Mathc initiation/002o

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	x_juwv.h

/* --------------------------------- */
/* save as x_juwv.h                  */
/* --------------------------------- */
double Ju_uwv(
double (*P_f)(double x, double y, double z),

double (*P_X)(double u, double v, double w),
double (*P_Y)(double u, double v, double w),
double (*P_Z)(double u, double v, double w),

double (*Pu0)(double v, double w),
double (*Pu1)(double v, double w),
   int   nu,
   
double w,

double v
)
{
pt3d   p;

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

 for(i = 0; i <= nu; i++)
 {
       if(i ==0 || i== nu){m = 1.;}
  else if(fmod(i,2) ==  0){m = 2.;}
  else                    {m = 4.;}
  
  u = ((*Pu0)(v,w)) + i*(((*Pu1)(v,w))-((*Pu0)(v,w)))/nu;
  
 
  p.x = u;
  p.y = v;   
  p.z = w;    
     
  M += m * (*P_f)( ((*P_X)(u,v,w)), 
                   ((*P_Y)(u,v,w)), 
                   ((*P_Z)(u,v,w)))
                          *
                   /* Jacobian */   
                      
                    fabs(
                    
              fxyz_x((*P_X),H,p) 
                       * 
   ( fxyz_y((*P_Y),H,p)*fxyz_z((*P_Z),H,p)
                       -
     fxyz_z((*P_Y),H,p)*fxyz_y((*P_Z),H,p) ) 
     
                       - 
                                       
              fxyz_y((*P_X),H,p) 
                       * 
   ( fxyz_x((*P_Y),H,p)*fxyz_z((*P_Z),H,p)
                       -
     fxyz_z((*P_Y),H,p)*fxyz_x((*P_Z),H,p) )
     
                       + 
                                       
              fxyz_z((*P_X),H,p) 
                       * 
   ( fxyz_x((*P_Y),H,p)*fxyz_y((*P_Z),H,p)
                       -
     fxyz_y((*P_Y),H,p)*fxyz_x((*P_Z),H,p) )
                        );  
 }

  return( ((((*Pu1)(v,w)) -((*Pu0)(v,w)))*M) / (3*nu) );
}
/* --------------------------------- */
double Jw_uwv(
double (*P_f)(double x, double y, double z),

double (*P_X)(double u, double v, double w),
double (*P_Y)(double u, double v, double w),
double (*P_Z)(double u, double v, double w),
   
double (*Pu0)(double v, double w),
double (*Pu1)(double v, double w),
   int   nu,

double (*Pw0)(double v),
double (*Pw1)(double v),
   int   nv,
   
double v
)
{
   int i = 0;
double m = 0.;
double M = 0.;

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

  M += m *  Ju_uwv( (*P_f),
                    (*P_X),(*P_Y),(*P_Z),                            
                    (*Pu0),(*Pu1),nu,
                    (((*Pw0)(v))+i*(((*Pw1)(v))-((*Pw0)(v)))/nv),
                             v);
 }

 return( ((((*Pw1)(v)) -((*Pw0)(v)))*M) / (3*nv) );
}
/* --------------------------------- */
double J_uwv(
double (*P_f)(double x, double y, double z), 

double (*P_X)(double u, double v, double w),
double (*P_Y)(double u, double v, double w),
double (*P_Z)(double u, double v, double w),
   
double (*Pu0)(double v, double w),
double (*Pu1)(double v, double w),
int      nu,

double (*Pw0)(double v),
double (*Pw1)(double v),
   int   nw,


double v0,
double v1,
   int nv
)
{
   int i = 0;
double m = 0.;
double M = 0.;

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

  M += m *  Jw_uwv( (*P_f),
                    (*P_X),(*P_Y),(*P_Z),                                
                    (*Pu0),(*Pu1),nu,
                    (*Pw0),(*Pw1),nv,
                    (v0+i*(v1-v0)/nv));
 }

  return( ((v1 -v0)*M) / (3*nv) );
}
/* --------------------------------- */
/* --------------------------------- */