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piecewise and if


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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