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//####//------------------------------------------------------------ |
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//####//------------------------------------------------------------ |
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//####// MAGiC |
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//####// Jean Christophe Cuilliere et Vincent FRANCOIS |
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//####// Departement de Genie Mecanique - UQTR |
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//####//------------------------------------------------------------ |
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//####// MAGIC est un projet de recherche de l equipe ERICCA |
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//####// du departement de genie mecanique de l Universite du Quebec a Trois Rivieres |
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//####// http://www.uqtr.ca/ericca |
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//####// http://www.uqtr.ca/ |
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//####//------------------------------------------------------------ |
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//####//------------------------------------------------------------ |
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//####// |
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//####// vct_outils.cpp |
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//####// |
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//####//------------------------------------------------------------ |
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//####//------------------------------------------------------------ |
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//####// COPYRIGHT 2000-2024 |
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//####// jeu 13 jun 2024 11:54:00 EDT |
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//####//------------------------------------------------------------ |
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//####//------------------------------------------------------------ |
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|
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#pragma hdrstop |
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|
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#include "vct_outils.h" |
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#pragma package(smart_init) |
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|
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VCT_OUTILS::VCT_OUTILS(double ord):ordre(ord) |
| 29 |
{ |
| 30 |
|
| 31 |
} |
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|
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double2 VCT_OUTILS::get_moment_dans_plan (double2 theta,std::vector<OT_VECTEUR_4DD>& ctrpts,int plan) |
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{ |
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|
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int nb_pts=ctrpts.size(); |
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|
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|
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|
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|
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double2 zer=0.; |
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double2 sum=0.; |
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for (int i=0;i<nb_pts;i++) |
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{ |
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//thi[i]=thi[i]*PI/180; |
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//double2 nori=ctrpts[i].norme(); |
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double2 x=ctrpts[i].x()^2; |
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double2 y=ctrpts[i].y()^2; |
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double2 z=ctrpts[i].z()^2; |
| 50 |
double2 nori; |
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|
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// double2 nori=ctrpts[i].norme(); |
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double2 cosi=0.; |
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double2 sini=0.; |
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if (plan==12) |
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{ |
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nori=(x+y)^0.5; |
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if (nori!=zer) { |
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cosi=ctrpts[i].get_x()/nori; |
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sini=ctrpts[i].get_y()/nori; |
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} |
| 62 |
} |
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if (plan==23) |
