += points[i].X()*points[i].Y();
}
Real A[2][2] =
{
{sumXX, sumX},
{sumX, (Real)numPoints}
};
Real B[2] =
{
sumXY,
sumY
};
Real X[2];
bool nonsingular = LinearSystem<Real>().Solve2(A, B, X);
if (nonsingular)
{
a = X[0];
b = X[1];
}
else
{
a = Math<Real>::MAX_REAL;
b = Math<Real>::MAX_REAL;
}
return nonsingular;
}
//----------------------------------------------------------------------------
template <typename Real>
Line2<Real> OrthogonalLineFit2 (int numPoints, const Vector2<Real>* points)
{
Line2<Real> line(Vector2<Real>::ZERO, Vector2<Real>::ZERO);
// Compute the mean of the points.
line.Origin = points[0];
int i;
for (i = 1; i < numPoints; ++i)
{
line.Origin += points[i];
}
Real invNumPoints = ((Real)1)/numPoints;
line.Origin *= 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] - line.Origin;
sumXX += diff[0]*diff[0];
sumXY += diff[0]*diff[1];
sumYY += diff[1]*diff[1];
}
sumXX *= invNumPoints;
sumXY *= invNumPoints;
sumYY *= invNumPoints;
// Set up the eigensolver.
EigenDecomposition<Real> esystem(2);
esystem(0,0) = sumYY;
esystem(0,1) = -sumXY;
esystem(1,0) = -sumXY;
esystem(1,1) = sumXX;
// Compute eigenstuff, smallest eigenvalue is in last position.
esystem.Solve(false);
// Unit-length direction for best-fit line.
line.Direction = esystem.GetEigenvector2(1);
return line;
}
//----------------------------------------------------------------------------
//----------------------------------------------------------------------------
// Explicit instantiation.
//----------------------------------------------------------------------------
template WM5_MATHEMATICS_ITEM
bool HeightLineFit2<float> (int, const Vector2<float>*, float&, float&);
template WM5_MATHEMATICS_ITEM
Line2<float> OrthogonalLineFit2<float> (int, const Vector2<float>*);
template WM5_MATHEMATICS_ITEM
bool HeightLineFit2<double> (int, const Vector2<double>*, double&, double&);
template WM5_MATHEMATICS_ITEM
Line2<double> OrthogonalLineFit2<double> (int, const Vector2<double>*);
//----------------------------------------------------------------------------
}
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