File:Циклоида.svg

%Рис к задаче 1.5.8 (20x120) - циклоида
 beginfig(1) ;
   numeric u;u = 0.8mm;
   numeric R; R=10u;
   path p,cycl;
   p:=(-R,0u)..(R,0u)..cycle;
   draw p withpen pencircle scaled 0.3u dashed withdots scaled 0.5u;
   numeric j,n,v,w,phi,nsteps;
   j=0;n=100;v=109.8u;w=-(v/R)*180/3.14;phi=180;nsteps=4;
   numeric r,i;
   for i:=0 upto 2*nsteps:
     r:=R-1/nsteps*R*i;
     for j:=0 step n/4 until n:
       draw (j*(v/n)+r*cosd(j*(w/n)+phi),r*sind(j*(w/n)+phi))
        withpen pencircle scaled 1u;
     endfor;
     cycl:=for j:=0 upto n:
       if j<>0:..fi(j*(v/n)+r*cosd(j*(w/n)+phi),r*sind(j*(w/n)+phi))
     endfor;      
     draw cycl dashed evenly scaled 1/2u
         withcolor (max(1-i/nsteps,0)*red+
       min(i/nsteps,2-i/nsteps)*green+
       max(i/nsteps-1,0)*blue);
   endfor;
 endfig ;