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foucault |
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//------------------------------------------------------------ |
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//------------------------------------------------------------ |
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// MAGiC |
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// Jean Christophe Cuillière et Vincent FRANCOIS |
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// Département de Génie Mécanique - UQTR |
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//------------------------------------------------------------ |
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// Le projet MAGIC est un projet de recherche du département |
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// de génie mécanique de l'Université du Québec à |
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// Trois Rivières |
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// Les librairies ne peuvent être utilisées sans l'accord |
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// des auteurs (contact : francois@uqtr.ca) |
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//------------------------------------------------------------ |
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//------------------------------------------------------------ |
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// |
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// stbspline.cpp |
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// |
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//------------------------------------------------------------ |
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//------------------------------------------------------------ |
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// COPYRIGHT 2000 |
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// Version du 02/03/2006 à 11H24 |
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//------------------------------------------------------------ |
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//------------------------------------------------------------ |
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#include "gestionversion.h" |
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#include "stbspline.h" |
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#include <vector> |
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#include "st_gestionnaire.h" |
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#include "tpl_fonction.h" |
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#include "constantegeo.h" |
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#include <math.h> |
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ST_B_SPLINE::ST_B_SPLINE(long LigneCourante,std::string idori,int bs_degre,std::vector<int> bs_indexptsctr,std::vector<int> bs_knots_multiplicities,std::vector<double> bs_knots):ST_COURBE(LigneCourante,idori),degre(bs_degre) |
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{ |
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int nb=bs_knots_multiplicities.size(); |
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for (int i=0;i<nb;i++) |
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{ |
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for (int j=0;j<bs_knots_multiplicities[i];j++) |
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knots.insert(knots.end(),bs_knots[i]); |
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} |
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nb_point=bs_indexptsctr.size(); |
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for (int i=0;i<nb_point;i++) |
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{ |
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indexptsctr.insert(indexptsctr.end(),bs_indexptsctr[i]); |
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//poids.insert(poids.end(),1.); |
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} |
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} |
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ST_B_SPLINE::ST_B_SPLINE(int bs_degre,std::vector<double> &vec_knots,std::vector<double> &vec_point,std::vector<double> &vec_poids):ST_COURBE(),degre(bs_degre) |
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{ |
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int nb=vec_knots.size(); |
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for (int i=0;i<nb;i++) |
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knots.insert(knots.end(),vec_knots[i]); |
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nb_point=vec_point.size()/3; |
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for (int i=0;i<nb_point;i++) |
