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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 "ot_mathematique.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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ptsctr.insert(ptsctr.end(),vec_point[3*i]);
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ptsctr.insert(ptsctr.end(),vec_point[3*i+1]);
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ptsctr.insert(ptsctr.end(),vec_point[3*i+2]);
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poids.insert(poids.end(),vec_poids[i]);
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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-12)==1) inter=nb_point-1;
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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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// Setup the binomial coefficients into th matrix Bin
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// Bin(i,j) = (i j)
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// The binomical coefficients are defined as follow
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// (n) n!
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// (k) = k!(n-k)! 0<=k<=n
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// and the following relationship applies
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// (n+1) (n) ( n )
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// ( k ) = (k) + (k-1)
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/*!
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\brief Setup a matrix containing binomial coefficients
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Setup the binomial coefficients into th matrix Bin
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\htmlonly
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\[ Bin(i,j) = \left( \begin{array}{c}i \\ j\end{array} \right)\]
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The binomical coefficients are defined as follow
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\[ \left(\begin{array}{c} n \\ k \end{array} \right)= \frac{ n!}{k!(n-k)!} \mbox{for $0\leq k \leq n$} \]
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and the following relationship applies
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\[ \left(\begin{array}{c} n+1 \\ k \end{array} \right) =
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\left(\begin{array}{c} n \\ k \end{array} \right) +
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\left(\begin{array}{c} n \\ k-1 \end{array} \right) \]
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\endhtmlonly
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\param Bin the binomial matrix
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\author Philippe Lavoie
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\date 24 January, 1997
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*/
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void ST_B_SPLINE::binomialCoef(double * Bin, int degre){
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#define Bin(i,j) (*(Bin+(i)*(3)+j))
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int n,k;
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// Setup the first line
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Bin(0,0) = 1.0 ;
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for(k=degre-1;k>0;--k)
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Bin(0,k) = 0.0 ;
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// Setup the other lines
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for(n=0;n<degre-1;n++){
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Bin(n+1,0) = 1.0 ;
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for(k=1;k<degre;k++)
