515 lines
14 KiB
C++
515 lines
14 KiB
C++
/****************************************************************************
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* VCGLib o o *
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* Visual and Computer Graphics Library o o *
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* _ O _ *
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* Copyright(C) 2004 \/)\/ *
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* Visual Computing Lab /\/| *
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* ISTI - Italian National Research Council | *
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* \ *
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* All rights reserved. *
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* *
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* This program is free software; you can redistribute it and/or modify *
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* it under the terms of the GNU General Public License as published by *
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* the Free Software Foundation; either version 2 of the License, or *
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* (at your option) any later version. *
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* *
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* This program is distributed in the hope that it will be useful, *
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* but WITHOUT ANY WARRANTY; without even the implied warranty of *
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
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* GNU General Public License (http://www.gnu.org/licenses/gpl.txt) *
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* for more details. *
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* *
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****************************************************************************/
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/****************************************************************************
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History
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$Log: point_matching.h,v $
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****************************************************************************/
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#ifndef _VCG_MATH_POINTMATCHING_H
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#define _VCG_MATH_POINTMATCHING_H
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#include <vcg/math/matrix33.h>
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#include <vcg/math/quaternion.h>
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#include <vcg/math/lin_algebra.h>
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namespace vcg
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{
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template<class ScalarType>
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class PointMatching
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{
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public:
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typedef Point3<ScalarType> Point3x;
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typedef Matrix33<ScalarType> Matrix33x;
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typedef Matrix44<ScalarType> Matrix44x;
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typedef Quaternion<ScalarType> Quaternionx;
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/*
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Compute a similarity matching (rigid + uniform scaling)
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simply create a temporary point set with the correct scaling factor
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*/
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static bool ComputeSimilarityMatchMatrix( Matrix44x &res,
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std::vector<Point3x> &Pfix, // vertici corrispondenti su fix (rossi)
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std::vector<Point3x> &Pmov) // normali scelti su mov (verdi)
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{
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Quaternionx qtmp;
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Point3x tr;
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std::vector<Point3x> Pnew(Pmov.size());
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ScalarType scalingFactor=0;
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for(size_t i=0;i<( Pmov.size()-1);++i)
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{
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scalingFactor += Distance(Pmov[i],Pmov[i+1])/ Distance(Pfix[i],Pfix[i+1]);
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#ifdef _DEBUG
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printf("Scaling Factor is %f",scalingFactor/(i+1));
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#endif
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}
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scalingFactor/=(Pmov.size()-1);
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for(size_t i=0;i<Pmov.size();++i)
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Pnew[i]=Pmov[i]/scalingFactor;
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bool ret=ComputeRigidMatchMatrix(res,Pfix,Pnew,qtmp,tr);
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if(!ret) return false;
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Matrix44x scaleM; scaleM.SetDiagonal(1.0/scalingFactor);
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res = res * scaleM;
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return true;
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}
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static bool ComputeRigidMatchMatrix( Matrix44x &res,
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std::vector<Point3x> &Pfix, // vertici corrispondenti su fix (rossi)
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std::vector<Point3x> &Pmov) // normali scelti su mov (verdi)
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{
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Quaternionx qtmp;
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Point3x tr;
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return ComputeRigidMatchMatrix(res,Pfix,Pmov,qtmp,tr);
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}
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/*
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Calcola la matrice di rototraslazione
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che porta i punti Pmov su Pfix
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Basata sul paper
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Besl, McKay
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A method for registration o f 3d Shapes
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IEEE TPAMI Vol 14, No 2 1992
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Esempio d'uso
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const int np=1000;
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std::vector<Point3x> pfix(np),pmov(np);
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Matrix44x Rot,Trn,RotRes;
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Rot.Rotate(30,Point3x(1,0,1));
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Trn.Translate(0,0,100);
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Rot=Trn*Rot;
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for(int i=0;i<np;++i){
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pfix[i]=Point3x(-150+rand()%1000,-150+rand()%1000,0);
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pmov[i]=Rot.Apply(pfix[i]);
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}
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ComputeRigidMatchMatrix(RotRes,pfix,pmov);
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RotRes.Invert();
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assert( RotRes==Rot);
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assert( RotRes.Apply(pmov[i]) == pfix[i] );
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*/
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static
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bool ComputeWeightedRigidMatchMatrix(Matrix44x &res,
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std::vector<Point3x> &Pfix,
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std::vector<Point3x> &Pmov,
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std::vector<ScalarType> weights,
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Quaternionx &q,
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Point3x &tr
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)
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{
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Matrix33x ccm;
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Point3x bfix,bmov; // baricenter of src e trg
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ccm.WeightedCrossCovariance(weights,Pmov,Pfix,bmov,bfix);
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Matrix33x cyc; // the cyclic components of the cross covariance matrix.