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{ |
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nori=(y+z)^0.5; |
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if (nori!=zer) { |
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cosi=ctrpts[i].get_y()/nori; |
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sini=ctrpts[i].get_z()/nori; |
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} |
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|
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} |
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if (plan==13) |
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{ |
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nori=(x+z)^0.5; |
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if (nori!=zer) { |
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cosi=ctrpts[i].get_x()/nori; |
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sini=ctrpts[i].get_z()/nori; |
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} |
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} |
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double2 costh=cos(theta); |
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double2 sinth=sin(theta); |
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double2 d_theta=sini*costh-cosi*sinth; |
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//sum=sum+ pow(li[i],4)*pow(d_theta,4); |
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double2 val1=nori^ordre; |
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double2 val2=d_theta^ordre; |
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double2 val=val1*val2; |
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sum=sum+ val; |
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} |
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return sum; |
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} |
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|
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|
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double2 VCT_OUTILS:: get_max(double2 a,double2 b) |
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{ |
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return((a<b)? b : a); |
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} |
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|
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double2 VCT_OUTILS:: get_min(double2 a,double2 b) |
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{ |
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return ((a>b)? b : a); |
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} |
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|
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double2 VCT_OUTILS::get_signe(double2 a,double2 b) |
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{ |
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double2 zer=0.; |
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double2 c=-1.; |
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if (b>=zer) |
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return a; |
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else |
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return c*a; |
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} |
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|
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void VCT_OUTILS::get_permutation(double2& a,double2& b) |
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{ |
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double2 tmp; |
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tmp = a; |
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a = b; |
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b = tmp; |
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} |
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void VCT_OUTILS::get_shift(double2&a,double2&b,double2&c,double2 d) |
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{ |
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a=b; |
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b=c; |
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c=d; |
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} |
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|
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void VCT_OUTILS::get_minimum_de_Brak(double2 &ax,double2 &bx,double2 &cx,double2 &fa,double2 &fb,double2 &fc,std::vector<OT_VECTEUR_4DD>& ctrpts,int plan) |
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{ |
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static const double2 GOLD=1.618034; |
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static const double2 GLIMIT=100.0; |
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static const double2 TINY=1.0e-20; |
