input latexmp;
setupLaTeXMP(class="article",options="12pt",fontencoding="T1",inputencoding="latin1",language="frenchb",packages="fourier,textpathmp");
input textpath;

prologues:=2;

input geometriesyr16;

figure(2u,u,15u,14u);
pair O,A,P[],N[],M[];
A=u*(10,7.5);
path cc;
cc=cercles(A,2.5u);
O=pointarc(cc,0);
marque_p:="plein";
for k=0 step 1 until 360:
  P[k]=pointarc(cc,k);
  M[k]=droite(A,P[k]) intersectionpoint cercles(P[k],O);
  N[k]=symetrie(M[k],P[k]);
endfor;
drawoptions(dashed evenly withcolor gris);
trace cc;
drawoptions(withcolor rouge);
path nephroidedefreeth;
nephroidedefreeth=M0
for k=1 upto 179:
  --M[k]
endfor
for k=180 upto 360:
  --N[k]
endfor
for k=180 upto 360:
  --M[k]
endfor
for k=0 upto 179:
  --N[k]
endfor
--cycle;
trace nephroidedefreeth;
drawoptions(withcolor bleu);
trace textpath("\Large Nephroïde de Freeth",nephroidedefreeth,0.5);
fin;
end