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cyc=ccm - ccm.transpose();
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Matrix44x QQ;
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QQ.SetZero();
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Point3x D(cyc[1][2],cyc[2][0],cyc[0][1]);
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Matrix33x RM;
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RM.SetZero();
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RM[0][0]=-ccm.Trace();
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RM[1][1]=-ccm.Trace();
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RM[2][2]=-ccm.Trace();
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RM += ccm + ccm.transpose();
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QQ[0][0] = ccm.Trace();
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QQ[0][1] = D[0]; QQ[0][2] = D[1]; QQ[0][3] = D[2];
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QQ[1][0] = D[0]; QQ[2][0] = D[1]; QQ[3][0] = D[2];
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int i,j;
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for(i=0;i<3;i++)
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for(j=0;j<3;j++)
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QQ[i+1][j+1]=RM[i][j];
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// printf(" Quaternion Matrix\n");
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// print(QQ);
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Point4d d;
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Matrix44x v;
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int nrot;
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Jacobi(QQ,d,v,nrot);
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// printf("Done %i iterations\n %f %f %f %f\n",nrot,d[0],d[1],d[2],d[3]);
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// print(v);
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// Now search the maximum eigenvalue
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double maxv=0;
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int maxind=-1;
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for(i=0;i<4;i++)
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if(maxv<fabs(d[i])) {
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q=Quaternionx(v[0][i],v[1][i],v[2][i],v[3][i]);
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maxind=i;
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maxv=d[i];
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}
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// The corresponding eigenvector define the searched rotation,
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Matrix44x Rot;
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q.ToMatrix(Rot);
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// the translation (last row) is simply the difference between the transformed src barycenter and the trg baricenter
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tr= (bfix - Rot *bmov);
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//res[3][0]=tr[0];res[3][1]=tr[1];res[3][2]=tr[2];
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Matrix44x Trn;
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Trn.SetTranslate(tr);
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res=Trn*Rot;
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return true;
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}
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static
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bool ComputeRigidMatchMatrix(Matrix44x &res,
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std::vector<Point3x> &Pfix,
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std::vector<Point3x> &Pmov,
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Quaternionx &q,
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Point3x &tr)
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{
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Matrix33x ccm;
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Point3x bfix,bmov; // baricenter of src e trg
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ccm.CrossCovariance(Pmov,Pfix,bmov,bfix);
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Matrix33x cyc; // the cyclic components of the cross covariance matrix.
