Mathc initiation/a444

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	x_ps_ts.h

/* ---------------------------------- */
/* save as x_ps_ts.h                  */
/* ---------------------------------- */
double paraSint_ts(

double (*P_Rx)(double s, double t),
double (*P_Ry)(double s, double t),
double (*P_Rz)(double s, double t),

double (*P_f)(double x, double y, double z),

double (*P_u)(double x),
double (*P_v)(double x),
   int    ny,
   
double     x
)
{
pt2d p;

   int i = 0;
double m = 0.;
double M = 0.;

 for(i = 0; i <= ny; i++)
 {
       if(i ==0 || i== ny){m = 1.;}
  else if(fmod(i,2) == 0){m = 2.;}
  else                   {m = 4.;}

 p.y = ((*P_u)(x)) + i*(((*P_v)(x))-((*P_u)(x)))/ny;
 p.x = x;

 M += m * (*P_f)((*P_Rx)(p.x,p.y), (*P_Ry)(p.x,p.y), (*P_Rz)(p.x,p.y))
                                  * 
                      N_Rs_x_Rt((*P_Rx),(*P_Ry), (*P_Rz),
                                     p);
 }

  return( ((((*P_v)(x)) -((*P_u)(x)))*M) / (3*ny) );
}
/* ---------------------------------- */
double parametricS_ts(

double (*P_Rx)(double s, double t),
double (*P_Ry)(double s, double t),
double (*P_Rz)(double s, double t),

double (*P_f)(double x, double y, double z),

double (*P_u)(double x),
double (*P_v)(double x),
   int    ny,

double ax,
double bx,
   int nx
)
{
   int i = 0;
double m = 0.;
double M = 0.;

 for(i = 0; i <= nx; i++)
 {
       if(i ==0 || i== nx){m = 1.;}
  else if(fmod(i,2) == 0){m = 2.;}
  else                   {m = 4.;}

  M += m * paraSint_ts( (*P_Rx),(*P_Ry),(*P_Rz),
                         (*P_f),
                         (*P_u),(*P_v),ny,
                         (ax + i*(bx-ax)/nx));
 }

  return( ((bx -ax)*M) / (3*nx) );
}
/* ---------------------------------- */
/* ---------------------------------- */