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if(n+1<k)
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Bin(n,k) = 0.0 ;
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else
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Bin(n+1,k) = Bin(n,k) + Bin(n,k-1) ;
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}
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#undef Bin
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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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//inter=get_intervalle(nb_point,degre,t,knots);
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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 *Cw)
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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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// somme ( Ni,p(t) * Wi * Pi ) / somme ( Ni,p(t) * Wi )
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double R[16] = {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0};
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double Sum_Ni_wi = 0;
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for (int j=0; j<=degre; j++)
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{
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Sum_Ni_wi += grand_n[j] * poids[inter-degre+j];
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}
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for (int j=0; j<=degre; j++)
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{
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R[j] = grand_n[j] * poids[inter-degre+j] / Sum_Ni_wi;
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}
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for (int i=0; i<3; i++)
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{
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Cw[i] = 0;
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for (int j=0; j<=degre; j++)
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{
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Cw[i] += R[j] * ptsctr[3*(inter-degre+j)+i];
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}
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}
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}
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void ST_B_SPLINE::deriver_pts(int nb_point,int degre,std::vector<double> &knots,std::vector<double> &ptsctr_x,int d,int r1,int r2,double *PK_x)
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{
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int r = r2-r1;
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#define PK_x(i,j) (*(PK_x+(i)*(degre+1)+j))
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for (int i=0; i<=r; i++)
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{
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PK_x(0,i)= ptsctr_x[r1+i];
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}
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for (int k=1; k<=d; k++)
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{
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int tmp = degre-k+1;
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for (int i=0; i<=r-k; i++)
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{
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PK_x(k,i)= tmp*(PK_x(k-1,i+1)-PK_x(k-1,i))/(knots[r1+i+degre+1]-knots[r1+i+k]);
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}
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}
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#undef PK_x // enlever (i,j)
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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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//inter=get_intervalle(nb_point,degre,t,knots);
