3D plot of discontinuous function

*To*: mathgroup at smc.vnet.net*Subject*: [mg24779] 3D plot of discontinuous function*From*: "Ulrich Bodenhofer" <ulrich.bodenhofer at scch.at>*Date*: Thu, 10 Aug 2000 00:32:12 -0400 (EDT)*Organization*: Software Competence Center Hagenberg (http://www.scch.at/)*Sender*: owner-wri-mathgroup at wolfram.com

Hi, I am currently struggling with a problem that seems more and more non-trivial: How can I make a 3D plot of a discontinuous function, where the manifolds of discontinuities are not necessarily parallel to the axes (*). If they were, I could split the plot into rectangles where the function is continuous and reassemble them with Show[]. In the more general case, however, I do not have an idea how to solve this. 1. Plot3D does not support plotting over non-rectangular areas. 2. Splitting the plot into regions that can be drawn with ParametricPlot3D is (1) difficult and tedious, and (2) does not support meshes with varying numbers of points either. Does anybody have a clue? Any help is gratefully appreciated! Regards, Ulrich (*) Simple example with discontinuities along the diagonal: characteristic function of the linear ordering of real numbers, i.e. f[x_,y_]:=If[x<=y,1,0];