       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];

```

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