vcglib/vcg/space/fitting3.h

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/****************************************************************************
* VCGLib o o *
* Visual and Computer Graphics Library o o *
* _ O _ *
* Copyright(C) 2004 \/)\/ *
* Visual Computing Lab /\/| *
* ISTI - Italian National Research Council | *
* \ *
* All rights reserved. *
* *
* This program is free software; you can redistribute it and/or modify *
* it under the terms of the GNU General Public License as published by *
* the Free Software Foundation; either version 2 of the License, or *
* (at your option) any later version. *
* *
* This program is distributed in the hope that it will be useful, *
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
* GNU General Public License (http://www.gnu.org/licenses/gpl.txt) *
* for more details. *
* *
****************************************************************************/
/****************************************************************************
History
$Log: not supported by cvs2svn $
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Revision 1.2 2005/10/13 14:59:57 ganovelli
versione con svd
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Revision 1.1 2005/03/14 17:04:24 ganovelli
created
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****************************************************************************/
#ifndef __VCGLIB_FITTING3
#define __VCGLIB_FITTING3
#include <vector>
#include <vcg/space/plane3.h>
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#include <vcg/math/matrix44.h>
#include <vcg/math/matrix33.h>
#include <vcg/math/lin_algebra.h>
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namespace vcg {
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template <class S>
Point3<S> PlaneFittingPoints(const std::vector< Point3<S> > & samples, Plane3<S> & p, Point4<S> & eval, Matrix44<S> & evec)
{
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Matrix44<S> m;m.SetZero();
typename std::vector< Point3<S> >::const_iterator it;
Point3<S> c; c.SetZero();
for(it = samples.begin(); it != samples.end(); ++it)
{
c += *it;
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}
c /= samples.size();
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for(it = samples.begin(); it != samples.end(); ++it)
{
Point3<S> p = (*it) - c;
for(int j = 0 ; j < 3;++j)
*(Point3<S>*)&m[j][0] += p * p[j];
}
m[0][3] = m[1][3] = m[2][3] = S(0);
m[3][3] = S(1);
m[3][0] = m[3][1] = m[3][2] = S(0);
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int n;
Point3<S> d;
Jacobi(m, eval, evec, n);
//Sort eigenvalues (tarinisort)
Point4<S> e;
e[0] = S(fabs(eval[0]));
e[1] = S(fabs(eval[1]));
e[2] = S(fabs(eval[2]));
int maxi, mini, medi;
if (e[1] > e[0]) { maxi = 1; mini = 0; } else { maxi = 0; mini = 1;}
if (e[maxi] < e[2]) { maxi = 2; } else if (e[mini] > e[2]) { mini = 2; };
medi = 3 - maxi -mini;
d[0] = evec[0][mini];
d[1] = evec[1][mini];
d[2] = evec[2][mini];
const S norm = d.Norm();
p.SetOffset(c.dot(d)/norm);
p.SetDirection(d/norm);
return Point3<S>(e[mini], e[medi], e[maxi]);
}
template <class S>
Point3<S> PlaneFittingPoints(const std::vector< Point3<S> > & samples, Plane3<S> & p)
{
Point4<S> eval;
Matrix44<S> evec;
return PlaneFittingPoints(samples, p, eval, evec);
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}
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template<class S>
inline double FIT_VExp( const Point3<S> & x, const int i )
{
assert(i>=0);
assert(i<4);
if(i==0) return 1;
else return x[i-1];
}
/** Fitting di piani: trova il piano che meglio approssima
l'insieme di punti dato
*/
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template<class S>
bool PlaneFittingPointsOld( std::vector< Point3<S> > & samples, Plane3<S> & p )
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{
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Point3<S> d;
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const int N = 4;
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S P[N][N]; // A = s' . s
S U[N][N];
int i,j,k,n;
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n = (int)samples.size();
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if(n<3)
return false;
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//printf("\n p_prima: %f %f %f %f \n",p.Offset(),p.Direction()[0],p.Direction()[1],p.Direction()[2]);
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for(i=0;i<N;++i)
{
for(j=i;j<N;++j)
{
P[i][j] = 0;
for(k=0;k<n;++k)
P[i][j] += FIT_VExp(samples[k],i) * FIT_VExp(samples[k],j);
}
for(j=0;j<i;++j)
P[i][j] = P[j][i];
}
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//printf("D \n");
//for(i=0;i<N;++i){
// printf("\n");
// for(j=0;j<N;++j)
// printf("%2.3f\t",P[i][j]);
//}
//
Matrix44<S> m;
for(i=0;i<N;++i)
for(j=0;j<N;++j)
m[i][j]=P[i][j];
// Point4<S> s;s.SetZero();
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//
// s.Normalize();
// printf("\n RES %f %f %f %f \n",s[0],s[1],s[2],s[3]);
//printf("\n GJ \n");
// for(i=0;i<N;++i){
// printf("\n");
// for(j=0;j<N;++j)
// printf("%2.3f\t",m[i][j]);
// }
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for(i=0;i<N;++i)
{
U[i][i] = 1.0;
for(j=0;j<i;++j)
U[i][j] = 0.0;
for(j=i+1;j<N;++j)
{
if(P[i][i]==0.0)
return false;
U[i][j] = P[i][j]/P[i][i];
for(k=j;k<N;++k)
P[j][k] -= U[i][j]*P[i][k];
}
}
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//printf("\n U \n");
//for(i=0;i<N;++i){
// printf("\n");
// for(j=0;j<N;++j)
// printf("%2.3f\t",U[i][j]);
//}
S norm = Point3<S>(U[1][2]*U[2][3]-U[1][3],-U[2][3],1).Norm();
p.SetDirection(Point3<S>(U[1][2]*U[2][3]-U[1][3],-U[2][3],1));
p.SetOffset(-(U[0][2]*U[2][3]-U[0][3]+U[0][1]*U[1][3]-U[0][1]*U[1][2]*U[2][3])/norm);
//printf("\n p: %f %f %f %f \n",p.Offset(),p.Direction()[0],p.Direction()[1],p.Direction()[2]);
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return true;
}
} // end namespace
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#endif