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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_bs_kieme(int nb_point,int degre,std::vector<double> &knots,std::vector<double> &ptsctr_x,double t,int d,double *CK)
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{
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int du = std::min(d,degre);
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for (int k=degre+1;k<=d;k++)
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{
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CK[k]=0.0;
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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_tout_fonction(inter,t,degre,knots,grand_n);
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#define grand_n(i,j) (*(grand_n+(i)*(degre+1)+j))
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double PK[256];
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deriver_pts(nb_point,degre,knots,ptsctr_x,du,inter-degre,inter,PK);
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#define PK(i,j) (*(PK+(i)*(degre+1)+j))
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for(int k=0; k<=du;k++)
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{
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CK[k] = 0.0;
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for(int j=0; j<=degre-k;j++)
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{
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CK[k] = CK[k]+ grand_n(j,degre-k)*PK(k,j); //PK(k,j) PK[k*degre+j]
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}
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}
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#undef PK // enlever (i,j)
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#undef grand_n // enlever (i,j)
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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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double Aders_x[16];
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double Aders_y[16];
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double Aders_z[16];
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std::vector<double> ptsctr_wx;
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std::vector<double> ptsctr_wy;
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std::vector<double> ptsctr_wz;
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double xyz[3];
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for (int i=0;i<nb_point;i++)
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{
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xyz[0]=ptsctr[3*i];
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xyz[1]=ptsctr[3*i+1];
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xyz[2]=ptsctr[3*i+2];
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ptsctr_wx.insert(ptsctr_wx.end(),poids[i]*xyz[0]);
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ptsctr_wy.insert(ptsctr_wy.end(),poids[i]*xyz[1]);
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ptsctr_wz.insert(ptsctr_wz.end(),poids[i]*xyz[2]);
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}
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deriver_bs_kieme(nb_point,degre,knots,ptsctr_wx,t,d,Aders_x);
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deriver_bs_kieme(nb_point,degre,knots,ptsctr_wy,t,d,Aders_y);
|
| 312 |
|
|
deriver_bs_kieme(nb_point,degre,knots,ptsctr_wz,t,d,Aders_z);
|
| 313 |
|
|
double Wders[16];
|
| 314 |
|
|
deriver_bs_kieme(nb_point,degre,knots,poids,t,d,Wders);
|
| 315 |
|
|
double Bin[256];
|
| 316 |
|
|
binomialCoef(Bin, d);
|
| 317 |
|
|
#define Bin(i,j) (*(Bin+(i)*(3)+j))
|
| 318 |
|
|
