       Re: piecewise and if

• To: mathgroup at smc.vnet.net
• Subject: [mg128629] Re: piecewise and if
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Sun, 11 Nov 2012 01:27:47 -0500 (EST)
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• Delivered-to: l-mathgroup@wolfram.com
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• References: <20121110070852.CB7D86968@smc.vnet.net>

```You can use ExclusionsStyle

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

g[x_, y_] := Piecewise[{{0, x == 0 && y == 0}}, f[x, y]];

Plot3D[g[x, y], {x, -1, 1}, {y, -1, 1},
ExclusionsStyle -> Lighter[Gray, .5]]

Bob Hanlon

On Sat, Nov 10, 2012 at 2:08 AM, Jon Joseph <josco.jon at gmail.com> wrote:
> 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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