(* Rebuilding the surfaces in Mathematica which appeared in the *)
(* New York Times Magazine (Photos of the American Artist *)
(* Hiroshi Sugimoto, December 5, 2004 *)
(* Oliver Knill, December 5, 2004, for Math21b, Harvard Fall 2004 *)
F1[f_,a_,b_,c_,d_,n_]:=ParametricPlot3D[f[u,v],{u,a,b},{v,c,d},
Boxed>False,Axes>False,PlotPoints>n,AspectRatio>1,
ViewPoint>{0,1,0},ViewVertical > {0,0,1}]
f1[u_,v_]:={Sinh[v] Cos[u],Sinh[v] Sin[u],NIntegrate[Sqrt[1Cosh[t]^2/4],{t,0,v}]}
S1=F1[f1,0,2Pi,0,ArcCosh[4],30]
f2[u_,v_]:={Sinh[v] Cos[u],Sinh[v] Sin[u],u}
S2=F1[f2,0,2Pi,10,10,50]
f3[u_,v_]:={Cos[u]/Cosh[v],Sin[u]/Cosh[v],vTan[v]+3 u}
S3=F1[f3,0,2Pi,1.5,1.5,50]
f4[u_,v_]:={Cos[u] Cos[v]*4/5,Sin[u] Cos[v]*4/5,
NIntegrate[Sqrt[1Sin[t]^2*u/(2Pi)],{t,0,v}]}
S4=F1[f4,0,2Pi,0,2Pi,30]
f5[u_,v_]:={Cosh[v] Cos[u],Cosh[v] Sin[u],NIntegrate[Sqrt[1Sinh[t]^2/4],{t,0,v}]}
S5=F1[f5,0,2Pi,ArcSinh[2],ArcSinh[2],30]
f6[u_,v_]:={2 Sqrt[1+u^2] Sin[v] Cos[uArcTan[u]]/(1+u^2 Sin[v]^2),
2 Sqrt[1+u^2] Sin[v] Sin[uArcTan[u]]/(1+u^2 Sin[v]^2),
Log[Tan[v/2]]+2 Cos[v]/(1+u^2 Sin[v]^2)};
S6=F1[f6,0,6,0,4,30]
Get["Graphics`ContourPlot3D`"];
eqn = 81 (x^3 + y^3 + z^3)  189 (x^2y + x^2z + y^2x + y^2z + z^2x + z^2y) +
54x y z + 126 (x y + x z + y z)  9 1(x^2+y^2+z^2)  9 (x+y+z)2;
(* eqn from http://wwwsop.inria.fr/galaad/exposition/ArtGallery/clebsh.html *)
S7=ContourPlot3D[eqn,{x,1,1},{y,1,1},{z,1,1}, Background>GrayLevel[0.0],
PlotPoints>5,Boxed>False,Axes>False]
