If possible how to display the min and max mean curvature values?
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This question needs more details to be meaningful. Consider adding more information to your question. – Apr 15 '16 at 05:28
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I am afraid , I don't have any more information.I just got a doubt whether it is possible to do so and if its not possible what could be the reason – kranthi kumar Apr 15 '16 at 06:34
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@RunnyKine. I think the question is perfectly clear and meaningful. – bubba Apr 15 '16 at 12:28
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Yes. The Enneper surface is a minimal surface, so its mean curvature is everywhere zero, and it has a bicubic parameterization. If you take the parametric equations given on that Wikipedia page, and restrict the parameter values to $(u,v) \in [0,1] \times [0,1]$, then you get a bicubic patch that is a rectangular region of the surface. Expressing this patch in Bezier form is just a change of basis.
In fact Cosin and Monterde showed that all minimal bicubic Bezier surfaces are affine transforms of a portion of the Enneper surface:
C. Cosın, and J. Monterde, Bezier surfaces of minimal area, Proc. Int. Conf. of Comput. Sci. ICCS 2002, LNCS 2330, Springer, Berlin Heidelberg, 2002, 72–81
To find out how to calculate and display mean curvature in Mathematica, look at Gray's book "Modern Differential Geometry of Curves and Surfaces".
bubba
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