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{ |
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double w=vec_poids[i]; |
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double x=vec_point[3*i]; |
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double y=vec_point[3*i+1]; |
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double z=vec_point[3*i+2]; |
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OT_VECTEUR_4D pt(w*x,w*y,w*z,w); |
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ptsctr.push_back(pt); |
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} |
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double xyz1[3]; |
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double xyz2[3]; |
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xyz1[0]=vec_point[0]; |
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xyz1[1]=vec_point[1]; |
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xyz1[2]=vec_point[2]; |
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xyz2[0]=vec_point[3*nb_point-3]; |
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xyz2[1]=vec_point[3*nb_point-2]; |
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xyz2[2]=vec_point[3*nb_point-1]; |
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periodique=0; |
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if (OPERATEUR::egal (xyz1[0],xyz2[0],1E-6)) |
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{ |
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if (OPERATEUR::egal (xyz1[1],xyz2[1],1E-6)) |
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{ |
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if (OPERATEUR::egal (xyz1[2],xyz2[2],1E-6)) |
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periodique=1; |
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} |
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} |
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if (periodique==1) |
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{ |
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int i=knots.size(); |
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periode=(knots[i-1]-knots[0]); |
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} |
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else periode=0; |
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} |
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ST_B_SPLINE::~ST_B_SPLINE() |
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{ |
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} |
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int ST_B_SPLINE::get_intervalle(int nb_point, int degre, double t, std::vector<double> &knots) |
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{ |
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int inter; |
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if (OPERATEUR::egal(t,knots[nb_point],1E-10)==1) inter=nb_point-1; |
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else if (OPERATEUR::egal(t,knots[degre],1E-10)==1) inter=degre; |
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else |
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{ |
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int low=degre; |
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int high=nb_point+1; |
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int mid=((low+high)/2); |
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while ((t<knots[mid-1]) || (t>=knots[mid])) |
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{ |
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if (t<knots[mid-1]) high=mid; |
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else low=mid; |
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mid=(low+high)/2; |
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} |
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inter=mid-1; |
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} |
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return inter; |
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} |
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void ST_B_SPLINE::binomialCoef(double * Bin, int d){ |
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int n,k; |
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// Setup the first line |
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Bin[0] = 1.0 ; |
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for(k=d-1;k>0;--k) |
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Bin[k] = 0.0 ; |
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// Setup the other lines |
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for(n=0;n<d-1;n++){ |
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Bin[(n+1)*d+0] = 1.0 ; |
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for(k=1;k<d;k++) |
