Mathc initiation/Fichiers h : c52a2

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	c00a1.c

/* --------------------------------- */
/* save as  c00a2.c                  */
/* --------------------------------- */
#include "x_hfile.h"
#include      "fa.h"
/* --------------------------------- */
int main(void)
{
double t  =  2.75;
	
 clrscrn();
 printf(" The curvature K of a smooth parametric"
        " curve C is :\n\n\n"

        " K = |f' g'' - g' f''| / "
        "[ (f')^2 - (g')^2 ]^(3/2)\n\n"

        " If P(f(t),g(t)) is a point on the curve  \n"
        " at which K != 0. The point M(h,k)"
        " is the center\n"
        " of the cuvature for P if   \n\n\n"
        " h = f - g'[f'^2 + g'^2] / [f'g''-f''g']\n"
        " k = g + f'[f'^2 + g'^2] / [f'g''-f''g']\n\n\n"

        " The radius is r = 1/|K| \n\n\n");
 stop();


 clrscrn();
 printf(" If a plane curve C has a parametrization\n\n"
        " x = f(t), y = g(t) and if f'' and g'' exist, \n\n\n "
        " then the curvature K at P(x,y) is  \n\n\n "
        " K = |f' g'' - g' f''| / [ (f')^2 - (g')^2 ]^(3/2)\n\n\n\n"

        " Find the curvature K of the curve at P(%+.2f,%+.2f) with\n\n\n"
        " f : t-> %s    \n"
        " g : t-> %s  \n\n",
        f(t),g(t), feq, geq);

 printf(" At the point P(%+.2f,%+.2f) K = %+.5f\n\n\n",
          f(t),g(t),Kt_2d(f,g,t));
 stop();
 

 clrscrn();      
 printf(" If P(f(t),g(t)) is a point on the curve  \n"
        " at which K != 0. The point M(h,k)"
        " is the center\n"
        " of the cuvature for P if   \n\n\n"
        " h = f - g'[f'^2 + g'^2] / [f'g''-f''g']\n"
        " k = g + f'[f'^2 + g'^2] / [f'g''-f''g']\n\n\n");
 printf(" At the point P(%+.2f,%+.2f)\n\n",f(t),g(t));
 printf(" The centre of the cuvature is M(%+.2f,%+.2f)\n\n\n",
               cx_2d(f,g,t),
               cy_2d(f,g,t));
 stop();

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

Calculer la courbure pour une fonction paramétrique 2d en langage c et gnuplot

Exemple de sortie écran :

 The curvature K of a smooth parametric curve C is :


 K = |f' g'' - g' f''| / [ (f')^2 - (g')^2 ]^(3/2)

 If P(f(t),g(t)) is a point on the curve  
 at which K != 0. The point M(h,k) is the center
 of the cuvature for P if   


 h = f - g'[f'^2 + g'^2] / [f'g''-f''g']
 k = g + f'[f'^2 + g'^2] / [f'g''-f''g']


 The radius is r = 1/|K| 


 Press return to continue.

Exemple de sortie écran :

 If a plane curve C has a parametrization

 x = f(t), y = g(t) and if f'' and g'' exist, 


  then the curvature K at P(x,y) is  


  K = |f' g'' - g' f''| / [ (f')^2 - (g')^2 ]^(3/2)



 Find the curvature K of the curve at P(+2.87,-0.56) with


 f : t-> 3*sin(t**2)    
 g : t-> 4-t**(3./2.)  

 At the point P(+2.87,-0.56) K = +1.39445


 Press return to continue.

Exemple de sortie écran :

 If P(f(t),g(t)) is a point on the curve  
 at which K != 0. The point M(h,k) is the center
 of the cuvature for P if   


 h = f - g'[f'^2 + g'^2] / [f'g''-f''g']
 k = g + f'[f'^2 + g'^2] / [f'g''-f''g']


 At the point P(+2.87,-0.56)

 The centre of the cuvature is M(+2.54,-1.20)


 Press return to continue.