%% d'apres les donnees de
%% http://www.mathcurve.com/courbes3d/cycloidspheric/cycloidspheric.shtml

-3 3 setxrange
-4 2 setyrange
70 setxunit

10 10 6 SetCamPos
0 0 0 SetCamView

-10 10 setxrange3d
-3 3 setyrange3d
2 setlinejoin
rouge

%% donnees
/a 1.8 def
/q 8 def
/w .7 def

%% calculs
/b a q div def
/h b a w Cos mul sub w Sin div def
/R a dup mul h dup mul add sqrt def

/g {
3 dict begin
   settvar
#rpn# (a/q)*((q - Cos(w))*Cos (t) + Cos (w)*Cos (t)*Cos (q*t) + Sin(t)*Sin(q*t))
#rpn# (a/q)*((q - Cos(w))*Sin (t) + Cos (w)*Sin (t)*Cos (q*t) - Cos(t)*Sin(q*t))
#rpn# (a/q)*(Sin (w*(1-Cos (q*t))))
end
} def

/g' {
3 dict begin
   settvar
#rpn# (a/q)*((Cos(w)-q)*Sin (t) - Cos (w)*Sin (t)*Cos (q*t) - q*Cos (w)*Cos (t)*Sin (q*t) + Cos(t)*Sin(q*t)+ q*Sin(t)*Cos(q*t))
#rpn# (a/q)*((q - Cos(w))*Cos (t) + Cos (w)*Cos (t)*Cos (q*t) - q*Cos (w)*Sin (t)*Sin (q*t) + Sin(t)*Sin(q*t) - q*Cos(t)*Cos (q*t))
#rpn# (a/q)*((q^2)*w*Cos(q*t) * Cos (w*(1-Cos (q*t))) - (w*q*Sin(q*t))*q*w*Sin (q*t) * Sin (w*(1-Cos (q*t))))
end
} def

/g'' {
3 dict begin
   settvar
#rpn# (a/q)*((Cos(w)-q)*Cos (t) - Cos (w)*Cos (t)*Cos (q*t) + q*Cos (w)*Sin (t)*Sin (q*t) + q*Cos (w)*Sin (t)*Sin (q*t) - (q^2)*Cos (w)*Cos (t)*Cos (q*t) - Sin(t)*Sin(q*t) + q*Cos(t)*Cos(q*t) + q*Cos(t)*Cos(q*t) - (q^2)*Sin(t)*Sin(q*t))
#rpn# (a/q)*((Cos(w)-q)*Sin (t) - Cos(w)*Sin(t)*Cos(q*t) - q*Cos(w)*Cos(t)*Sin(q*t) - q*Cos(w)*Cos(t)*Sin(q*t) - (q^2)*Cos(w)*Sin(t)*Cos(q*t) + Cos(t)*Sin(q*t) + q*Sin(t)*Cos(q*t) + q*Sin(t)*Cos (q*t) + (q^2)*Cos(t)*Sin(q*t))
#rpn# (a/q)*(q*w*Sin (q*t) * Cos (w*(1-Cos (q*t))))
end
} def


% 0 pi 2 mul {g} CourbeR3
% stop

.3 setlinewidth
/aretescachees false def
noir

GetCamPos setlightsrc
solidgridOff

0 2 pi mul (g) .05 [300 12] newtube
dup (rouge) outputcolors

R .1 sub [36 36] newsphere
{0 0 h translatepoint3d} solidtransform
dup (.5 setfillopacity jaune) outputcolors
solidfuz
drawsolid**