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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 "Wm5ApprCylinderFit3.h"
#include "Wm5ApprLineFit3.h"
#include "Wm5PolynomialRoots.h"
namespace Wm5
{
//----------------------------------------------------------------------------
template <typename Real>
CylinderFit3<Real>::CylinderFit3 (int numPoints, const Vector3<Real>* points,
Vector3<Real>& center, Vector3<Real>& axis, Real& radius, Real& height,
bool inputsAreInitialGuess)
{
Real invRSqr = (Real)1;
if (!inputsAreInitialGuess)
{
// Find the least-squares line that fits the data and use it as an
// initial guess for the cylinder axis.
Line3<Real> line = OrthogonalLineFit3(numPoints, points);
center = line.Origin;
axis = line.Direction;
}
mError = Math<Real>::MAX_REAL;
const int iMax = 8;
int i;
for (i = 0; i < iMax; ++i)
{
mError = UpdateInvRSqr(numPoints, points, center, axis, invRSqr);
mError = UpdateDirection(numPoints, points, center, axis, invRSqr);
mError = UpdateCenter(numPoints, points, center, axis, invRSqr);
}
// Compute the radius.
radius = Math<Real>::InvSqrt(invRSqr);
// Project points onto fitted axis to determine extent of cylinder along
// the axis.
Real tMin = axis.Dot(points[0] - center);
Real tMax = tMin;
for (i = 1; i < numPoints; ++i)
{
Real t = axis.Dot(points[i] - center);
if (t < tMin)
{
tMin = t;
}
else if (t > tMax)
{
tMax = t;
}
}
// Compute the height. Adjust the center to point that projects to
// midpoint of extent.
height = tMax - tMin;
center += (((Real)0.5)*(tMin + tMax))*axis;
}
//----------------------------------------------------------------------------
template <typename Real>
CylinderFit3<Real>::operator Real ()
{
return mError;
}
//----------------------------------------------------------------------------
template <typename Real>
Real CylinderFit3<Real>::UpdateInvRSqr (int numPoints,
const Vector3<Real>* points, const Vector3<Real>& center,
const Vector3<Real>& axis, Real& invRSqr)
{
Real aSum = (Real)0, aaSum = (Real)0;
for (int i = 0; i < numPoints; ++i)
{
Vector3<Real> delta = points[i] - center;
Vector3<Real> deltaCrossAxis = delta.Cross(axis);
Real len2 = deltaCrossAxis.SquaredLength();
aSum += len2;
aaSum += len2*len2;
}
invRSqr = aSum/aaSum;
Real min = (Real)1 - invRSqr*aSum/(Real)numPoints;
return min;
}
//----------------------------------------------------------------------------
template <typename Real>
Real CylinderFit3<Real>::UpdateDirection (int numPoints,
const Vector3<Real>* points, const Vector3<Real>& center,
Vector3<Real>& axis, Real& invRSqr)
{
Real invNumPoints = ((Real)1)/(Real)numPoints;
int i;
Vector3<Real> delta, deltaCrossAxis, deltaCrossVDir;
Real a, b, c;
// Compute the direction of steepest descent.
Vector3<Real> vDir = Vector3<Real>::ZERO;
Real aMean = (Real)0, aaMean = (Real)0;
for (i = 0; i < numPoints; ++i)
{
delta = points[i] - center;
deltaCrossAxis = delta.Cross(axis);
a = invRSqr*deltaCrossAxis.SquaredLength() - (Real)1;
aMean += a;
aaMean += a*a;
vDir.X() += a*(axis.X()*(delta.Y()*delta.Y() +
delta.Z()*delta.Z()) - delta.X()*(axis.Y()*delta.Y() +
axis.Z()*delta.Z()));
vDir.Y() += a*(axis.Y()*(delta.X()*delta.X() +
delta.Z()*delta.Z()) - delta.Y()*(axis.X()*delta.X() +
axis.Z()*delta.Z()));
vDir.Z() += a*(axis.Z()*(delta.X()*delta.X() +
delta.Y()*delta.Y()) - delta.Z()*(axis.X()*delta.X() +
axis.Y()*delta.Y()));
}
aMean *= invNumPoints;
aaMean *= invNumPoints;
if (vDir.Normalize() < Math<Real>::ZERO_TOLERANCE)
{
return aaMean;
}
// Compute the 4th-degree polynomial for the line of steepest descent.