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double2 ulim,u,r,q,fu; |
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//double2(*func)(double2,vector<OT_VECTEUR_4DD>&,int)=&moment; |
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double2 dtheta=0.0001; |
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|
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//aptimisation de la valeur de theta |
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|
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int idx_pts_depart1=-1; |
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int idx_pts_depart2=-1; |
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int nb_pts=ctrpts.size(); |
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double2 min_y; |
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double2 min_x; |
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int cfait1=-1; |
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int cfait2=-1; |
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int indx1,indx2; |
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if (plan==12) { |
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indx1=0; |
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indx2=1; |
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} |
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if (plan==23) { |
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indx1=1; |
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indx2=2; |
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} |
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if (plan==13) { |
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indx1=0; |
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indx2=2; |
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} |
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|
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OT_VECTEUR_4DD bary; |
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for (int i=0;i<nb_pts;i++) |
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{ |
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bary=bary+ctrpts[i]; |
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} |
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bary=1./nb_pts*bary; |
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/* |
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|
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for (int i=0;i<nb_pts;i++) |
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{ |
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ctrpts[i]=ctrpts[i]-bary; |
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OT_VECTEUR_4DD pt=ctrpts[i]; |
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if (pt[indx1]>dtheta&&pt[indx2]>dtheta) |
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{ |
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if (cfait1<0) |
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{ |
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min_y=pt[indx2]; |
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idx_pts_depart1=i; |
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cfait1=1; |
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} |
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if(pt[indx2]<min_y){ |
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min_y=pt[indx2]; |
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idx_pts_depart1=i; |
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} |
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} |
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|
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if (pt[indx1]>dtheta&&pt[indx2]>dtheta) |
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{ |
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if(cfait2<0) |
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{ |
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min_x=pt[indx1]; |
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idx_pts_depart2=i; |
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cfait2=1; |
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} |
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if(pt[indx1]<min_x){ |
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min_x=pt[indx1]; |
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idx_pts_depart2=i; |
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} |
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} |
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|
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} |
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int idx_pts_depart; |
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if(idx_pts_depart1>=0) idx_pts_depart= idx_pts_depart1; |
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else idx_pts_depart= idx_pts_depart2; |
