ConchoidFit.cpp

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// onchoidFit.cpp: implementation of the ConchoidFit class.
//
//////////////////////////////////////////////////////////////////////
#include "stdafx.h"
#include "ConchoidFit.h"
#include "SphereFit.h"
#include <FECore/tools.h>
#include <stdio.h>
using namespace std;

//////////////////////////////////////////////////////////////////////
// Construction/Destruction
//////////////////////////////////////////////////////////////////////

ConchoidFit::ConchoidFit()
{

}

ConchoidFit::~ConchoidFit()
{

}

ConchoidFit* pfitter;
double func(double l)
{
	ConchoidFit& fit = *pfitter;
	return fit.ObjFunc(l);
}

vec3d ConchoidFit::GetOrientation(const vector<vec3d>& y)
{
	vec3d o;
	int N = (int)y.size();
	for (int i=0; i<N; ++i)
	{
		vec3d r = y[i] - m_rc;
		o += r;
	}
	o.Normalize();

	return o;
}

void ConchoidFit::FindMinimum()
{
	// bracket the minimum
	pfitter = this;
	double la = m_a;
	double lb = m_b;
	double lc = 0;
	double fa, fb, fc;
	mnbrak(&la, &lb, &lc, &fa, &fb, &fc, func);

	// find the minimum using Brent's method
	double lmin;
	double Fmin = brent(la, lb, lc, func, 0.01, &lmin);

	// we have found the minimum, so set the new center
	if (lmin != 0)
	{
		vec3d p(lmin,0,0);
		m_q.RotateVector(p);

		m_rc = m_rc + p;
	}
	printf("Center of conchoid: (%lg, %lg, %lg)\n", m_rc.x, m_rc.y, m_rc.z);
}

// complete fit algorithm
void ConchoidFit::Fit(const vector<vec3d>& y, int maxiter)
{
	m_y = y;

	// fit a sphere to the data
	SphereFit s;
	s.Fit(y);

	// the center of the sphere is our starting center for the conchoid
	m_rc = s.m_rc;

	// the orientation is the average orientation to this center
	vec3d o = GetOrientation(y);

	// set up the quaternions
	m_q = quatd(vec3d(1,0,0), o);
	m_qi = m_q.Inverse();

	// find the minimum
	m_a = -s.m_R*0.5;
	m_b = 0;
	FindMinimum();

	// determine the final conchoid parameters
	Regression(y, m_rc, m_qi, m_a, m_b);
}

void ConchoidFit::Apply(vector<vec3d>& y)
{
	int N = (int) y.size();
	for (int i=0; i<N; ++i)
	{
		vec3d r = y[i];
		Transform(m_rc, m_q, r);
		double l = m_a + m_b*r.x;

		vec3d q = y[i] - m_rc;
		q.Normalize();
		y[i] = m_rc + q*l;
	}
}

void ConchoidFit::Regression(const vector<vec3d>& y, vec3d& rc, quatd& q, double& a, double& b)
{
	int i;
	double x, r;
	quatd qi = m_q.Inverse();

	double sx = 0, sy = 0;
	double sx2 = 0, sxy = 0;

	int m = 0;

	int N = (int) y.size();
	for (i=0; i<N; ++i)
	{
		// calculate the polar coordinates of the point
		vec3d p = Transform(rc, q, y[i]);
		r = p.Length();	// = r
		p.Normalize();
		x = p.x;		// = cos(theta)

		// do the summations
		sx += x;
		sy += r;
		sx2 += x*x;
		sxy += x*r;
		++m;
	}

	// calculate the least square solution
	b = (m*sxy - sx*sy) / (m*sx2 - sx*sx);
	a = (sy - b*sx)/m;
}

double ConchoidFit::ObjFunc(double l)
{
	// calculate a new center
	vec3d rc;
	if (l != 0)
	{
		vec3d p(l,0,0);
		m_q.RotateVector(p);

		rc = m_rc + p;
	}
	else rc = m_rc;

	double a, b;
	Regression(m_y, rc, m_qi, a, b);

	// calculate the objective function
	double F = 0, df;
	int m = 0;
	double x, y;
	int N = (int) m_y.size();
	for (int i=0; i<N; ++i)
	{
		vec3d p = Transform(rc, m_qi, m_y[i]);
		y = p.Length();
		p.Normalize();
		x = p.x;

		df = y - a - b*x;

		F += df*df;
		++m;
	}

	return F / m;
}