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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 "Wm5ApprQuadraticFit3.h"
#include "Wm5EigenDecomposition.h"
namespace Wm5
{
//----------------------------------------------------------------------------
template <typename Real>
Real QuadraticFit3 (int numPoints, const Vector3<Real>* points,
Real coeff[10])
{
EigenDecomposition<Real> esystem(10);
int row, col;
for (row = 0; row < 10; ++row)
{
for (col = 0; col < 10; ++col)
{
esystem(row,col) = (Real)0;
}
}
for (int i = 0; i < numPoints; ++i)
{
Real x = points[i].X();
Real y = points[i].Y();
Real z = points[i].Z();
Real x2 = x*x;
Real y2 = y*y;
Real z2 = z*z;
Real xy = x*y;
Real xz = x*z;
Real yz = y*z;
Real x3 = x*x2;
Real xy2 = x*y2;
Real xz2 = x*z2;
Real x2y = x*xy;
Real x2z = x*xz;
Real xyz = x*y*z;
Real y3 = y*y2;
Real yz2 = y*z2;
Real y2z = y*yz;
Real z3 = z*z2;
Real fX4 = x*x3;
Real x2y2 = x*xy2;
Real x2z2 = x*xz2;
Real x3y = x*x2y;
Real x3z = x*x2z;
Real x2yz = x*xyz;
Real y4 = y*y3;
Real y2z2 = y*yz2;
Real xy3 = x*y3;
Real xy2z = x*y2z;
Real y3z = y*y2z;
Real fZ4 = z*z3;
Real xyz2 = x*yz2;
Real xz3 = x*z3;
Real yz3 = y*z3;
esystem(0,1) += x;
esystem(0,2) += y;
esystem(0,3) += z;
esystem(0,4) += x2;
esystem(0,5) += y2;
esystem(0,6) += z2;
esystem(0,7) += xy;
esystem(0,8) += xz;
esystem(0,9) += yz;
esystem(1,4) += x3;
esystem(1,5) += xy2;
esystem(1,6) += xz2;
esystem(1,7) += x2y;
esystem(1,8) += x2z;
esystem(1,9) += xyz;
esystem(2,5) += y3;
esystem(2,6) += yz2;
esystem(2,9) += y2z;
esystem(3,6) += z3;
esystem(4,4) += fX4;
esystem(4,5) += x2y2;
esystem(4,6) += x2z2;
esystem(4,7) += x3y;
esystem(4,8) += x3z;
esystem(4,9) += x2yz;
esystem(5,5) += y4;
esystem(5,6) += y2z2;
esystem(5,7) += xy3;
esystem(5,8) += xy2z;
esystem(5,9) += y3z;
esystem(6,6) += fZ4;
esystem(6,7) += xyz2;
esystem(6,8) += xz3;
esystem(6,9) += yz3;
esystem(9,9) += y2z2;
}
esystem(0,0) = (Real)numPoints;
esystem(1,1) = esystem(0,4);
esystem(1,2) = esystem(0,7);
esystem(1,3) = esystem(0,8);
esystem(2,2) = esystem(0,5);
esystem(2,3) = esystem(0,9);
esystem(2,4) = esystem(1,7);
esystem(2,7) = esystem(1,5);
esystem(2,8) = esystem(1,9);
esystem(3,3) = esystem(0,6);
esystem(3,4) = esystem(1,8);
esystem(3,5) = esystem(2,9);
esystem(3,7) = esystem(1,9);
esystem(3,8) = esystem(1,6);
esystem(3,9) = esystem(2,6);
esystem(7,7) = esystem(4,5);
esystem(7,8) = esystem(4,9);
esystem(7,9) = esystem(5,8);
esystem(8,8) = esystem(4,6);
esystem(8,9) = esystem(6,7);
esystem(9,9) = esystem(5,6);
for (row = 0; row < 10; ++row)
{
for (col = 0; col < row; ++col)
{
esystem(row,col) = esystem(col,row);
}
}
Real invNumPoints = ((Real)1)/(Real)numPoints;
for (row = 0; row < 10; ++row)
{
for (col = 0; col < 10; ++col)
{
esystem(row,col) *= invNumPoints;
}
}
esystem.Solve(true);
GVector<Real> evector = esystem.GetEigenvector(0);
memcpy(coeff, (Real*)evector, 10*sizeof(Real));
// For an exact fit, numeric round-off errors might make the minimum
// eigenvalue just slightly negative. Return the absolute value since
// the application might rely on the return value being nonnegative.
