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  • $\begingroup$ Thanks, but for the other example, I can't make it work by setting a small value instead of zero, could you have a look? $\endgroup$ Commented Sep 20, 2013 at 2:45
  • $\begingroup$ @xslittlegrass Are you sure? The Abs[]example works here by using the same trick $\endgroup$ Commented Sep 20, 2013 at 2:54
  • $\begingroup$ @Jens I guess yes, here is a screen shot i.imgur.com/8eBA2ju.png?1 $\endgroup$ Commented Sep 20, 2013 at 3:04
  • $\begingroup$ Thanks a lot! But it seems there is something else other than the steeply change of the function maximals. For example, consider this f[x_, y_] := (Cos[x] + Cos[y]) Exp[I x y] Exp[x/2] Plot3D[Abs[f[x, y]] == 0.001, {x, 0, 8 Pi}, {y, 0, 8 Pi}, PlotPoints -> 40, PlotRange -> All] ContourPlot[Abs[f[x, y]] == 0.00001, {x, 0, 8 Pi}, {y, 0, 8 Pi}]. The function maximals change quit a lot in the region, but ContourPlot still works quit well. Do you have any idea why it works? $\endgroup$ Commented Sep 20, 2013 at 17:46
  • $\begingroup$ I'm thinking that if the bad behave part is the steeply change of the maximals, we may re-scale the function in the second example to make the maximals well behave, and than use the the same trick f[x, y]*f[x, y] == 0.000001 as you did in the first example. $\endgroup$ Commented Sep 20, 2013 at 17:50