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Consider the following code.

RegionPlot[Print[{x, y}], {x, -2, 2}, {y, -2, 2}, PlotPoints -> 2]
{-1.996,-1.996}
{Region`Private`RegionVar[1],Region`Private`RegionVar[2]}
{-2.,-2.}
{2.,-2.}
{-2.,2.}
{2.,2.}

My question is: what is RegionPlot doing to create the first two lines of output? I do not understand why the first sample point is {-1.996, -1.996} and why the second sample point is {Region`Private`RegionVar[1],Region`Private`RegionVar[2]}.

I am running this in Mathematica 9. I do not recall this happening in an earlier version.

Edit: I changed the code above to give a better minimal working example. I leave below the code I first gave along with its truncated output.

myFunc[pt_] := Module[ {bool},
  bool = Sin[ pt[[1]] ] > 0;
  Print[pt, bool];
  If[ bool, Return[True], Return[False] ];
];

RegionPlot[myFunc[ {x, y} ], {x, -2, 2}, {y, -2, 2}, PlotPoints -> 2]
{-1.996,-1.996}False

{Region`Private`RegionVar[1],Region`Private`RegionVar[2]}Sin[Region`Private`RegionVar[1]]>0

{-2.,-2.}False

{2.,-2.}True
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2  
I can confirm that this doesn't happen in version 8.0.4.0 but in version 9.0.0.0 - no idea what changed... –  Jens Feb 8 '13 at 3:10
1  
As a clue this resembles the behavior of regular Plot[] which first evaluates the function with a numeric argument, then a symbolic arg, followed by the remaining numeric values. –  george2079 Feb 8 '13 at 23:23

1 Answer 1

up vote 0 down vote accepted

According to a representative at Wolfram Research

This behavior doesn't appear to be documented, but also doesn't appear to be a bug of any kind. I apologize, we have no information about this aspect of the internal workings of RegionPlot.

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