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OT_VECTEUR_4DD dept=ctrpts[idx_pts_depart]; |
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|
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double2 theta_depart=atan(dept[indx2]/dept[indx1]); |
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|
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ax=theta_depart;//0.; */ |
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ax=0.; |
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bx=ax+dtheta; |
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cx=bx+dtheta; |
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double2 fva=get_moment_dans_plan(ax,ctrpts,plan);//(*func)(ax,ctrpts,plan); |
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double2 fvb=get_moment_dans_plan(bx,ctrpts,plan);//(*func)(bx,ctrpts,plan); |
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double2 fvc=get_moment_dans_plan(cx,ctrpts,plan);//(*func)(cx,ctrpts,plan); |
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cx=cx+dtheta; |
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double2 fvc_plus_dth=get_moment_dans_plan(cx,ctrpts,plan); |
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|
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while (fvb> fva) |
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{ |
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ax=bx; |
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bx=ax+dtheta; |
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fva=get_moment_dans_plan(ax,ctrpts,plan);//(*func)(ax,ctrpts,plan); |
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fvb=get_moment_dans_plan(bx,ctrpts,plan);//(*func)(bx,ctrpts,plan); |
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} |
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|
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if (fvb<fva) |
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{ |
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cx=bx+dtheta; |
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while (fvb> fvc) |
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{ |
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bx=cx; |
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cx=bx+dtheta; |
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fvb=get_moment_dans_plan(bx,ctrpts,plan);//(*func)(bx,ctrpts,plan); |
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fvc=get_moment_dans_plan(cx,ctrpts,plan);//(*func)(cx,ctrpts,plan); |
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} |
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} |
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|
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fa=get_moment_dans_plan(ax,ctrpts,plan);//(*func)(ax,ctrpts,plan); |
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fb=get_moment_dans_plan(bx,ctrpts,plan);//(*func)(bx,ctrpts,plan); |
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if (fb>fa) |
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{ |
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std::swap(ax,bx); |
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std::swap(fb,fa); |
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} |
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cx=bx+GOLD*(bx-ax); |
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fc=get_moment_dans_plan(cx,ctrpts,plan);//(*func)(cx,ctrpts,plan); |
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double2 d=2.; |
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double2 zer=0.; |
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while (fb>fc) |
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{ |
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r=(bx-ax)*(fb-fc); |
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q=(bx-cx)*(fb-fa); |
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u=bx-((bx-cx)*q-(bx-ax)*r)/(d*get_signe(get_max((q-r).get_fabs(),TINY),q-r));//(d*Sign(Max(abs(q-r),TINY),q-r)); |
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ulim=bx+GLIMIT*(cx-bx); |
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if ((bx-u)*(u-cx)>zer) |
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{ |
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fu=get_moment_dans_plan(u,ctrpts,plan);//(*func)(u,ctrpts,plan); |
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if (fu<fc) |
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{ |
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ax=bx; |
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bx=u; |
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fa=fb; |
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fb=fu; |
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return; |
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} |
