Mathc initiation/a220

Sommaire

Installer et compiler ces fichiers dans votre répertoire de travail.

	c00a.c

/* --------------------------------- */
/* save as c00a.c                    */
/* --------------------------------- */
#include "x_hfile.h"
#include      "fa.h"
/* --------------------------------- */
int main(void)
{
double     n = 2*200;

CTRL_splot p;

  p.xmin = -1;
  p.xmax = +1;             
  p.ymin = -1;
  p.ymax = +1;

tvalue t; 
 	
  t.min   =    PI/4.; 
  t.max   =  5*PI/4.;   
  t.step  =       .1;  
  
tvalue c; 
 	
  c.min   =       0.; 
  c.max   =     2*PI;   
  c.step  =       .1;
    
double  m = CurveLength2d_simpson(f,g,t.min,t.max,n);

 clrscrn();
 printf(" With \n\n");
 printf(" f : t-> %s  \n", feq);
 printf(" g : t-> %s\n\n", geq);
 printf(" %+.2f < t < %+.2f \n\n",t.min,t.max);

  G_Curve_2d(p,
             f,g,
             c,t
            );

 printf(" ... load \"a_main.plt\" ... with gnuplot.\n\n");
 
 stop(); 

 clrscrn();
 printf(" If a curve C has a smooth parametrization \n\n"
        "      f : t->  %s , g : t->  %s \n\n"
        " And if C does not intersect itself,\n"
        " except possibly for t= a and t = b,\n"
        " then the length L of C is        \n\n"
        "     / b\n"
        "    |   \n"
        "    |    [Df(t)^2 + Dg(t)^2]^1/2 dt = %.7f\n"
        "    |   \n"
        "   /   a\n\n\n"
        " with a = %f\n" 
        "      b = %f\n\n\n", feq, geq, 
                                     m,
                           t.min,t.max);

    G_length(p,
             f,g,
             t
            );

 printf(" ... load \"a_main.plt\" ... with gnuplot.\n\n");
 
 stop(); 

 return 0;
}
/* --------------------------------- */
/* --------------------------------- */

If a curve C has a smooth parametrization with gnuplot in c language

Exemple de sortie écran :

 With 

 f : t-> cos(t)  
 g : t-> sin(t)

 +0.79 < t < +3.93 

 ... load "a_main.plt" ... with gnuplot.

 Press return to continue.

Exemple de sortie écran :

 If a curve C has a smooth parametrization 

      f : t->  cos(t) , g : t->  sin(t) 

 And if C does not intersect itself,
 except possibly for t= a and t = b,
 then the length L of C is        

     / b
    |   
    |    [Df(t)^2 + Dg(t)^2]^1/2 dt = 3.1415926
    |   
   /   a


 with a = 0.785398
      b = 3.926991


 ... load "a_main.plt" ... with gnuplot.

 Press return to continue.