for(int k=0;k<=d;k++)
|
| 319 |
|
|
{
|
| 320 |
|
|
double v_x = Aders_x[k];
|
| 321 |
|
|
double v_y = Aders_y[k];
|
| 322 |
|
|
double v_z = Aders_z[k];
|
| 323 |
|
|
for(int i=1;i<=k;i++)
|
| 324 |
|
|
{
|
| 325 |
|
|
v_x = v_x - Bin(k-1,i-1)*Wders[i]*CK_x[k-i];
|
| 326 |
|
|
v_y = v_y - Bin(k-1,i-1)*Wders[i]*CK_y[k-i];
|
| 327 |
|
|
v_z = v_z - Bin(k-1,i-1)*Wders[i]*CK_z[k-i];
|
| 328 |
|
|
}
|
| 329 |
|
|
CK_x[k] = v_x/Wders[0];
|
| 330 |
|
|
CK_y[k] = v_y/Wders[0];
|
| 331 |
|
|
CK_z[k] = v_z/Wders[0];
|
| 332 |
|
|
}
|
| 333 |
|
|
#undef Bin // enlever (i,j)
|
| 334 |
|
|
}
|
| 335 |
|
|
|
| 336 |
|
|
void ST_B_SPLINE::deriver(double t,double *dxyz)
|
| 337 |
|
|
{
|
| 338 |
|
|
double CK_x[2];
|
| 339 |
|
|
double CK_y[2];
|
| 340 |
|
|
double CK_z[2];
|
| 341 |
|
|
deriver_kieme(t,1,CK_x,CK_y,CK_z);
|
| 342 |
|
|
dxyz[0]=CK_x[1];
|
| 343 |
|
|
dxyz[1]=CK_y[1];
|
| 344 |
|
|
dxyz[2]=CK_z[1];
|
| 345 |
|
|
}
|
| 346 |
|
|
|
| 347 |
|
|
void ST_B_SPLINE::deriver_seconde(double t,double *ddxyz,double* dxyz ,double* xyz )
|
| 348 |
|
|
{
|
| 349 |
|
|
double CK_x[3];
|
| 350 |
|
|
double CK_y[3];
|
| 351 |
|
|
double CK_z[3];
|
| 352 |
|
|
deriver_kieme(t,2,CK_x,CK_y,CK_z);
|
| 353 |
|
|
ddxyz[0]=CK_x[2];
|
| 354 |
|
|
ddxyz[1]=CK_y[2];
|
| 355 |
|
|
ddxyz[2]=CK_z[2];
|
| 356 |
|
|
if (dxyz!=NULL)
|
| 357 |
|
|
{
|
| 358 |
|
|
dxyz[0]=CK_x[1];
|
| 359 |
|
|
dxyz[1]=CK_y[1];
|
| 360 |
|
|
dxyz[2]=CK_z[1];
|
| 361 |
|
|
}
|
| 362 |
|
|
if (xyz!=NULL)
|
| 363 |
|
|
{
|
| 364 |
|
|
xyz[0]=CK_x[0];
|
| 365 |
|
|
xyz[1]=CK_y[0];
|
| 366 |
|
|
xyz[2]=CK_z[0];
|
| 367 |
|
|
}
|
| 368 |
|
|
}
|
| 369 |
|
|
|
| 370 |
|
|
|
| 371 |
|
|
|
| 372 |
|
|
void ST_B_SPLINE::inverser(double& t,double *xyz,double precision)
|
| 373 |
|
|
{
|
| 374 |
|
|
int code;
|
| 375 |
|
|
int num_point=nb_point;
|
| 376 |
|
|
do
|
| 377 |
|
|
{
|
| 378 |
|
|
code=inverser2(t,xyz,num_point,precision);
|
| 379 |
|
|
num_point=num_point*2;
|
| 380 |
|
|
}
|
| 381 |
|
|
while (code==0);
|
| 382 |
|
|
}
|
| 383 |
|
|
|
| 384 |
|
|
int ST_B_SPLINE::inverser2(double& t,double *xyz,int num_test,double precision)
|
| 385 |
|
|
{
|
| 386 |
|
|
double xyz1[3];
|
| 387 |
|
|
double dxyz1[3];
|
| 388 |
|
|
double ddxyz1[3];
|
| 389 |
|
|
double ti;
|
| 390 |
|
|
double eps;
|
| 391 |
|
|
double tmin=get_tmin();
|
| 392 |
|
|
double tmax=get_tmax();
|
| 393 |
|
|
OT_VECTEUR_3D Pt(xyz[0],xyz[1],xyz[2]);
|
| 394 |
|
|
double distance_ref=1e308;
|
| 395 |
|
|
int ref;
|
| 396 |
|
|
|
| 397 |
|
|
for (int i=0;i<num_test+1;i++)
|
| 398 |
|
|
{
|
| 399 |
|
|
double t=tmin+i*1./num_test*(tmax-tmin);
|
| 400 |
|
|
evaluer(t,xyz1);
|
| 401 |
|
|
OT_VECTEUR_3D Ct(xyz1[0],xyz1[1],xyz1[2]);
|
| 402 |
|
|
OT_VECTEUR_3D Distance = Ct-Pt;
|
| 403 |
|
|
double longueur=Distance.get_longueur2();
|
| 404 |
|
|
if (longueur<distance_ref)
|
| 405 |
|
|
{
|
| 406 |
|
|
distance_ref=longueur;
|
| 407 |
|
|
ref=i;
|
| 408 |
|
|
}
|
| 409 |
|
|
}
|
| 410 |
|
|
|
| 411 |
|
|
double tii=tmin+ref*1./num_test*(tmax-tmin);
|
| 412 |
|
|
int compteur=0;
|
| 413 |
|
|
do
|
| 414 |
|
|
{
|
| 415 |
|
|
compteur++;
|
| 416 |
|
|
ti=tii;
|
| 417 |
|
|
deriver_seconde(ti,ddxyz1,dxyz1,xyz1);
|
| 418 |
|
|
OT_VECTEUR_3D Ct(xyz1[0],xyz1[1],xyz1[2]);
|
| 419 |
|
|
OT_VECTEUR_3D Ct_deriver(dxyz1[0],dxyz1[1],dxyz1[2]);
|
| 420 |
|
|
OT_VECTEUR_3D Ct_deriver_seconde(ddxyz1[0],ddxyz1[1],ddxyz1[2]);
|
| 421 |
|
|
OT_VECTEUR_3D Distance = Ct-Pt;
|
| 422 |
|
|
tii=ti-Ct_deriver*Distance/(Ct_deriver_seconde*Distance+Ct_deriver.get_longueur2());
|
| 423 |
|
|
if (periodique==1)
|
| 424 |
|
|
{
|
| 425 |
|
|
if (tii<get_tmin()) tii=get_tmax()-(get_tmin()-tii);
|
| 426 |
|
|
if (tii>get_tmax()) tii=get_tmin()+(tii-get_tmax());
|
| 427 |
|
|
}
|
| 428 |
|
|
else
|
| 429 |
|
|
{
|
| 430 |
|
|
if (tii<get_tmin()) tii=get_tmin();
|
| 431 |
