Re: 3D plot of discontinuous function

*To*: mathgroup at smc.vnet.net*Subject*: [mg24803] Re: [mg24779] 3D plot of discontinuous function*From*: Andrzej Kozlowski <andrzej at tuins.ac.jp>*Date*: Sun, 13 Aug 2000 03:16:42 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Here is the simplest method I can think of. I will use your example. The method woudl normally produce several error messags, so we first supress them: In[1]:= Off[Plot3D::"plnc"] In[2]:= Off[Plot3D::"gval"] In[3]:= Off[Graphics3D::"nlist3"] Now, we define two functions f and g by: In[4]:= f[x_, y_] := If[x > y, 1, Indeterminate] In[5]:= g[x_, y_] := If[x < y, 0, Indeterminate] and two graphs: In[6]:= p1 = Plot3D[f[x, y], {x, -1, 1}, {y, -1, 1}, PlotPoints -> 50, DisplayFunction -> Identity]; In[7]:= p2 = Plot3D[g[x, y], {x, -1, 1}, {y, -1, 1},PlotPoints -> 50, DisplayFunction -> Identity]; Now In[8]:= Show[p1, p2, ViewPoint -> {-5.339, -2.848, 2.830}, DisplayFunction -> $DisplayFunction] produces a reasonable representation of a discontinuous function. -- Andrzej Kozlowski Toyama International University, JAPAN For Mathematica related links and resources try: <http://www.sstreams.com/Mathematica/> on 8/10/00 6:32 AM, Ulrich Bodenhofer at ulrich.bodenhofer at scch.at wrote: > 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]; > > > >