       Re: 3D plot of discontinuous function

• To: mathgroup at smc.vnet.net
• Subject: [mg24804] Re: [mg24779] 3D plot of discontinuous function
• From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
• Date: Sun, 13 Aug 2000 03:16:43 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```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:=
On[Plot3D::"plnc"]
In:=
On[Plot3D::"gval"]
In:=
On[Graphics3D::"nlist3"]

Evaluating

In:=
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:=
> Off[Plot3D::"plnc"]
> In:=
> Off[Plot3D::"gval"]
> In:=
> Off[Graphics3D::"nlist3"]
>
>
> Now, we define two functions f and g by:
>
> In:=
> f[x_, y_] := If[x > y, 1, Indeterminate]
>
> In:=
> g[x_, y_] := If[x < y, 0, Indeterminate]
>
> and two graphs:
>
> In:=
> p1 = Plot3D[f[x, y], {x, -1, 1}, {y, -1, 1}, PlotPoints -> 50,
> DisplayFunction -> Identity];
>
> In:=
> p2 = Plot3D[g[x, y], {x, -1, 1}, {y, -1, 1},PlotPoints -> 50, DisplayFunction
> -> Identity];
>
> Now
>
> In:=
> Show[p1, p2, ViewPoint -> {-5.339, -2.848, 2.830},
> DisplayFunction -> \$DisplayFunction]
>
> produces a reasonable representation of a discontinuous function.
>

```

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