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if(n+1<k) |
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Bin[(n+1)*d+k] = 0.0 ; |
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else |
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Bin[(n+1)*d+k] = Bin[n*d+k] + Bin[n*d+k-1] ; |
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} |
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} |
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void ST_B_SPLINE::get_valeur_fonction(int inter, double t, int degre, std::vector<double> &knots,double *grand_n) |
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{ |
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double saved; |
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grand_n[0]=1.0; |
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double gauche[16]; |
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double droite[16]; |
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for (int j=1;j<=degre;j++) |
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{ |
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gauche[j-1]= t-knots[inter-j+1]; |
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droite[j-1]=knots[inter+j]-t; |
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saved=0.0; |
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for (int r=0;r<j;r++) |
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{ |
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double temp=grand_n[r]/(droite[r]+ gauche[j-r-1]); |
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grand_n[r]=saved+droite[r]* temp; |
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saved=gauche[j-r-1]*temp; |
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} |
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grand_n[j]=saved; |
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} |
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} |
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void ST_B_SPLINE::evaluer(double t,double *xyz) |
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{ |
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if (est_periodique()) |
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{ |
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double tmin=get_tmin(); |
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double tmax=get_tmax(); |
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while (t>tmax) t -= periode; |
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while (t<tmin) t += periode; |
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} |
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int inter = get_intervalle(nb_point,degre,t, knots); |
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double grand_n[256]; |
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get_valeur_fonction(inter,t,degre,knots,grand_n); |
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OT_VECTEUR_4D sp(0,0,0,0) ; |
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for (int j=0; j<=degre; j++) |
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{ |
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sp += grand_n[j] * ptsctr[inter-degre+j]; |
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} |
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// transform homogeneous coordinates to 3D coordinates |
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for (int i=0; i<3; i++) |
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xyz[i] = sp[i]/sp.w(); |
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} |
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/* |
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void ST_B_SPLINE::get_tout_fonction(int inter, double t, int degre, std::vector<double> &knots,double *grand_n) |
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{ |
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#define grand_n(i,j) (*(grand_n+(i)*(degre+1)+j)) |
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double saved; |
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grand_n(0,0)=1.0; |
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double gauche[16]; |
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double droite[16]; |
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for (int j=1;j<=degre;j++) |
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{ |
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gauche[j-1]= t-knots[inter-j+1]; |
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droite[j-1]=knots[inter+j]-t; |
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saved=0.0; |
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for (int r=0;r<j;r++) |
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{ |
