Re: piecewise and if

• To: mathgroup at smc.vnet.net
• Subject: [mg128630] Re: piecewise and if
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Sun, 11 Nov 2012 01:28:08 -0500 (EST)
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```Or perhaps more straightforwardly, set exclusions to none:

Plot3D[g[x, y], {x, -1, 1}, {y, -1, 1}, Exclusions -> None]

Bob Hanlon

On Sat, Nov 10, 2012 at 11:30 AM, Bob Hanlon <hanlonr357 at gmail.com> wrote:
> 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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