       Re: piecewise and if

• To: mathgroup at smc.vnet.net
• Subject: [mg128628] Re: piecewise and if
• From: "djmpark" <djmpark at comcast.net>
• Date: Sun, 11 Nov 2012 01:27:27 -0500 (EST)
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```Jon,

I seems a mysterious feature, perhaps a bug, that plotting g[x,y] gives that
segmentation of the surface. But note that the Exclusion option says that
the excluded region must be one dimensional if the object is two
dimensional. Maybe the algorithm is trying to use Exclusion.

f[x_, y_] := Exp[-1/(x^2 + y^2)]

g2[x_, y_] := Piecewise[{{0, Abs[x^2 + y^2] == 0}}, f[x, y]]

Plot3D[g2[x, y], {x, -1, 1}, {y, -1, 1}]

Or maybe something like this:

RevolutionPlot3D[Exp[-1/r^2], {r, 0.05, 1}]

David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/index.html

From: Jon Joseph [mailto:josco.jon at gmail.com]

I think these two functions should be the same but their plots show a clear
difference:

f[x_, y_] := Exp[-1/(x^2 + y^2)] (* this function undefined at (0,0) *)

g[x_, y_] := Piecewise[{{0, x == 0 && y == 0}}, f[x, y]]  (* Redefine so the
hole is plugged *)

h[x_, y_] := If[x == 0 && y == 0, 0, f[x, y]]  (* Another, I think,
equivalent way to redefine f[x, y] *)

On my machine,   "8.0 for Mac OS X x86 (64-bit) (October 5, 2011)"

when I

Plot3D[g[x, y], {x, -1,1}, {y, -1,1}]

Plot3D[h[x, y], {x, -1,1}, {y, -1,1}]

I see clear gaps along y=0 and x=0 for the g[x, y] plot and h[x, y] works
properly.  Am I misusing Piecewise?

Thanks, Jon.

```

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