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grand_n(j,r)=(droite[r]+ gauche[j-r-1]); |
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double temp = grand_n(r,j-1)/grand_n(j,r); |
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grand_n(r,j)= saved+droite[r]*temp; |
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saved=gauche[j-r-1]*temp; |
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} |
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grand_n(j,j)=saved; |
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} |
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#undef grand_n // enlever (i,j) |
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} */ |
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void ST_B_SPLINE::deriver_fonction(int inter,double t,int degre,int dd,std::vector<double> &knots,double *f_deriver) |
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{ |
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#define f_deriver(i,j) (*(f_deriver+(i)*(degre+1)+j)) |
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#define grand_n(i,j) (*(grand_n+(i)*(degre+1)+j)) |
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#define a(i,j) (*(a+(i)*(dd+1)+j)) |
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double *grand_n=new double[(degre+1)*(degre+1)]; |
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double saved; |
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grand_n(0,0)=1.0; |
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double *gauche=new double[degre+1]; |
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double *droite=new double[degre+1]; |
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for (int j=1;j<=degre;j++) |
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{ |
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gauche[j]= t-knots[inter-j+1]; |
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droite[j]=knots[inter+j]-t; |
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saved=0.0; |
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for (int r=0;r<j;r++) |
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{ |
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grand_n(j,r)=(droite[r+1]+ gauche[j-r]); |
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double temp = grand_n(r,j-1)/grand_n(j,r); |
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grand_n(r,j)= saved+droite[r+1]*temp; |
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saved=gauche[j-r]*temp; |
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} |
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grand_n(j,j)=saved; |
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} |
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for (int j=0;j<=degre;j++) |
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{ |
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f_deriver(0,j)= grand_n(j,degre); |
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} |
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double *a=new double[(degre+1)*(degre+1)]; |
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for (int r=0;r<=degre;r++) |
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{ |
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int s1=0; int s2=1; |
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a(0,0)=1.0; |
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for (int k=1;k<=dd; k++) |
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{ |
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double d=0.0; |
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int rk=r-k; int pk=degre-k; |
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if(r>=k) |
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{ |
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a(s2,0)=a(s1,0)/grand_n(pk+1,rk); |
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d= a(s2,0)* grand_n(rk,pk); |
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} |
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int j1; int j2; |
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if(rk>=-1) j1=1; |
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else j1= -rk; |
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if(r-1<=pk) j2=k-1; |
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else j2=degre-r; |
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for (int j=j1;j<=j2;j++) |
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{ |
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a(s2,j) = (a(s1,j)-a(s1,j-1))/grand_n(pk+1,rk+j); |
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d+=a(s2,j)*grand_n(rk+j,pk); |
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} |
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if(r<=pk) |
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{ |
