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% Hundekurven-compared-text-de:
% SourceCode for EULER by W#B: 14.11.2005, Public Domain
%      EULER is a program for quick and interactive computations with real
%      and complex numbers, matrices, or with intervals.
%      Euler is freeware under the GNU general public license.
%      The Euler homepage is at http://www.rene-grothmann.de
% ==================================================================
>function radiodrome(y, k=1, d0=1)
## x   - vektor over vektor y, y(i) <> 0!!
## d0 .. normal distance of point of return (1/x'=0)
## k  .. parameter of radiodrome (factor of velocities)
##  W#B: 24.10.2005
$yy=abs(y)/d0;
$if abs(k)==1; x=sign(k)*((yy^2-1)/4-log(yy)/2);
$ else; k1=1+k; k2=1-k;  x=1/2*((yy^k1-1)/k1-(yy^k2-1)/k2);  endif;
$return x*d0;
$endfunction
>function radiodrome0(k=1, d0=1)
## x   - value x at y=0
## if no zeropoint exists, returns x=0
##    (as k=0 will give correct x=0, test for both)
## d0 .. normal distance of point of return (1/x'=0)
##  W#B: 29.10.2005
$if abs(k)>=1;  x=0;  "radiodrome0: no zeropoint";
$ else; k1=1+k; k2=1-k;  x=k/(k1*k2);  endif;
$return x*d0;
$endfunction
>function traktrix(y, d0=1)
## x   - vektor over vektor y, 0 < |y(i)| <= |d0|!!
## d0 .. normal distance of cusp (1/x'=0)
## ## !returns only positive branch (x > 0)
##  W#B: 06.11.2005
$yy=abs(y/d0); rr=sqrt(1-yy^2); x=log((1+rr)/yy)-rr;
$return x*d0;
$endfunction
>function konchoide(y, b=1, d0=1)
## x   - vektor over vektor y
## b  .. distance parameter
## d0 .. normal distance of pole
## !returns only positive branch (x > 0)
##  W#B: 17.11.2005
$x=(d0-y)/y*sqrt(b^2-y^2);
$return x;
$endfunction
% -----------------------------------------------------------------
>d=1;
>xmin=0; xmax=2*d; ymin=0; ymax=d; 
>delta0=0.000001; delta1=0.001; delta2=0.05;
>clg; reset; hold on;
>setplot(xmin,xmax,ymin,ymax+delta2); keepsquare(0); scaling(0);  
>y=ymin+delta0:delta1:ymax; x=radiodrome(y,1,d);
>plotarea(x,y);
>color(1);  linewidth(1); xplot();
>color(10); textcolor(10); linewidth(2); plot(x,y);
> label("RADIODROME", radiodrome(0.2,1,d)+delta2, 0.2+delta2);
>color(12); textcolor(12); x=traktrix(y,d); plot(x,y);
> label("TRAKTRIX", traktrix(0.3)+delta2, 0.3+delta2);
>color(3);   textcolor(3);    x=konchoide(y,d,d); plot(x,y);
> label("KONCHOIDE", konchoide(0.4,d,d)+delta2, 0.4+delta2);
> "done"
% ------------------------------------------------------------------