Mathc matrices/08z

Application

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	c00e.c

/* ------------------------------------ */
/*  Save as :   c00e.c                  */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */
#define   RAb R2
#define   CA  C3
#define   Cb  C1
#define   Rv  C3
/* ------------------------------------ */
# define FREEV C1
/* ------------------------------------ */
int main(void)
{
double ab[RAb*(CA+Cb)]={ 
+4, +3, -1,   -0, /* V1|0  See c00a.c */ 
-1, -1, +2,   -0  /* V2|0             */      
};

double Projp[Rv*C1] ={
 -6.454545454546, 
 -6.272727272728, 
+11.636363636364  
};

double **Ab      = ca_A_mR(ab, i_Abr_Ac_bc_mR(RAb, CA, Cb));
double **Ab_free =             i_Abr_Ac_bc_mR(CA,  CA, Cb + FREEV);
double **b_free  =                       i_mR(CA,      Cb + FREEV); 

double **A       =    c_Ab_A_mR(Ab,      i_mR(RAb, CA));  
double **At      = transpose_mR(A,       i_mR(CA, RAb));
 
double **vPp      =      ca_A_mR(Projp,   i_mR(Rv,C1));   
double **v1      =                       i_mR(Rv,C1); 
double **v2      =                       i_mR(Rv,C1);
double **vQ      =                       i_mR(Rv,C1);


/*  Compute the free variables (b_free) */
      gj_PP_mR(Ab,NO);                
  put_zeroR_mR(Ab,Ab_free);           
  put_freeV_mR(Ab_free); 
      gj_PP_mR(Ab_free,YES); 
     c_Ab_b_mR(Ab_free,b_free);    
  
  clrscrn();
  printf(" Compute the orthogonal vectors to:         (See c00a .c)\n\n" 
         " v1:");      
  p_mR(c_c_mR(At,(C1), v1,C1), S10,P4,C1);       
  printf(" v2:");      
  p_mR(c_c_mR(At,(C2), v2,C1), S10,P4,C1);

  printf(" vQ is orthogonal to the vectors v1 and v2.\n\n"
         " The equation of a plan defined by v1 and v2\n"
         " is ax + by + cz=0, where a,b,c are the coordinates\n"
         " of the vector orthogonal (vQ).\n\n"
         " vQ:");       
  p_mR(c_c_mR(b_free,C2, vQ,C1), S10,P12,C1);                     
  stop();

  clrscrn();
  printf(" vPp is the projection of a point P onto the plan (See c00d.c)\n\n"
         " vPp:");   
  p_mR(vPp, S10,P12,C1);   
  printf(" vQ is orthogonal to the plan defined by the vectors v1 and v2.\n\n"
         " vQ:");   
  p_mR(vQ, S10,P12,C1);   
  printf(" dot(vPp,vQ)  = %.9f\n\n"
         " The dot product of vQ and vPp say that the vector vPp   \n"
         " is orthogonal to the vector vQ. Then the point p is in\n"
         " the plan v1 and v2.\n\n",
           dot_R(vPp,vQ));    
  stop();  
  
  f_mR(Ab);
  f_mR(Ab_free);
  f_mR(b_free);
  f_mR(v1);          
  f_mR(v2);
  f_mR(vQ);
    
  return 0;
}
/* ------------------------------------ */
/* ------------------------------------ */

 Vérifiez si la projection d'un point P appartient au plan. Si la projection du point P, le vecteur vPp, est perpendiculaire au vecteur vQ, alors le produit scalaire de ces deux vecteurs est nul et le point Pp est bien dans le plan.

Exemple de sortie écran :

                                                       
 Compute the orthogonal vectors to:         (See c00a .c)

 v1:
   +4.0000 
   +3.0000 
   -1.0000 

 v2:
   -1.0000 
   -1.0000 
   +2.0000 

 vQ is orthogonal to the vectors v1 and v2.

 The equation of a plan defined by v1 and v2
 is ax + by + cz=0, where a,b,c are the coordinates
 of the vector orthogonal (vQ).

 vQ:
-5.000000000000 
+7.000000000000 
+1.000000000000 

 Press return to continue. 


 vPp is the projection of a point P onto the plan (See c00d.c)

 vPp:
-6.454545454546 
-6.272727272728 
+11.636363636364 

 vQ is orthogonal to the plan defined by the vectors v1 and v2.

 vQ:
-5.000000000000 
+7.000000000000 
+1.000000000000 

 dot(vPp,vQ)  = -0.000000000

 The dot product of vQ and vPp say that the vector vPp   
 is orthogonal to the vector vQ. Then the point p is in
 the plan v1 and v2.

 Press return to continue.