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a(s2,k) = -a(s1,k-1)/grand_n(pk+1,r); |
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d+=a(s2,k)*grand_n(r,pk); |
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} |
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f_deriver(k,r)=d; |
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int j=s1; s1=s2; s2=j; |
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} |
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} |
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int r=degre; |
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for (int k=1;k<=dd;k++) |
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{ |
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for (int j=0;j<=degre;j++) |
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{ |
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f_deriver(k,j)*=r; |
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} |
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r*=(degre-k); |
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} |
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delete [] a; |
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delete [] grand_n; |
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delete [] gauche; |
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delete [] droite; |
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#undef f_deriver |
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#undef grand_n |
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#undef a |
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} |
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void ST_B_SPLINE::deriver_bs_kieme(int nb_point,int degre,std::vector<double> &knots,std::vector<OT_VECTEUR_4D> &ptsctr_x,double t,int d, OT_VECTEUR_4D * CK) |
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{ |
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int du = std::min(d,degre); |
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int inter = get_intervalle(nb_point,degre,t, knots); |
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double derF[256]; |
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deriver_fonction(inter, t,degre,du,knots,derF); |
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#define derF(i,j) (*(derF+(i)*(degre+1)+j)) |
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for(int k=du;k>=0;--k) |
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{ |
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CK[k] = OT_VECTEUR_4D(0,0,0,0); |
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for(int j=degre;j>=0;--j) |
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{ |
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CK[k] += derF(k,j)*ptsctr_x[inter-degre+j]; |
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} |
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} |
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#undef derF |
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} |
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void ST_B_SPLINE::deriver_kieme(double t,int d, double *CK_x,double *CK_y,double *CK_z) |
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{ |
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int i,k; |
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OT_VECTEUR_4D dersW[16], ders[16]; |
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OT_VECTEUR_4D v; |
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deriver_bs_kieme(nb_point, degre, knots, ptsctr, t, d, dersW); |
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double Bin[256]; |
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int dbin=d+1; |
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binomialCoef(Bin, dbin); |
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#define Bin(i,j) (*(Bin+(i)*(dbin)+j)) |
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for(k=0;k<=d;k++) |
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{ |
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ders[k] = dersW[k]; |
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for(i=k ;i>0 ;--i) |
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ders[k] -= (Bin(k,i)*dersW[i].w())*ders[k-i]; |
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ders[k]/=dersW[0].w(); |
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} |
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for (int i=0; i<=d; i++) |
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{ |
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CK_x[i]=ders[i][0]; |
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CK_y[i]=ders[i][1]; |
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CK_z[i]=ders[i][2]; |
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} |
