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drawing half planes / spaces with Mathematica


Does anybody use Mathematica in order to draw half planes or/and a
half spaces?
I mean from the applied mathematics point of view! Like those
encountered in the
mathematical theory of elasticity/piezoelectrecity etc.
For example in Boussinesq / Cerruti problem (3D) and their
2D counterpart Flamant problem.

Let me be more specific...

Suppose I have the following drawing
(note that in another post I ask how it is possible to produce
the same output more directly!)

surf = Block[{$DisplayFunction = Identity}, ParametricPlot[{13*Cos[u],
4*Sin[u]}, {u, 0, 2*Pi}, PlotStyle -> Thickness[0.008],
     PlotPoints -> 100]];
surfgray = surf /. Line[x_] :> {GrayLevel[0.95], Polygon[x]};
halfspa = Block[{$DisplayFunction = Identity},
ParametricPlot[13*{Cos[u], Sin[u]}, {u, Pi, 2*Pi}, PlotStyle ->
     PlotPoints -> 100]];
halfspagr = halfspa /. Line[x_] :> {GrayLevel[0.95], Polygon[x]};
Show[surfgray, halfspagr, surf, halfspa, Axes -> False];

I would like the obtained half space to be smooth but not SO smooth as
a sphere. In other words I am looking in a way deform halfspa curve in
way that it will not lost its smoothness (that is continuoous
derivatives everywhere!)
but it will not have everywhere the same radious.

Thanks a lot for any ideas!


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