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else if (fu>fb) |
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{ |
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cx=u; |
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fc=fu; |
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return; |
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} |
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u=cx+GOLD*(cx-bx); |
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fu=get_moment_dans_plan(u,ctrpts,plan); |
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} |
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else if ((cx-u)*(u-ulim)>zer) |
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{ |
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fu=get_moment_dans_plan(u,ctrpts,plan); |
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if (fu<fc) |
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{ |
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bx=cx; |
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cx=u; |
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u=cx+GOLD*(cx-bx); |
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get_shift(fb,fc,fu,get_moment_dans_plan(u,ctrpts,plan)); |
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} |
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} |
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else if ((u-ulim)*(ulim-cx)>=zer) |
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{ |
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u=ulim; |
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fu=get_moment_dans_plan(u,ctrpts,plan); |
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} |
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else |
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{ |
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u=cx+GOLD*(cx-bx); |
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fu=get_moment_dans_plan(u,ctrpts,plan); |
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} |
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get_shift(ax,bx,cx,u); |
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get_shift(fa,fb,fc,fu); |
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} |
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} |
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|
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|
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|
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|
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std::vector<OT_VECTEUR_4DD> VCT_OUTILS::get_system_axes(std::vector<OT_VECTEUR_4DD>& ctrpts) |
| 304 |
{ |
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double e1_proj[3]; |
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double e2_proj[3]; |
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double normal_palan_project[3]; |
| 308 |
double normal_au_plan[3]; |
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double theta,c,s; |
| 310 |
double root[3]={0.,0.,0.}; |
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OT_ALGORITHME_GEOMETRIQUE algo; |
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int pris=0; |
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OT_MATRICE_3D P, P_1; |
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|
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std::vector<OT_VECTEUR_4DD> syst_axe; |
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int nb_points=ctrpts.size(); |
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std::vector<OT_VECTEUR_4DD> ctrpts_proj; |
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OT_VECTEUR_4DD axe1,axe2,axe3,axe4; |
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double2 ax,bx,cx,fa,fb,fc; |
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int plan=12; |
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|
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double2 z0=ctrpts[0].get_z() ; |
| 323 |
double2 y0=ctrpts[0].get_y() ; |
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double2 x0=ctrpts[0].get_x() ; |
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|
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int cmpt1=0; |
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int cmpt2=0; |
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int cmpt3=0; |
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for (int i=0;i<nb_points;i++) |
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{ |
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if (ctrpts[i].get_x()==x0) cmpt1++; |
| 332 |
if (ctrpts[i].get_y()==y0) cmpt2++; |
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if (ctrpts[i].get_z()==z0) cmpt3++; |
| 334 |
} |
| 335 |
|
| 336 |
if (cmpt1==nb_points) { |
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plan=23; |