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} |
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void ST_B_SPLINE::deriver(double t,double *dxyz) |
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{ |
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if (est_periodique()) |
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{ |
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double tmin=get_tmin(); |
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double tmax=get_tmax(); |
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|
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while (t>tmax) t -= periode; |
| 344 |
|
|
while (t<tmin) t += periode; |
| 345 |
|
|
} |
| 346 |
|
|
double CK_x[2]; |
| 347 |
|
|
double CK_y[2]; |
| 348 |
|
|
double CK_z[2]; |
| 349 |
|
|
deriver_kieme(t,1,CK_x,CK_y,CK_z); |
| 350 |
|
|
dxyz[0]=CK_x[1]; |
| 351 |
|
|
dxyz[1]=CK_y[1]; |
| 352 |
|
|
dxyz[2]=CK_z[1]; |
| 353 |
|
|
} |
| 354 |
|
|
|
| 355 |
|
|
void ST_B_SPLINE::deriver_seconde(double t,double *ddxyz,double* dxyz ,double* xyz ) |
| 356 |
|
|
{ |
| 357 |
|
|
if (est_periodique()) |
| 358 |
|
|
{ |
| 359 |
|
|
double tmin=get_tmin(); |
| 360 |
|
|
double tmax=get_tmax(); |
| 361 |
|
|
while (t>tmax) t -= periode; |
| 362 |
|
|
while (t<tmin) t += periode; |
| 363 |
|
|
} |
| 364 |
|
|
double CK_x[3]; |
| 365 |
|
|
double CK_y[3]; |
| 366 |
|
|
double CK_z[3]; |
| 367 |
|
|
deriver_kieme(t,2,CK_x,CK_y,CK_z); |
| 368 |
|
|
ddxyz[0]=CK_x[2]; |
| 369 |
|
|
ddxyz[1]=CK_y[2]; |
| 370 |
|
|
ddxyz[2]=CK_z[2]; |
| 371 |
|
|
if (dxyz!=NULL) |
| 372 |
|
|
{ |
| 373 |
|
|
dxyz[0]=CK_x[1]; |
| 374 |
|
|
dxyz[1]=CK_y[1]; |
| 375 |
|
|
dxyz[2]=CK_z[1]; |
| 376 |
|
|
} |
| 377 |
|
|
if (xyz!=NULL) |
| 378 |
|
|
{ |
| 379 |
|
|
xyz[0]=CK_x[0]; |
| 380 |
|
|
xyz[1]=CK_y[0]; |
| 381 |
|
|
xyz[2]=CK_z[0]; |
| 382 |
|
|
} |
| 383 |
|
|
} |
| 384 |
|
|
|
| 385 |
|
|
|
| 386 |
|
|
|
| 387 |
|
|
void ST_B_SPLINE::inverser(double& t,double *xyz,double precision) |
| 388 |
|
|
{ |
| 389 |
|
|
int code; |
| 390 |
|
|
int num_point=nb_point; |
| 391 |
|
|
do |
| 392 |
|
|
{ |
| 393 |
|
|
code=inverser2(t,xyz,num_point,precision); |
| 394 |
|
|
num_point=num_point*2; |
| 395 |
|
|
} |
| 396 |
|
|
while (code==0 && num_point < 100000); |
| 397 |
|
|
} |
| 398 |
|
|
|
| 399 |
|
|
int ST_B_SPLINE::inverser2(double& t,double *xyz,int num_test,double precision) |
| 400 |
|
|
{ |
| 401 |
|
|
double xyz1[3]; |
| 402 |
|
|
double dxyz1[3]; |
| 403 |
|
|
double ddxyz1[3]; |
| 404 |
|
|
double ti; |
| 405 |
|
|
double eps; |
| 406 |
|
|
double tmin=get_tmin(); |
| 407 |
|
|
double tmax=get_tmax(); |
| 408 |
|
|
OT_VECTEUR_3D Pt(xyz[0],xyz[1],xyz[2]); |
| 409 |
|
|
double distance_ref=1e308; |
| 410 |
|
|
int ref; |
| 411 |
|
|
|
| 412 |
|
|
for (int i=0;i<num_test+1;i++) |
| 413 |
|
|
{ |
| 414 |
|
|
double t=tmin+i*1./num_test*(tmax-tmin); |
| 415 |
|
|
evaluer(t,xyz1); |
| 416 |
|
|
OT_VECTEUR_3D Ct(xyz1[0],xyz1[1],xyz1[2]); |
| 417 |
|
|
OT_VECTEUR_3D Distance = Ct-Pt; |
| 418 |
|
|
double longueur=Distance.get_longueur2(); |
| 419 |
|
|
if (longueur<distance_ref) |
| 420 |
|
|
{ |
| 421 |
|
|
distance_ref=longueur; |
| 422 |
|
|
ref=i; |
| 423 |
|
|
} |
| 424 |
|
|
} |
| 425 |
|
|
|
| 426 |
|
|
double tii=tmin+ref*1./num_test*(tmax-tmin); |
| 427 |
|
|
int compteur=0; |
| 428 |
|
|
do |
| 429 |
|
|
{ |
| 430 |
|
|
compteur++; |
| 431 |
|
|
ti=tii; |
| 432 |
|
|
deriver_seconde(ti,ddxyz1,dxyz1,xyz1); |
| 433 |
|
|
OT_VECTEUR_3D Ct(xyz1[0],xyz1[1],xyz1[2]); |
| 434 |
|
|
OT_VECTEUR_3D Ct_deriver(dxyz1[0],dxyz1[1],dxyz1[2]); |
| 435 |
|
|
OT_VECTEUR_3D Ct_deriver_seconde(ddxyz1[0],ddxyz1[1],ddxyz1[2]); |
| 436 |
|
|
OT_VECTEUR_3D Distance = Ct-Pt; |
| 437 |
|
|
tii=ti-Ct_deriver*Distance/(Ct_deriver_seconde*Distance+Ct_deriver.get_longueur2()); |
| 438 |
|
|
if (periodique==1) |
| 439 |
|
|
{ |
| 440 |
|
|
if (tii<get_tmin()) tii=get_tmax()-(get_tmin()-tii); |
| 441 |
|
|
if (tii>get_tmax()) tii=get_tmin()+(tii-get_tmax()); |
| 442 |
|
|
} |
| 443 |
|
|
else |
| 444 |
|
|
{ |
| 445 |
|
|
if (tii<get_tmin()) tii=get_tmin(); |
| 446 |
|
|
if (tii>get_tmax()) tii=get_tmax(); |
| 447 |
|
|
} |
| 448 |
|
|
eps=fabs(tii-ti); |
| 449 |
|
|
if (compteur>500) return 0; |
| 450 |
|
|
} |
| 451 |
|
|
while (eps>precision); |
| 452 |
|
|
t=ti; |
| 453 |
|
|
return 1; |
| 454 |
|
|
} |
| 455 |
|
|
|
| 456 |
|
|
double ST_B_SPLINE::get_tmin() |
| 457 |
|
|
{ |
| 458 |
|
|
return knots[0]; |
| 459 |
|
|
} |
| 460 |
|
|
double ST_B_SPLINE::get_tmax() |
| 461 |
|
|
{ |
| 462 |
|
|
int i=knots.size(); |
| 463 |
|
|
return knots[i-1]; |
| 464 |
|
|
} |
| 465 |
|
|
|
| 466 |
|
|
double equation_longueur(ST_B_SPLINE& bsp,double t) |
| 467 |
|
|
{ |
| 468 |
|
|
double dxyz[3]; |
| 469 |
|
|
bsp.deriver(t,dxyz); |
| 470 |
|
|
return sqrt(dxyz[0]*dxyz[0]+dxyz[1]*dxyz[1]+dxyz[2]*dxyz[2]); |
| 471 |
|
|