Real abMean = (Real)0, acMean = (Real)0;
Real bbMean = (Real)0, bcMean = (Real)0, ccMean = (Real)0;
for (i = 0; i < numPoints; ++i)
{
delta = points[i] - center;
deltaCrossAxis = delta.Cross(axis);
deltaCrossVDir = delta.Cross(vDir);
a = invRSqr*deltaCrossAxis.SquaredLength() - (Real)1;
b = invRSqr*(deltaCrossAxis.Dot(deltaCrossVDir));
c = invRSqr*deltaCrossVDir.SquaredLength();
abMean += a*b;
acMean += a*c;
bbMean += b*b;
bcMean += b*c;
ccMean += c*c;
}
abMean *= invNumPoints;
acMean *= invNumPoints;
bbMean *= invNumPoints;
bcMean *= invNumPoints;
ccMean *= invNumPoints;
Polynomial1<Real> poly(4);
poly[0] = aaMean;
poly[1] = -((Real)4)*abMean;
poly[2] = ((Real)2)*acMean + ((Real)4)*bbMean;
poly[3] = -((Real)4)*bcMean;
poly[4] = ccMean;
Polynomial1<Real> derPoly = poly.GetDerivative();
PolynomialRoots<Real> polyRoots(Math<Real>::ZERO_TOLERANCE);
polyRoots.FindA(derPoly[0], derPoly[1], derPoly[2], derPoly[3]);
int count = polyRoots.GetCount();
const Real* roots = polyRoots.GetRoots();
Real pMin = poly((Real)0);
int iMin = -1;
for (i = 0; i < count; ++i)
{
Real value = poly(roots[i]);
if (value < pMin)
{
pMin = value;
iMin = i;
}
}
if (iMin >= 0)
{
axis -= roots[iMin]*vDir;
Real length = axis.Normalize();
invRSqr *= length*length;
}
return pMin;
}
//----------------------------------------------------------------------------
template <typename Real>
Real CylinderFit3<Real>::UpdateCenter (int numPoints,
const Vector3<Real>* points, Vector3<Real>& center,
const Vector3<Real>& axis, const Real& invRSqr)
{
Real invNumPoints = ((Real)1)/(Real)numPoints;
int i;
Vector3<Real> delta, deltaCrossAxis, cDirCrossAxis;
Real a, b, c;
// Compute the direction of steepest descent.
Vector3<Real> cDir = Vector3<Real>::ZERO;
Real aMean = (Real)0, aaMean = (Real)0;
for (i = 0; i < numPoints; ++i)
{
delta = points[i] - center;
deltaCrossAxis = delta.Cross(axis);
a = invRSqr*deltaCrossAxis.SquaredLength() - (Real)1;
aMean += a;
aaMean += a*a;
cDir += a*(delta - axis.Dot(delta)*axis); // |axis|=1 assumed
}
aMean *= invNumPoints;
aaMean *= invNumPoints;
if (cDir.Normalize() < Math<Real>::ZERO_TOLERANCE)
{
return aaMean;
}
// Compute the 4th-degree polynomial for the line of steepest descent.
cDirCrossAxis = cDir.Cross(axis);
c = cDirCrossAxis.SquaredLength()*invNumPoints*invRSqr;
Real bMean = (Real)0, abMean = (Real)0, bbMean = (Real)0;
for (i = 0; i < numPoints; ++i)
{
delta = points[i] - center;
deltaCrossAxis = delta.Cross(axis);
a = invRSqr*deltaCrossAxis.SquaredLength() - (Real)1;
b = invRSqr*(deltaCrossAxis.Dot(cDirCrossAxis));
bMean += b;
abMean += a*b;
bbMean += b*b;
}
bMean *= invNumPoints;
abMean *= invNumPoints;
bbMean *= invNumPoints;
Polynomial1<Real> poly(4);
poly[0] = aaMean;
poly[1] = ((Real)4)*abMean;
poly[2] = ((Real)2)*c*aMean + ((Real)4)*bbMean;
poly[3] = ((Real)4)*c*bMean;
poly[4] = c*c;
Polynomial1<Real> derPoly = poly.GetDerivative();
PolynomialRoots<Real> polyRoots(Math<Real>::ZERO_TOLERANCE);
polyRoots.FindA(derPoly[0], derPoly[1], derPoly[2], derPoly[3]);
int count = polyRoots.GetCount();
const Real* roots = polyRoots.GetRoots();
Real pMin = poly((Real)0);
int iMin = -1;
for (i = 0; i < count; ++i)
{
Real value = poly(roots[i]);
if (value < pMin)
{
pMin = value;
iMin = i;
}
}
if (iMin >= 0)
{
center -= roots[iMin]*cDir;
}
return pMin;
}
//----------------------------------------------------------------------------
//----------------------------------------------------------------------------
// Explicit instantiation.
//----------------------------------------------------------------------------
template WM5_MATHEMATICS_ITEM
class CylinderFit3<float>;
template WM5_MATHEMATICS_ITEM
class CylinderFit3<double>;
//----------------------------------------------------------------------------
}
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