Mathc gnuplot/Application : Tangente de P à l'axes des x d'une courbe

/* ------------------------------------ */
/*  Save as :   c01.c                   */
/* ------------------------------------ */
#include "x_ahfile.h"
#include       "fe.h"
/* ------------------------------------ */
int main(void)
{
double c = PI/4;

 printf(" Let C be the curve consisting of all"
        " ordered pairs (f(t),g(t)).\n\n"
        " With\n\n"
        " f : t-> %s\n\n"
        " g : t-> %s\n\n", feq, geq);

 printf(" With c = %0.3f, the equation of the tangent is :\n\n"
        " y =  ((Dg/Dy)(c))(x-f(c))+g(c) = ",c);
 eq_Tan(f,g,DgDf,c);

 printf("\n\n\n");

 printf(" Find PA, the length of the tangent from P to the x axis.\n\n");

 printf(" P(%6.3f, %6.3f)    P(f(c), g(c))                 \n",
        f(c),g(c));

 printf(" A(%6.3f,  0.000)    A(f(c)-g(c)/(DgDf)(c), 0)\n\n\n",
          f(c)-g(c)/(DgDf)(c));

 printf(" PA =  sqrt(g(c)**2*(1+(DgDf(c)**2))/(DgDf(c)**2))\n"
        "    = %6.3f\n\n",
       sqrt(pow(g(c),2)*(1/pow(DgDf(c),2)+1)) );

     G_TanLx(i_WGnuplot(-10.,10.,-5.,5.),
             i_time(0,2.*PI,.05),
             c,
             f,g,DgDf);

 printf(" To see the curve C, open the file \"a_main.plt\""
        " with Gnuplot.\n\n"
        "\n Press return to continue");
 getchar();

 return 0;
}

Le résultat.

Let C be the curve consisting of all ordered pairs (f(t),g(t)).
.
With
.
f : t-> a*sin(k1*t)
g : t-> b*cos(k2*t)
.
With c = 0.785, the equation of the tangent is :
y =  ((Dg/Dy)(c))(x-f(c))+g(c) =  0.500*x +1.414
.
Find PA, the length of the tangent from P to the x axis.
P( 1.414,  2.121)    P(f(c), g(c))                 
A(-2.828,  0.000)    A(f(c)-g(c)/(DgDf)(c), 0)
.
PA =  sqrt(g(c)**2*(1+(DgDf(c)**2))/(DgDf(c)**2))
   =  4.743
.
To see the curve C, open the file "a_main.plt" with Gnuplot.

Résultat dans gnuplot

Les fichiers h de ce chapitre

	`x_ahfile.h` Appel des fichiers

/* ------------------------------------ */
/*  Save as :   x_ahfile.h              */
/* ------------------------------------ */
#include    <stdio.h>
#include   <stdlib.h>
#include    <ctype.h>
#include     <time.h>
#include     <math.h>
#include   <string.h>
/* ------------------------------------ */
#include     "xdef.h"
#include     "xplt.h"
/* ------------------------------------ */
#include   "kg_tan.h"

	`fe.h` La fonction à dessiner

/* ------------------------------------ */
/*  Save as :   fe.h                    */
/* ------------------------------------ */
double f(
double t)
{
double a=2;
double k1=3;

        return( a*sin(k1*t) );
}
char  feq[] =  "a*sin(k1*t)";
/* ------------------------------------ */
double Df(
double t)
{
double a=2;
double k1=3;

        return( a*cos(k1*t)*k1);
}
char  Dfeq[] =  "a*cos(k1*t)*k1";
/* ------------------------------------ */
double g(
double t)
{
double b =3;
double k2=1;
        return( b*cos(k2*t) );
}
char  geq[] =  "b*cos(k2*t)";
/* ------------------------------------ */
double Dg(
double t)
{
double b =3;
double k2=1;
        return(  -b*sin(k2*t)*k2 );
}
char  Dgeq[] =  "-b*sin(k2*t)*k2";
/* ------------------------------------ */
double DgDf(
double t)
{
        return(Dg(t)/Df(t));
}

	`kg_tan.h` La fonction graphique

/* ------------------------------------ */
/*  Save as :   kg_tan.h                */
/* ------------------------------------ */
void eq_Tan(
double (*P_f)  (double t),
double (*P_g)  (double t),
double (*PDgDf)(double t),
double c
)
{
  printf(" %0.3f*x %+0.3f",
(*PDgDf)(c),(-(*PDgDf)(c)*(*P_f)(c)+(*P_g)(c)));
}
/* ------------------------------------ */
void G_TanLx(
W_Ctrl W,
t_Ctrl T,
double c,
double (*P_f)  (double t),
double (*P_g)  (double t),
double (*PDgDf)(double t)
)
{
FILE *fp;
double t;

        fp = fopen("a_main.plt","w");
fprintf(fp," set zeroaxis\n"
           " plot [%0.3f:%0.3f] [%0.3f:%0.3f]\\\n"
           " \"a_pts.plt\" with line lt 1,   \\\n"
           " %0.6f*x %+0.6f,                 \\\n"
           " \"axp.plt\" with linesp lt 3      \n"
           " reset",
        W.xmini,W.xmaxi,W.ymini,W.ymaxi,
(*PDgDf)(c),(-(*PDgDf)(c)*(*P_f)(c)+(*P_g)(c)));
 fclose(fp);

        fp = fopen("a_pts.plt","w");
 for(t=T.mini; t<=T.maxi; t+=T.step)
     fprintf(fp," %6.6f %6.6f\n",(*P_f)(t),(*P_g)(t));
 fclose(fp);

        fp = fopen("axp.plt","w");
     fprintf(fp," %0.6f %0.6f\n",(*P_f)(c),(*P_g)(c));
     fprintf(fp," %0.6f  0.  \n",
                 (*P_f)(c)-(*P_g)(c)/(*PDgDf)(c));
     fclose(fp);
}