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MathGroup Archive 2000

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Re: 3D plot of discontinuous function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg24951] Re: 3D plot of discontinuous function
  • From: "Ulrich Bodenhofer" <ulrich.bodenhofer at scch.at>
  • Date: Fri, 25 Aug 2000 00:02:25 -0400 (EDT)
  • Organization: Software Competence Center Hagenberg (http://www.scch.at/)
  • References: <8mtcar$7tr@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Dear Andrzej,

first of all, thank you very much for spending the effort to write
such a detailed description of how to solve my problem.
Indeed, it solved the problem perfectly! I succeeded in producing
magnificent pictures of really exotic functions (some types of
pathological fuzzy relations, by the way). In order to make it
a little easier, I defined the following function:

  Plot3DPart :=
      DeleteCases[
          DeleteCases[Graphics3D[Plot3D[##]], Indeterminate,
             Infinity], {_?NumberQ, _?NumberQ}, Infinity] &;

Now, I can plot the parts really easy, e.g.

   f[x_, y_] := If[x <=y, 1, Indeterminate];
   g[x_, y_] := If[x >y, 0, Indeterminate];

   p1=Plot3DPart[f[x, y], {x, 0, 1}, {y, 0, 1}, DisplayFunction -> Identity,
                              PlotPoints -> 26];
   p2=Plot3DPart[g[x, y], {x, 0, 1}, {y, 0, 1}, DisplayFunction -> Identity,
                              PlotPoints -> 26];

   Show[p1, p2, DisplayFunction -> $DisplayFunction];

For complicated functions, however, this is still tedious work. Actually,
I had to create up to 22 different graphics objects for visualizing one
single function. But I suppose there is no way otherwise, since it is not
realistic that some sophisticated method will ever be able to detect the
discontinuities automatically. Just another aspect: The method you suggest
is not only perfect for visualizing discontinuities, but also for lines of
non-differentiability.
I do not dare to post attachments to the newsgroup.
However, if you (or anybody else in this group) are (is) interested in nice
examples of plots of nasty functions, just contact me, and I will send some.

Thanks a lot again,
Ulrich


-----Original Message-----
From: Andrzej Kozlowski [mailto:andrzej at tuins.ac.jp]
To: mathgroup at smc.vnet.net
Subject: [mg24951] Re: [mg24779] 3D plot of discontinuous function


A small addition to the previous method. The graphic objects constructed in
my previous solution are "illegitimate", in the sense that they contain the
non-numerical vlaue "Indeterminate" where a number is expacted. However, we
can easily convert them to perfectly legitimate grahic objects and even
obtain a better picture as follows:

p1 = DeleteCases[
      DeleteCases[Graphics3D[p1], Indeterminate,
        Infinity], {_?NumberQ, _?NumberQ}, Infinity];

p2 = DeleteCases[
      DeleteCases[Graphics3D[p2], Indeterminate,
        Infinity], {_?NumberQ, _?NumberQ}, Infinity];


We can now turn on the error messages with:

In[27]:=
On[Plot3D::"plnc"]
In[28]:=
On[Plot3D::"gval"]
In[29]:=
On[Graphics3D::"nlist3"]

Evaluating

In[30]:=
Show[p1, p2, DisplayFunction -> $DisplayFunction]

will produce a slightly better picture without any error messages.

Andrzej


on 8/10/00 7:51 PM, Andrzej Kozlowski at andrzej at tuins.ac.jp wrote:

> 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.
>





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