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cyc=ccm-ccm.transpose();
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Matrix44x QQ;
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QQ.SetZero();
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Point3x D(cyc[1][2],cyc[2][0],cyc[0][1]);
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Matrix33x RM;
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RM.SetZero();
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RM[0][0]=-ccm.Trace();
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RM[1][1]=-ccm.Trace();
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RM[2][2]=-ccm.Trace();
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RM += ccm + ccm.transpose();
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QQ[0][0] = ccm.Trace();
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QQ[0][1] = D[0]; QQ[0][2] = D[1]; QQ[0][3] = D[2];
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QQ[1][0] = D[0]; QQ[2][0] = D[1]; QQ[3][0] = D[2];
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int i,j;
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for(i=0;i<3;i++)
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for(j=0;j<3;j++)
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QQ[i+1][j+1]=RM[i][j];
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// printf(" Quaternion Matrix\n");
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// print(QQ);
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Point4d d;
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Matrix44x v;
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int nrot;
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//QQ.Jacobi(d,v,nrot);
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Jacobi(QQ,d,v,nrot);
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// printf("Done %i iterations\n %f %f %f %f\n",nrot,d[0],d[1],d[2],d[3]);
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// print(v);
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// Now search the maximum eigenvalue
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double maxv=0;
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int maxind=-1;
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for(i=0;i<4;i++)
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if(maxv<fabs(d[i])) {
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q=Quaternionx(v[0][i],v[1][i],v[2][i],v[3][i]);
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maxind=i;
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maxv=d[i];
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}
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// The corresponding eigenvector define the searched rotation,
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Matrix44x Rot;
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q.ToMatrix(Rot);
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// the translation (last row) is simply the difference between the transformed src barycenter and the trg baricenter
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tr= (bfix - Rot*bmov);
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//res[3][0]=tr[0];res[3][1]=tr[1];res[3][2]=tr[2];
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Matrix44x Trn;
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Trn.SetTranslate(tr);
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res=Trn*Rot;
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return true;
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}
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// Dati due insiemi di punti e normali corrispondenti calcola la migliore trasformazione
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// che li fa corrispondere
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static bool ComputeMatchMatrix( Matrix44x &res,
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std::vector<Point3x> &Ps, // vertici corrispondenti su src (rossi)
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std::vector<Point3x> &Ns, // normali corrispondenti su src (rossi)
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std::vector<Point3x> &Pt) // vertici scelti su trg (verdi)
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// vector<Point3x> &Nt) // normali scelti su trg (verdi)
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{
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assert(0);
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// Da qui in poi non compila che ha bisogno dei minimiquadrati
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#if 0
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int sz=Ps.size();
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Matrix<double> A(sz,12);
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Vector<double> b(sz);
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Vector<double> x(12);
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//inizializzo il vettore per minimi quadrati
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// la matrice di trasf che calcolo con LeastSquares cerca avvicinare il piu'
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// possibile le coppie di punti che trovo ho scelto
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// Le coppie di punti sono gia' trasformate secondo la matrice <In> quindi come scelta iniziale
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// per il metodo minimiquadrati scelgo l'identica (e.g. se ho allineato a mano perfettamente e
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// le due mesh sono perfettamente uguali DEVE restituire l'identica)
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res.SetIdentity();
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int i,j,k;
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for(i=0; i<=2; ++i)
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for(j=0; j<=3; ++j)
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x[i*4+j] = res[i][j];
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//costruzione della matrice
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for(i=0;i<sz;++i)
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{
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for(j=0;j<3;++j)
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for(k=0;k<4;++k)
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if(k<3)
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{
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A[i][k+j*4] = Ns[i][j]*Pt[i][k];
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}
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else
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{
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A[i][k+j*4] = Ns[i][j];
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}