|
|
if (tii>get_tmax()) tii=get_tmax();
|
| 432 |
|
|
}
|
| 433 |
|
|
eps=fabs(tii-ti);
|
| 434 |
|
|
if (compteur>500) return 0;
|
| 435 |
|
|
}
|
| 436 |
|
|
while (eps>precision);
|
| 437 |
|
|
t=ti;
|
| 438 |
|
|
if ((periodique==1) && (OPERATEUR::egal(t,get_tmax(),1e-12)) t=get_tmin();
|
| 439 |
|
|
return 1;
|
| 440 |
|
|
}
|
| 441 |
|
|
|
| 442 |
|
|
double ST_B_SPLINE::get_tmin()
|
| 443 |
|
|
{
|
| 444 |
|
|
return knots[0];
|
| 445 |
|
|
}
|
| 446 |
|
|
double ST_B_SPLINE::get_tmax()
|
| 447 |
|
|
{
|
| 448 |
|
|
int i=knots.size();
|
| 449 |
|
|
return knots[i-1];
|
| 450 |
|
|
}
|
| 451 |
|
|
|
| 452 |
|
|
double equation_longueur(ST_B_SPLINE& bsp,double t)
|
| 453 |
|
|
{
|
| 454 |
|
|
double dxyz[3];
|
| 455 |
|
|
bsp.deriver(t,dxyz);
|
| 456 |
|
|
return sqrt(dxyz[0]*dxyz[0]+dxyz[1]*dxyz[1]+dxyz[2]*dxyz[2]);
|
| 457 |
|
|
}
|
| 458 |
|
|
|
| 459 |
|
|
|
| 460 |
|
|
double ST_B_SPLINE::get_longueur(double t1,double t2,double precis)
|
| 461 |
|
|
{
|
| 462 |
|
|
TPL_FONCTION1<double,ST_B_SPLINE,double> longueur_bsp(*this,equation_longueur);
|
| 463 |
|
|
return longueur_bsp.integrer_gauss_2(t1,t2);
|
| 464 |
|
|
}
|
| 465 |
|
|
|
| 466 |
|
|
|
| 467 |
|
|
int ST_B_SPLINE::est_periodique(void)
|
| 468 |
|
|
{
|
| 469 |
|
|
return periodique;
|
| 470 |
|
|
}
|
| 471 |
|
|
double ST_B_SPLINE::get_periode(void)
|
| 472 |
|
|
{
|
| 473 |
|
|
return periode;
|
| 474 |
|
|
}
|
| 475 |
|
|
|
| 476 |
|
|
int ST_B_SPLINE::get_type_geometrique(TPL_LISTE_ENTITE<double> ¶m)
|
| 477 |
|
|
{
|
| 478 |
|
|
for(int i=0;i<nb_point-(degre+1);i++)
|
| 479 |
|
|
{
|
| 480 |
|
|
param.ajouter(knots[i]);
|
| 481 |
|
|
}
|
| 482 |
|
|
double xyz[3];
|
| 483 |
|
|
for(int i=0;i<nb_point;i++)
|
| 484 |
|
|
{
|
| 485 |
|
|
xyz[0]=ptsctr[3*i];
|
| 486 |
|
|
xyz[1]=ptsctr[3*i+1];
|
| 487 |
|
|
xyz[2]=ptsctr[3*i+2];
|
| 488 |
|
|
param.ajouter(xyz[0]);
|
| 489 |
|
|
param.ajouter(xyz[1]);
|
| 490 |
|
|
param.ajouter(xyz[2]);
|
| 491 |
|
|
}
|
| 492 |
|
|
for(int i=0;i<nb_point;i++)
|
| 493 |
|
|
{
|
| 494 |
|
|
param.ajouter(poids[i]);
|
| 495 |
|
|
}
|
| 496 |
|
|
param.ajouter(degre);
|
| 497 |
|
|
return MGCo_BSPLINE;
|
| 498 |
|
|
}
|
| 499 |
|
|
|
| 500 |
|
|
void ST_B_SPLINE::initialiser(ST_GESTIONNAIRE *gest)
|
| 501 |
|
|
{
|
| 502 |
|
|
int i=indexptsctr.size();
|
| 503 |
|
|
ST_POINT* point1=gest->lst_point.getid(indexptsctr[0]);
|
| 504 |
|
|
ST_POINT* point2=gest->lst_point.getid(indexptsctr[i-1]);
|
| 505 |
|
|
double xyz1[3];
|
| 506 |
|
|
double xyz2[3];
|
| 507 |
|
|
point1->evaluer(xyz1);
|
| 508 |
|
|
point2->evaluer(xyz2);
|
| 509 |
|
|
periodique=0;
|
| 510 |
|
|
if (OPERATEUR::egal (xyz1[0],xyz2[0],1E-6))
|
| 511 |
|
|
{
|
| 512 |
|
|
if (OPERATEUR::egal (xyz1[1],xyz2[1],1E-6))
|
| 513 |
|
|
{
|
| 514 |
|
|
if (OPERATEUR::egal (xyz1[2],xyz2[2],1E-6))
|
| 515 |
|
|
periodique=1;
|
| 516 |
|
|
}
|
| 517 |
|
|
}
|
| 518 |
|
|
|
| 519 |
|
|
if (periodique==1)
|
| 520 |
|
|
{
|
| 521 |
|
|
int i=knots.size();
|
| 522 |
|
|
periode=(knots[i-1]-knots[0]);
|
| 523 |
|
|
}
|
| 524 |
|
|
else periode=0;
|
| 525 |
|
|
|
| 526 |
|
|
int nbptsctr=indexptsctr.size();
|
| 527 |
|
|
for (int i=0;i<nbptsctr;i++)
|
| 528 |
|
|
{
|
| 529 |
|
|
ST_POINT* stpoint=gest->lst_point.getid(indexptsctr[i]);
|
| 530 |
|
|
double xyz[3];
|
| 531 |
|
|
stpoint->evaluer(xyz);
|
| 532 |
|
|
ptsctr.insert(ptsctr.end(),xyz[0]);
|
| 533 |
|
|
ptsctr.insert(ptsctr.end(),xyz[1]);
|
| 534 |
|
|
ptsctr.insert(ptsctr.end(),xyz[2]);
|
| 535 |
|
|
}
|
| 536 |
|
|
}
|
| 537 |
|
|
|
| 538 |
|
|
|
| 539 |
|
|
|
| 540 |
|
|
|
| 541 |
|
|
|
| 542 |
|
|
void ST_B_SPLINE::est_util(ST_GESTIONNAIRE* gest)
|
| 543 |
|
|
{
|
| 544 |
|
|
util=true;
|
| 545 |
|
|
for (int i=0;i<nb_point;i++)
|
| 546 |
|
|
gest->lst_point.getid(indexptsctr[i])->est_util(gest);
|
| 547 |
|
|
}
|
| 548 |
|
|
|