return Math<Real>::FAbs(esystem.GetEigenvalue(0));
}
//----------------------------------------------------------------------------
template <typename Real>
Real QuadraticSphereFit3 (int numPoints, const Vector3<Real>* points,
Vector3<Real>& center, Real& radius)
{
EigenDecomposition<Real> esystem(5);
int row, col;
for (row = 0; row < 5; ++row)
{
for (col = 0; col < 5; ++col)
{
esystem(row,col) = (Real)0;
}
}
for (int i = 0; i < numPoints; ++i)
{
Real x = points[i].X();
Real y = points[i].Y();
Real z = points[i].Z();
Real x2 = x*x;
Real y2 = y*y;
Real z2 = z*z;
Real xy = x*y;
Real xz = x*z;
Real yz = y*z;
Real r2 = x2+y2+z2;
Real xr2 = x*r2;
Real yr2 = y*r2;
Real zr2 = z*r2;
Real r4 = r2*r2;
esystem(0,1) += x;
esystem(0,2) += y;
esystem(0,3) += z;
esystem(0,4) += r2;
esystem(1,1) += x2;
esystem(1,2) += xy;
esystem(1,3) += xz;
esystem(1,4) += xr2;
esystem(2,2) += y2;
esystem(2,3) += yz;
esystem(2,4) += yr2;
esystem(3,3) += z2;
esystem(3,4) += zr2;
esystem(4,4) += r4;
}
esystem(0,0) = (Real)numPoints;
for (row = 0; row < 5; ++row)
{
for (col = 0; col < row; ++col)
{
esystem(row,col) = esystem(col,row);
}
}
Real invNumPoints = ((Real)1)/(Real)numPoints;
for (row = 0; row < 5; ++row)
{
for (col = 0; col < 5; ++col)
{
esystem(row,col) *= invNumPoints;
}
}
esystem.Solve(true);
GVector<Real> evector = esystem.GetEigenvector(0);
Real inv = ((Real)1)/evector[4]; // beware zero divide
Real coeff[4];
for (row = 0; row < 4; ++row)
{
coeff[row] = inv*evector[row];
}
center[0] = -((Real)0.5)*coeff[1];
center[1] = -((Real)0.5)*coeff[2];
center[2] = -((Real)0.5)*coeff[3];
radius = Math<Real>::Sqrt(Math<Real>::FAbs(center[0]*center[0] +
center[1]*center[1] + center[2]*center[2] - coeff[0]));
// For an exact fit, numeric round-off errors might make the minimum
// eigenvalue just slightly negative. Return the absolute value since
// the application might rely on the return value being nonnegative.
return Math<Real>::FAbs(esystem.GetEigenvalue(0));
}
//----------------------------------------------------------------------------
//----------------------------------------------------------------------------
// Explicit instantiation.
//----------------------------------------------------------------------------
template WM5_MATHEMATICS_ITEM
float QuadraticFit3<float> (int, const Vector3<float>*, float[10]);
template WM5_MATHEMATICS_ITEM
float QuadraticSphereFit3<float> (int, const Vector3<float>*,
Vector3<float>&, float&);
template WM5_MATHEMATICS_ITEM
double QuadraticFit3<double> (int, const Vector3<double>*, double[10]);
template WM5_MATHEMATICS_ITEM
double QuadraticSphereFit3<double> (int, const Vector3<double>*,
Vector3<double>&, double&);
//----------------------------------------------------------------------------
}
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