Unexpected behavior of Plot3D

*To*: mathgroup at smc.vnet.net*Subject*: [mg116505] Unexpected behavior of Plot3D*From*: Alexey <lehin.p at gmail.com>*Date*: Thu, 17 Feb 2011 05:19:50 -0500 (EST)

Hello, According to the documentation for Plot3D, combination of options PlotPoints -> 25 and MaxRecursion -> 0 should result in computing a rectangular grid of values of the function with dimensions 25x25. In some cases it seems to be true: In[1]:= Reap[Plot3D[Sin[x y], {x, 0, Pi}, {y, 0, Pi}, PlotPoints -> 25, MaxRecursion -> 0, EvaluationMonitor :> Sow[{x, y}]]][[2, 1]] // Length Out[1]= 625 But if we call the same function through a definition, say f[x_, y_] = Sin[x y], we get unexpected and enormous increasing of the number of evaluations of the function: In[1]:= f[x_, y_] = Sin[x y]; pts = Reap[ Plot3D[f[x, y], {x, 0, Pi}, {y, 0, Pi}, PlotPoints -> 25, MaxRecursion -> 0, EvaluationMonitor :> Sow[{x, y}]]][[2, 1]]; pts // Length ListPlot[pts] Union[pts, SameTest -> (Abs[Norm[#1 - #2]] < 10^-7 &)] // Length Out[3]= 2500 Out[4]= - Graphics - Out[5]= 625 As you can see the most of the points differ from each other with norm < 10^-7. These points are so close that cannot be discerned by eye from each other and obviously do not improve the plot. So I'm wondering what is the reason for such behavior? Is there a way to switch it off?