parametricplot3d

4 Cups / 4個のカップ by TANAKA Juuyoh (田中十洋) on Flickr.

Via Flickr:
(* === Following code of Mathematica 8 generates this image. === *)

a = 12; (* center hole size of a torus *)
b1 = 5; (* the number of angles *)
b2 = 3; (* the number of waves *)
b3 = 1; (* the number of knots *)
c = -80; (* distance from the center of rotation *)
d = 4; (* the number of tori *)
h1 = 2; (* width of a torus *)
h2 = 2; (* width of a torus *)
h3 = 2; (* height of a torus *)

SetOptions[ParametricPlot3D,
PlotRange -> Full, Mesh -> None, Boxed -> False, Axes -> None,
PlotPoints -> 600, ImageSize -> 3000, Background -> RGBColor[{240, 250, 220}/255],
PlotStyle -> Directive[Specularity[White, 90], Texture[Import[“D:/tmp/94.jpg”]]],
TextureCoordinateFunction -> ({#4, #5 Pi} &), Lighting -> “Neutral”];

g[v_] := Cos[2 Cos[Cos[Cos[v]]]];
x = t (a - h1 Cos[t] + h2 Sin[b1 s]) Cos[b3 (s + Pi/(2 b1))] + c;
y = t (a - h1 Cos[t] + h2 Sin[b1 s]) Sin[b3 (s + Pi/(2 b1))] + c;
z = t (a - h3 (g[t] + Sin[b2 t])) + c;
rm = Table[{x, y, z}.RotationMatrix[2 i Pi/d, {1, 0, 0}], {i, d}];

ParametricPlot3D[rm, {t, 0, 6 Pi}, {s, 0, 2 Pi}]

(*—
The Texture
Another shapes and colors, and the meaning of this code in the set description

*)

3

(* The Global Enneper - Weierstrass representation of minimal surfaces *)
phi[f_, g_, eta_] := {(1 - g^2) f, I (1 + g^2) f, 2 f g} eta ;
X[z0_, f_, g_, eta_] :=  X[z0, f, g, eta] =
         Re[Integrate[phi[f, g, eta], {z, z0, Z}]] /. Z -> r Exp[I th] ;
Xeval = X[0, 1, z, 1] ; 
   
     ParametricPlot3D[Xeval, {th, 0, 2 Pi}, {r, 0, 2.0},
             Boxed -> False, PlotPoints -> {100, 20}]