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b[i] = Ps[i]*Ns[i];
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}
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const int maxiter = 4096;
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int iter;
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LSquareGC(x,A,b,1e-16,maxiter,iter);
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TRACE("LSQ Solution");
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for(int ind=0; ind<12; ++ind) {
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if((ind%4)==0) TRACE("\n");
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TRACE("%8.5lf ", x[ind]);
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} TRACE("\n");
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if(iter==maxiter)
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{
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TRACE("I minimi quadrati non convergono!!\n");
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return false;
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}
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else { TRACE("Convergenza in %d passi\n",iter); }
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//Devo riapplicare la matrice di trasformazione globale a
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//trg inserendo il risultato nel vettore trgvert contenente
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//copia dei suoi vertici
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Matrix44x tmp;
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for(i=0; i<=2; ++i)
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for(j=0; j<=3; ++j)
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res[j][i] = x[i*4+j];
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res[0][3] = 0.0;
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res[1][3] = 0.0;
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res[2][3] = 0.0;
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res[3][3] = 1.0;
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/*
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res.Transpose();
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Point3x scv,shv,rtv,trv;
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res.Decompose(scv,shv,rtv,trv);
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vcg::print(res);
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printf("Scale %f %f %f\n",scv[0],scv[1],scv[2]);
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printf("Shear %f %f %f\n",shv[0],shv[1],shv[2]);
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printf("Rotat %f %f %f\n",rtv[0],rtv[1],rtv[2]);
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printf("Trans %f %f %f\n",trv[0],trv[1],trv[2]);
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printf("----\n"); res.Decompose(scv,shv,rtv,trv);
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vcg::print(res);
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printf("Scale %f %f %f\n",scv[0],scv[1],scv[2]);
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printf("Shear %f %f %f\n",shv[0],shv[1],shv[2]);
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printf("Rotat %f %f %f\n",rtv[0],rtv[1],rtv[2]);
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printf("Trans %f %f %f\n",trv[0],trv[1],trv[2]);
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res.Transpose();
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*/
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#endif
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return true;
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}
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/*
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****** Questa parte per compilare ha bisogno di leastsquares e matrici generiche
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****** Da controllare meglio
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static void CreatePairMatrix( Matrix<double> & A2, const Point3x & p, const Point3x & n, double d )
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{
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double t1 = p[0]*p[0];
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double t2 = n[0]*n[0];
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double t4 = t1*n[0];
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double t5 = t4*n[1];
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double t6 = t4*n[2];
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double t7 = p[0]*t2;
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double t8 = t7*p[1];
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double t9 = p[0]*n[0];
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double t10 = p[1]*n[1];
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double t11 = t9*t10;
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double t12 = p[1]*n[2];
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double t13 = t9*t12;
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double t14 = t7*p[2];
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double t15 = p[2]*n[1];
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double t16 = t9*t15;
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double t17 = p[2]*n[2];
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double t18 = t9*t17;
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double t19 = t9*n[1];
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double t20 = t9*n[2];
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double t21 = t9*d;
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double t22 = n[1]*n[1];
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double t25 = t1*n[1]*n[2];
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double t26 = p[0]*t22;
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double t27 = t26*p[1];
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double t28 = p[0]*n[1];
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double t29 = t28*t12;
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double t30 = t26*p[2];
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double t31 = t28*t17;
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double t32 = t28*n[2];
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double t33 = t28*d;
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double t34 = n[2]*n[2];
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double t36 = p[0]*t34;
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double t41 = p[1]*p[1]; double t43 = t41*n[0];
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double t46 = p[1]*t2; double t48 = p[1]*n[0];
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double t49 = t48*t15; double t50 = t48*t17;
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double t51 = t48*n[1]; double t52 = t48*n[2];