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normal_au_plan[0]=1.; |
| 339 |
normal_au_plan[1]=0.; |
| 340 |
normal_au_plan[2]=0.; |
| 341 |
} |
| 342 |
if (cmpt2==nb_points) { |
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plan=13; |
| 344 |
normal_au_plan[0]=0.; |
| 345 |
normal_au_plan[1]=1.; |
| 346 |
normal_au_plan[2]=0.; |
| 347 |
} |
| 348 |
if (cmpt3==nb_points) { |
| 349 |
plan=12; |
| 350 |
normal_au_plan[0]=0.; |
| 351 |
normal_au_plan[1]=0.; |
| 352 |
normal_au_plan[2]=1.; |
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} |
| 354 |
|
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|
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get_minimum_de_Brak(ax,bx,cx,fa,fb,fc,ctrpts,plan); |
| 357 |
|
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theta= bx.get_x(); |
| 359 |
if (theta==1e-6) theta=0.; |
| 360 |
c=cos(theta); |
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s=sin(theta); |
| 362 |
|
| 363 |
if (plan==12) |
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{ |
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axe1.change_x(c); |
| 366 |
axe1.change_y(s); |
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axe1.change_z(0.); |
| 368 |
axe1.change_w(0.); |
| 369 |
|
| 370 |
axe2.change_x(-s); |
| 371 |
axe2.change_y(c); |
| 372 |
axe2.change_z(0); |
| 373 |
axe2.change_w(0); |
| 374 |
} |
| 375 |
if (plan==13) |
| 376 |
{ |
| 377 |
axe1.change_x(c); |
| 378 |
axe1.change_y(0.); |
| 379 |
axe1.change_z(s); |
| 380 |
axe1.change_w(0.); |
| 381 |
|
| 382 |
axe2.change_x(-s); |
| 383 |
axe2.change_y(0); |
| 384 |
axe2.change_z(c); |
| 385 |
axe2.change_w(0); |
| 386 |
} |
| 387 |
if (plan==23) |
| 388 |
{ |
| 389 |
axe1.change_x(0); |
| 390 |
axe1.change_y(c); |
| 391 |
axe1.change_z(s); |
| 392 |
axe1.change_w(0.); |
| 393 |
|
| 394 |
axe2.change_x(0); |
| 395 |
axe2.change_y(-s); |
| 396 |
axe2.change_z(c); |
| 397 |
axe2.change_w(0); |
| 398 |
} |
| 399 |
|
| 400 |
if (cmpt1==nb_points||cmpt2==nb_points||cmpt3==nb_points) |
| 401 |
{ |
| 402 |
|
| 403 |
axe3[0]=normal_au_plan[0]; |
| 404 |
axe3[1]=normal_au_plan[1]; |
| 405 |
axe3[2]=normal_au_plan[2]; |
| 406 |
|
| 407 |
syst_axe.insert( syst_axe.end(),axe1); |
| 408 |
syst_axe.insert( syst_axe.end(),axe2); |
| 409 |
syst_axe.insert( syst_axe.end(),axe3); |
| 410 |
|
| 411 |
return syst_axe; |
| 412 |
} |
| 413 |
|
| 414 |
normal_palan_project[0] =s; |
| 415 |
normal_palan_project[1] =-c; |
| 416 |
normal_palan_project[2] =0.; |
| 417 |
|
| 418 |
|
| 419 |
for (int i=0;i<nb_points;i++) |
| 420 |
{ |
| 421 |
OT_VECTEUR_4DD pt_proj; |
| 422 |
double pnt[3]; |
| 423 |
double proj_pnt[3]; |
| 424 |
|
| 425 |
pnt[0] =(ctrpts[i].get_x()).get_x(); |
| 426 |
pnt[1] =(ctrpts[i].get_y()).get_x(); |
| 427 |
pnt[2] =(ctrpts[i].get_z()).get_x(); |
| 428 |
|
| 429 |
algo.Proj3D_Point_Plan (normal_palan_project, root, pnt, proj_pnt); |
| 430 |
|
| 431 |
if ((proj_pnt[0]!=0.||proj_pnt[1]!=0.||proj_pnt[2]!=0)&&!pris) |
| 432 |
{ |
| 433 |
e1_proj[0]=proj_pnt[0]; |
| 434 |
e1_proj[1]=proj_pnt[1]; |
| 435 |
e1_proj[2]=proj_pnt[2]; |
| 436 |
double norm=sqrt(pow(proj_pnt[0],2)+pow(proj_pnt[1],2)+pow(proj_pnt[2],2)); |
| 437 |
|
| 438 |
e1_proj[0]=e1_proj[0]/norm; |
| 439 |
e1_proj[1]=e1_proj[1]/norm; |
| 440 |
e1_proj[2]=e1_proj[2]/norm; |
| 441 |
|
| 442 |
e2_proj[0]=normal_palan_project[1]*e1_proj[2]-normal_palan_project[2]*e1_proj[1]; |
| 443 |
e2_proj[1]=normal_palan_project[2]*e1_proj[0]-normal_palan_project[0]*e1_proj[2]; |
| 444 |
e2_proj[2]=normal_palan_project[0]*e1_proj[1]-normal_palan_project[1]*e1_proj[0]; |
| 445 |
|
| 446 |
OT_VECTEUR_3D V1(e1_proj[0],e2_proj[0],normal_palan_project[0]); |
| 447 |
OT_VECTEUR_3D V2(e1_proj[1],e2_proj[1],normal_palan_project[1]); |
| 448 |
OT_VECTEUR_3D V3(e1_proj[2],e2_proj[2],normal_palan_project[2]); |
| 449 |
|
| 450 |
P.change_vecteur1(V1); |
| 451 |
P.change_vecteur2(V2); |
| 452 |
P.change_vecteur3(V3); |
| 453 |
|
| 454 |
P_1=P.inverse(); |
| 455 |
pris=1; |
| 456 |
} |
| 457 |
|
| 458 |
OT_VECTEUR_3D V_PT(proj_pnt[0],proj_pnt[1],proj_pnt[2]); |
| 459 |
|
| 460 |
OT_VECTEUR_3D V=P_1*V_PT; |
| 461 |
|
| 462 |
|
| 463 |
pt_proj.change_x(V[0]); |
| 464 |
pt_proj.change_y(V[1]); |
| 465 |
pt_proj.change_z(V[2]); |
| 466 |
|
| 467 |
ctrpts_proj.insert(ctrpts_proj.end(),pt_proj); |
| 468 |
} |
| 469 |
|
| 470 |
get_minimum_de_Brak(ax,bx,cx,fa,fb,fc,ctrpts_proj,plan); |
| 471 |
|
| 472 |
theta= bx.get_x(); |
| 473 |
c=cos(theta); |
| 474 |
s=sin(theta); |
| 475 |
OT_VECTEUR_3D Vp(c,s,0.); |
| 476 |
double nnv_x=Vp*P.get_vecteur1(); |
| 477 |
double nnv_y=Vp*P.get_vecteur2(); |
| 478 |
double nnv_z=Vp*P.get_vecteur3(); |
| 479 |
|
| 480 |
axe2.change_x(nnv_x); |
| 481 |
axe2.change_y(nnv_y); |
| 482 |
axe2.change_z(nnv_z); |
| 483 |
|
| 484 |
double2 val=axe1*axe2; |
| 485 |
|
| 486 |
axe3[0]=axe1[1]*axe2[2]-axe1[2]*axe2[1]; |
| 487 |
axe3[1]=axe1[2]*axe2[0]-axe1[2]*axe2[2]; |
| 488 |
axe3[2]=axe1[0]*axe2[1]-axe1[2]*axe2[0]; |
