drawing half planes / spaces with Mathematica

*To*: mathgroup at smc.vnet.net*Subject*: [mg75930] drawing half planes / spaces with Mathematica*From*: dimitris <dimmechan at yahoo.com>*Date*: Sun, 13 May 2007 05:56:09 -0400 (EDT)

Hello. 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!) In[2611]:= 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 -> Thickness[0.008], 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 a 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! Dimitris