} |
| 472 |
|
|
|
| 473 |
|
|
|
| 474 |
|
|
double ST_B_SPLINE::get_longueur(double t1,double t2,double precis) |
| 475 |
|
|
{ |
| 476 |
|
|
TPL_FONCTION1<double,ST_B_SPLINE,double> longueur_bsp(*this,equation_longueur); |
| 477 |
|
|
return longueur_bsp.integrer_gauss_2(t1,t2); |
| 478 |
|
|
} |
| 479 |
|
|
|
| 480 |
|
|
|
| 481 |
|
|
int ST_B_SPLINE::est_periodique(void) |
| 482 |
|
|
{ |
| 483 |
|
|
return periodique; |
| 484 |
|
|
} |
| 485 |
|
|
double ST_B_SPLINE::get_periode(void) |
| 486 |
|
|
{ |
| 487 |
|
|
return periode; |
| 488 |
|
|
} |
| 489 |
|
|
|
| 490 |
|
|
int ST_B_SPLINE::get_type_geometrique(TPL_LISTE_ENTITE<double> ¶m) |
| 491 |
|
|
{ |
| 492 |
|
|
for(int i=0;i<nb_point-(degre+1);i++) |
| 493 |
|
|
{ |
| 494 |
|
|
param.ajouter(knots[i]); |
| 495 |
|
|
} |
| 496 |
|
|
double xyz[3]; |
| 497 |
|
|
for(int i=0;i<nb_point;i++) |
| 498 |
|
|
{ |
| 499 |
|
|
xyz[0]=ptsctr[i].x()/ptsctr[i].w(); |
| 500 |
|
|
xyz[1]=ptsctr[i].y()/ptsctr[i].w(); |
| 501 |
|
|
xyz[2]=ptsctr[i].z()/ptsctr[i].w(); |
| 502 |
|
|
param.ajouter(xyz[0]); |
| 503 |
|
|
param.ajouter(xyz[1]); |
| 504 |
|
|
param.ajouter(xyz[2]); |
| 505 |
|
|
} |
| 506 |
|
|
for(int i=0;i<nb_point;i++) |
| 507 |
|
|
{ |
| 508 |
|
|
param.ajouter(ptsctr[i].w()); |
| 509 |
|
|
} |
| 510 |
|
|
param.ajouter(degre); |
| 511 |
|
|
return MGCo_BSPLINE; |
| 512 |
|
|
} |
| 513 |
|
|
|
| 514 |
|
|
void ST_B_SPLINE::initialiser(ST_GESTIONNAIRE *gest) |
| 515 |
|
|
{ |
| 516 |
|
|
int i=indexptsctr.size(); |
| 517 |
|
|
ST_POINT* point1=gest->lst_point.getid(indexptsctr[0]); |
| 518 |
|
|
ST_POINT* point2=gest->lst_point.getid(indexptsctr[i-1]); |
| 519 |
|
|
double xyz1[3]; |
| 520 |
|
|
double xyz2[3]; |
| 521 |
|
|
point1->evaluer(xyz1); |
| 522 |
|
|
point2->evaluer(xyz2); |
| 523 |
|
|
periodique=0; |
| 524 |
|
|
if (OPERATEUR::egal (xyz1[0],xyz2[0],1E-6)) |
| 525 |
|
|
{ |
| 526 |
|
|
if (OPERATEUR::egal (xyz1[1],xyz2[1],1E-6)) |
| 527 |
|
|
{ |
| 528 |
|
|
if (OPERATEUR::egal (xyz1[2],xyz2[2],1E-6)) |
| 529 |
|
|
periodique=1; |
| 530 |
|
|
} |
| 531 |
|
|
} |
| 532 |
|
|
|
| 533 |
|
|
if (periodique==1) |
| 534 |
|
|
{ |
| 535 |
|
|
int i=knots.size(); |
| 536 |
|
|
periode=(knots[i-1]-knots[0]); |
| 537 |
|
|
} |
| 538 |
|
|
else periode=0; |
| 539 |
|
|
|
| 540 |
|
|
int nbptsctr=indexptsctr.size(); |
| 541 |
|
|
for (int i=0;i<nbptsctr;i++) |
| 542 |
|
|
{ |
| 543 |
|
|
ST_POINT* stpoint=gest->lst_point.getid(indexptsctr[i]); |
| 544 |
|
|
double xyz[3]; |
| 545 |
|
|
stpoint->evaluer(xyz); |
| 546 |
|
|
OT_VECTEUR_4D pt(xyz[0],xyz[1],xyz[2],1); |
| 547 |
|
|
ptsctr.insert(ptsctr.end(),pt); |
| 548 |
|
|
} |
| 549 |
|
|
} |
| 550 |
|
|
|
| 551 |
|
|
|
| 552 |
|
|
|
| 553 |
|
|
|
| 554 |
|
|
|
| 555 |
|
|
void ST_B_SPLINE::est_util(ST_GESTIONNAIRE* gest) |
| 556 |
|
|
{ |
| 557 |
|
|
util=true; |
| 558 |
|
|
for (int i=0;i<nb_point;i++) |
| 559 |
|
|
gest->lst_point.getid(indexptsctr[i])->est_util(gest); |
| 560 |
|
|
} |
| 561 |
|
|
|
| 562 |
|
|
|
| 563 |
|
|
|
| 564 |
|
|
|
| 565 |
|
|
void ST_B_SPLINE::get_param_NURBS(int& indx_premier_ptctr,TPL_LISTE_ENTITE<double> ¶m) |
| 566 |
|
|
{ |
| 567 |
|
|
|
| 568 |
|
|
// the order stock of the parameters is: |
| 569 |
|
|
// 1/ the variante type =1 (dimension one) |
| 570 |
|
|
// 2/ the order of the spline in two dirction the second direction is zero |
| 571 |
|
|
// 3/ the number of the control points |
| 572 |
|
|
// 4/ the knots vector |
| 573 |
|
|
// 5/ the control points cordinates in homogeneos forms |
| 574 |
|
|
|
| 575 |
|
|
// The first parameter indicate the code access |
| 576 |
|
|
param.ajouter(1); |
| 577 |
|
|
// The follewing two parameters of the list indicate the orders of the net points |
| 578 |
|
|
|
| 579 |
|
|
param.ajouter(degre+1); |
| 580 |
|
|
param.ajouter(0); |
| 581 |
|
|
|
| 582 |
|
|
// The follewing two parameters indicate the number of rows and colons of the control points |
| 583 |
|
|
// respectively to the two parameters directions |
| 584 |
|
|
|
| 585 |
|
|
param.ajouter(nb_point); |
| 586 |
|
|
param.ajouter(0); |
| 587 |
|
|
|
| 588 |
|
|
// this present the knot vector in the u-direction |
| 589 |
|
|
|
| 590 |
|
|
for(unsigned int i=0;i<knots.size();i++) |
| 591 |
|
|
{ |
| 592 |
|
|
param.ajouter(knots[i]); |
| 593 |
|
|
} |
| 594 |
|
|
|
| 595 |
|
|
// in the following we construct the control point vector |
| 596 |
|
|
|
| 597 |
|
|
for(unsigned int pt=0;pt<ptsctr.size();pt++) |
| 598 |
|
|
{ |
| 599 |
|
|
double w=ptsctr[pt].w(); |
| 600 |
|
|
double inv_w=1/w; |
| 601 |
|
|
double x=ptsctr[pt].x()*inv_w; |
| 602 |
|
|
double y=ptsctr[pt].y()*inv_w; |
| 603 |
|
|
double z=ptsctr[pt].z()*inv_w; |
| 604 |
|
|
param.ajouter(x); |
| 605 |
|
|
param.ajouter(y); |
| 606 |
|
|
param.ajouter(z); |
| 607 |
|
|
param.ajouter(w); |
| 608 |
|
|
} |
| 609 |
|
|
indx_premier_ptctr=5+knots.size(); |
| 610 |
|
|
} |