| 489 |
|
| 490 |
axe3[3]=0.; |
| 491 |
|
| 492 |
|
| 493 |
syst_axe.insert( syst_axe.end(),axe1); |
| 494 |
syst_axe.insert( syst_axe.end(),axe2); |
| 495 |
syst_axe.insert( syst_axe.end(),axe3); |
| 496 |
|
| 497 |
return syst_axe; |
| 498 |
} |
| 499 |
|
| 500 |
|
| 501 |
|
| 502 |
|
| 503 |
OT_MATRICE_3D VCT_OUTILS::get_system_axes(OT_VECTEUR_4DD& root,std::vector<OT_VECTEUR_4DD>& axes,std::vector<OT_VECTEUR_4DD>& ctrpts) |
| 504 |
{ |
| 505 |
|
| 506 |
double normal_palan_project[3]; |
| 507 |
double origine[3]; |
| 508 |
double2 ax,bx,cx,fa,fb,fc; |
| 509 |
double theta,cosin,sinus; |
| 510 |
OT_MATRICE_3D p,qT, pT,q; |
| 511 |
std::vector<OT_VECTEUR_4DD> ctrpts_proj; |
| 512 |
std::vector<OT_VECTEUR_4DD> syst_axe; |
| 513 |
int nb_points=ctrpts.size(); |
| 514 |
OT_ALGORITHME_GEOMETRIQUE algo; |
| 515 |
|
| 516 |
normal_palan_project[0] =(axes[2].get_x()).get_x(); |
| 517 |
normal_palan_project[1] =(axes[2].get_y()).get_x(); |
| 518 |
normal_palan_project[2] =(axes[2].get_z()).get_x(); |
| 519 |
origine[0] =root[0].get_x(); |
| 520 |
origine[1] =root[1].get_x(); |
| 521 |
origine[2] =root[2].get_x(); |
| 522 |
|
| 523 |
OT_VECTEUR_3D V1((axes[0].get_x()).get_x(),(axes[0].get_y()).get_x(),(axes[0].get_z()).get_x()); |
| 524 |
OT_VECTEUR_3D V2((axes[1].get_x()).get_x(),(axes[1].get_y()).get_x(),(axes[1].get_z()).get_x()); |
| 525 |
OT_VECTEUR_3D V3((axes[2].get_x()).get_x(),(axes[2].get_y()).get_x(),(axes[2].get_z()).get_x()); |
| 526 |
|
| 527 |
p.change_vecteur1(V1); |
| 528 |
p.change_vecteur2(V2); |
| 529 |
p.change_vecteur3(V3); |
| 530 |
pT=p.transpose(); |
| 531 |
|
| 532 |
for (int i=0;i<nb_points;i++) |
| 533 |
{ |
| 534 |
OT_VECTEUR_4DD pt_proj; |
| 535 |
double point[3]; |
| 536 |
double proj_pnt[3]; |
| 537 |
|
| 538 |
|
| 539 |
point[0] =(ctrpts[i].get_x()).get_x(); |
| 540 |
point[1] =(ctrpts[i].get_y()).get_x(); |
| 541 |
point[2] =(ctrpts[i].get_z()).get_x(); |
| 542 |
|
| 543 |
algo.Proj3D_Point_Plan (normal_palan_project, origine, point, proj_pnt); |
| 544 |
for (int i=0;i<3;i++) |
| 545 |
{ |
| 546 |
proj_pnt[i]-= origine[i]; |
| 547 |
} |
| 548 |
|
| 549 |
OT_VECTEUR_3D V_PT(proj_pnt[0],proj_pnt[1],proj_pnt[2]); |
| 550 |
|
| 551 |
OT_VECTEUR_3D V=pT*V_PT; |
| 552 |
|
| 553 |
|
| 554 |
pt_proj.change_x(V[0]); |
| 555 |
pt_proj.change_y(V[1]); |
| 556 |
pt_proj.change_z(V[2]); |
| 557 |
|
| 558 |
ctrpts_proj.insert(ctrpts_proj.end(),pt_proj); |
| 559 |
|
| 560 |
} |
| 561 |
|
| 562 |
get_minimum_de_Brak(ax,bx,cx,fa,fb,fc,ctrpts_proj,12); |
| 563 |
|
| 564 |
theta= bx.get_x(); |
| 565 |
cosin=cos(theta); |
| 566 |
sinus=sin(theta); |
| 567 |
|
| 568 |
OT_VECTEUR_4DD e1,e2,e3; |
| 569 |
|
| 570 |
e1.change_x(cosin); |
| 571 |
e1.change_y(sinus); |
| 572 |
e1.change_z(0.); |
| 573 |
e1.change_w(0.); |
| 574 |
|
| 575 |
e2.change_x(-sinus); |
| 576 |
e2.change_y(cosin); |
| 577 |
e2.change_z(0); |
| 578 |
e2.change_w(0); |
| 579 |
e3=e1^e2; |
| 580 |
|
| 581 |
|
| 582 |
|
| 583 |
|
| 584 |
V1.change_x(cosin); |
| 585 |
V1.change_y(sinus); |
| 586 |
V1.change_z(0); |
| 587 |
|
| 588 |
V2.change_x((e2[0].get_x())); |
| 589 |
V2.change_y((e2[1].get_x())); |
| 590 |
V2.change_z((e2[2].get_x())); |
| 591 |
|
| 592 |
V3.change_x((e3[0].get_x())); |
| 593 |
V3.change_y((e3[1].get_x())); |
| 594 |
V3.change_z((e3[2].get_x())); |
| 595 |
q.change_vecteur1(V1); |
| 596 |
q.change_vecteur2(V2); |
| 597 |
q.change_vecteur3(V3); |
| 598 |
qT=q.transpose(); |
| 599 |
syst_axe.insert( syst_axe.end(),e1); |
| 600 |
syst_axe.insert( syst_axe.end(),e2); |
| 601 |
syst_axe.insert( syst_axe.end(),e3); |
| 602 |
|
| 603 |
OT_MATRICE_3D w=p*q; //les vecteurs de la base est en colone |
| 604 |
//w=w.inverse(); |
| 605 |
|
| 606 |
return w; |
| 607 |
} |
| 608 |
|
| 609 |
|
| 610 |
|
| 611 |
OT_VECTEUR_4DD VCT_OUTILS::get_plan_medien(std::vector<OT_VECTEUR_4DD>& ctrpts) |
| 612 |
{ |
| 613 |
int nb_pts=ctrpts.size(); |
| 614 |
OT_MATRICE_3D p; |
| 615 |
OT_VECTEUR_3D v; |
| 616 |
for (int i=0;i<nb_pts;i++) |
| 617 |
{ |
| 618 |
OT_VECTEUR_4DD pt=ctrpts[i]; |
| 619 |
p(0,0)=p(0,0)+pt[0].get_x()*pt[0].get_x(); |
| 620 |
p(0,1)=p(0,0)+pt[0].get_x()*pt[1].get_x(); |
| 621 |
p(0,2)=p(0,0)+pt[0].get_x(); |
| 622 |
p(1,1)=p(0,0)+pt[1].get_x()*pt[1].get_x(); |
| 623 |
p(1,2)=p(0,0)+pt[1].get_x(); |
| 624 |
v[0]=v[0]+pt[0].get_x()*pt[2].get_x(); |
| 625 |
v[1]=v[1]+pt[1].get_x()*pt[2].get_x(); |
| 626 |
v[2]=v[1]+pt[2].get_x(); |
| 627 |
} |
| 628 |
p(1,0)=p(0,1); |
| 629 |
p(2,0)=p(0,2); |
| 630 |
p(2,1)=p(2,1); |
| 631 |
|
| 632 |
p=p.inverse(); |
| 633 |
OT_VECTEUR_3D param=p*v; |
| 634 |
OT_VECTEUR_4DD tparam(param[0],param[1],1,0.); |
| 635 |
tparam=tparam.vecteur_norme(); |
| 636 |
double2 nor= tparam.norme(); |
| 637 |
double2 prec=1e-5 ; |
| 638 |
for (int j=0;j<4;j++) |
| 639 |
{ |
| 640 |
if (tparam[j].get_fabs()<prec) |
| 641 |
tparam[j]=0.; |
| 642 |
} |
| 643 |
tparam[3]=tparam[3]/nor; |
| 644 |
return tparam; |
| 645 |
|
| 646 |
} |
