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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 "Wm5ApprPlaneFit3.h"
#include "Wm5EigenDecomposition.h"
#include "Wm5LinearSystem.h"
namespace Wm5
{
//----------------------------------------------------------------------------
template <typename Real>
bool HeightPlaneFit3 (int numPoints, const Vector3<Real>* points, Real& a,
Real& b, Real& c)
{
// 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 sumX = (Real)0, sumY = (Real)0, sumZ = (Real)0.0;
Real sumXX = (Real)0, sumXY = (Real)0, sumXZ = (Real)0;
Real sumYY = (Real)0, sumYZ = (Real)0;
int i;
for (i = 0; i < numPoints; ++i)
{
sumX += points[i][0];
sumY += points[i][1];
sumZ += points[i][2];
sumXX += points[i][0]*points[i][0];
sumXY += points[i][0]*points[i][1];
sumXZ += points[i][0]*points[i][2];
sumYY += points[i][1]*points[i][1];
sumYZ += points[i][1]*points[i][2];
}
Real A[3][3] =
{
{sumXX, sumXY, sumX},
{sumXY, sumYY, sumY},
{sumX, sumY, (Real)numPoints}
};
Real B[3] =
{
sumXZ,
sumYZ,
sumZ
};
Real X[3];
bool nonsingular = LinearSystem<Real>().Solve3(A, B, X);
if (nonsingular)
{
a = X[0];
b = X[1];
c = X[2];
}
else
{
a = Math<Real>::MAX_REAL;
b = Math<Real>::MAX_REAL;
c = Math<Real>::MAX_REAL;
}
return nonsingular;
}
//----------------------------------------------------------------------------
template <typename Real>
Plane3<Real> OrthogonalPlaneFit3 (int numPoints, const Vector3<Real>* points)
{
// Compute the mean of the points.
Vector3<Real> origin = Vector3<Real>::ZERO;
int i;
for (i = 0; i < numPoints; i++)
{
origin += points[i];
}
Real invNumPoints = ((Real)1)/numPoints;
origin *= invNumPoints;
// compute sums of products
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] - origin;
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;
// Compute eigenstuff, smallest eigenvalue is in last position.
esystem.Solve(false);
// Get plane normal.
Vector3<Real> normal = esystem.GetEigenvector3(2);
// The minimum energy.
return Plane3<Real>(normal, origin);
}
//----------------------------------------------------------------------------
//----------------------------------------------------------------------------
// Explicit instantiation.
//----------------------------------------------------------------------------
template WM5_MATHEMATICS_ITEM
bool HeightPlaneFit3<float> (int, const Vector3<float>*, float&, float&,
float&);
template WM5_MATHEMATICS_ITEM
Plane3<float> OrthogonalPlaneFit3<float> (int, const Vector3<float>*);
template WM5_MATHEMATICS_ITEM
bool HeightPlaneFit3<double> (int, const Vector3<double>*, double&, double&,
double&);
template WM5_MATHEMATICS_ITEM
Plane3<double> OrthogonalPlaneFit3<double> (int, const Vector3<double>*);
//----------------------------------------------------------------------------
}
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