MathGroup Archive 2001

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3dplots again


the following code produces spherical calottes

but the surface has a strange look, "unsmooth".
it seems the lighting in mathematics does not
there are distict rectangles,
but the color is "jumpy".

is there a way of making this surface looking smoother.
and i think
this time the paramtetrization is not the problem.
the surface is not overlapping.


-=-=-=-=-=-=-=-=-=-

Outline[h_,t_]:=
  If[N[Abs[h]]<0.01,{t,
      0},(h^2+1)/(2*h)*{Sign[h]*Sin[t*(Pi-N[2*ArcTan[1/Abs[h]]])],
          Cos[t*(Pi-N[2*ArcTan[1/Abs[h]]])]}+{0,(h^2+1)/(2*h)-1/h}]

Outline[BaseRadius_,Height_,t_]:=BaseRadius*Outline[Height/BaseRadius,t]

Calotte[h_,u_,v_]:=
  Append[Outline[h,v][[1]]*{Cos[Pi*u],Sin[Pi*u]},Outline[h,v][[2]]]

Calotte[BaseRadius_,Height_,u_,v_]:=
  Append[Append[Outline[BaseRadius,Height,v][[1]]*{Cos[Pi*u],Sin[Pi*u]},
      Outline[BaseRadius,Height,v][[2]]],EdgeForm[]]

ParametricPlot3D[Calotte[1,0.5,u,v],{u,-1,1},{v,0,1},PlotPoints->50]

--
Erich Neuwirth, Computer Supported Didactics Working Group
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