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double t57 = p[1]*t22; double t59 = t10*t17;
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double t60 = t10*n[2]; double t63 = p[1]*t34;
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double t66 = p[2]*p[2]; double t68 = t66*n[0];
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double t72 = p[2]*n[0]; double t73 = t72*n[1];
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double t74 = t72*n[2]; double t80 = t15*n[2];
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A2[0][0] = t1*t2; A2[0][1] = t5; A2[0][2] = t6;
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A2[0][3] = t8; A2[0][4] = t11; A2[0][5] = t13;
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A2[0][6] = t14; A2[0][7] = t16; A2[0][8] = t18;
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A2[0][9] = t7; A2[0][10] = t19; A2[0][11] = t20;
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A2[0][12] = -t21;
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A2[1][1] = t1*t22; A2[1][2] = t25; A2[1][3] = t11;
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A2[1][4] = t27; A2[1][5] = t29; A2[1][6] = t16;
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A2[1][7] = t30; A2[1][8] = t31; A2[1][9] = t19;
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A2[1][10] = t26; A2[1][11] = t32; A2[1][12] = -t33;
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A2[2][2] = t1*t34; A2[2][3] = t13; A2[2][4] = t29;
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A2[2][5] = t36*p[1]; A2[2][6] = t18; A2[2][7] = t31;
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A2[2][8] = t36*p[2]; A2[2][9] = t20; A2[2][10] = t32;
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A2[2][11] = t36; A2[2][12] = -p[0]*n[2]*d;
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A2[3][3] = t41*t2; A2[3][4] = t43*n[1]; A2[3][5] = t43*n[2];
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A2[3][6] = t46*p[2]; A2[3][7] = t49; A2[3][8] = t50;
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A2[3][9] = t46; A2[3][10] = t51; A2[3][11] = t52;
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A2[3][12] = -t48*d;
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A2[4][4] = t41*t22; A2[4][5] = t41*n[1]*n[2]; A2[4][6] = t49;
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A2[4][7] = t57*p[2]; A2[4][8] = t59; A2[4][9] = t51;
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A2[4][10] = t57; A2[4][11] = t60; A2[4][12] = -t10*d;
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A2[5][5] = t41*t34; A2[5][6] = t50; A2[5][7] = t59;
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A2[5][8] = t63*p[2]; A2[5][9] = t52; A2[5][10] = t60;
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A2[5][11] = t63; A2[5][12] = -t12*d;
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A2[6][6] = t66*t2; A2[6][7] = t68*n[1]; A2[6][8] = t68*n[2];
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A2[6][9] = p[2]*t2; A2[6][10] = t73; A2[6][11] = t74;
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A2[6][12] = -t72*d;
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A2[7][7] = t66*t22; A2[7][8] = t66*n[1]*n[2]; A2[7][9] = t73;
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A2[7][10] = p[2]*t22; A2[7][11] = t80; A2[7][12] = -t15*d;
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A2[8][8] = t66*t34; A2[8][9] = t74; A2[8][10] = t80;
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A2[8][11] = p[2]*t34; A2[8][12] = -t17*d;
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A2[9][9] = t2; A2[9][10] = n[0]*n[1];
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A2[9][11] = n[0]*n[2]; A2[9][12] = -n[0]*d;
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A2[10][10] = t22; A2[10][11] = n[1]*n[2]; A2[10][12] = -n[1]*d;
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A2[11][11] = t34; A2[11][12] = -n[2]*d;
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A2[12][12] = d*d;
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}
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// Dati due insiemi di punti e normali corrispondenti calcola la migliore trasformazione
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// che li fa corrispondere
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static bool ComputeMatchMatrix2( Matrix44x &res,
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std::vector<Point3x> &Ps, // vertici corrispondenti su src (rossi)
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std::vector<Point3x> &Ns, // normali corrispondenti su src (rossi)
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std::vector<Point3x> &Pt) // vertici scelti su trg (verdi)
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//vector<Point3x> &Nt) // normali scelti su trg (verdi)
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{
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const int N = 13;
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int i,j,k;
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|
|
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Matrixd AT(N,N);
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Matrixd TT(N,N);
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|
// Azzeramento matrice totale (solo tri-superiore)
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|
for(i=0;i<N;++i)
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for(j=i;j<N;++j)
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AT[i][j] = 0;
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|
// Calcolo matrici locali e somma
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|
for(k=0;k<Ps.size();++k)
|
|
{
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|
CreatePairMatrix(TT,Pt[k],Ns[k],Ps[k]*Ns[k]);
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|
for(i=0;i<N;++i)
|
|
for(j=i;j<N;++j)
|
|
AT[i][j] += TT[i][j];
|
|
}
|
|
|
|
for(i=0;i<N;++i)
|
|
for(j=0;j<i;++j)
|
|
AT[i][j] = AT[j][i];
|
|
|
|
std::vector<double> q;
|
|
double error;
|
|
affine_ls2(AT,q,error);
|
|
//printf("error: %g \n",error);
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res[0][0] = q[0];
|
|
res[0][1] = q[1];
|
|
res[0][2] = q[2];
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|
res[0][3] = 0;
|
|
res[1][0] = q[3];
|
|
res[1][1] = q[4];
|
|
res[1][2] = q[5];
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|
res[1][3] = 0;
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|
res[2][0] = q[6];
|
|
res[2][1] = q[7];
|
|
res[2][2] = q[8];
|
|
res[2][3] = 0;
|
|
res[3][0] = q[9];
|
|
res[3][1] = q[10];
|
|
res[3][2] = q[11];
|
|
res[3][3] = q[12];
|
|
|
|
return true;
|
|
}
|
|
*/
|
|
};
|
|
} // end namespace
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|
|
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#endif
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