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  • $\begingroup$ When I make pts = RandomReal[20, {1000, 2}] and then Show[{Graphics@{Red, PointSize@Large, Point@Pick[pts, f@pts]}, Graphics[curve, ImageSize -> Large]}] some points show up at the lower left outline but not inside the Q $\endgroup$ Commented Nov 20, 2015 at 19:45
  • $\begingroup$ @eldo It is due to nonzero point size. Note that all point are at the lower part. May be RandomReal[50, {1000, 2}] is better. $\endgroup$ Commented Nov 20, 2015 at 19:49
  • $\begingroup$ @eldo please, check the update. Do you obtain the same figure? $\endgroup$ Commented Nov 20, 2015 at 19:55
  • $\begingroup$ Perfect +1 ---------- $\endgroup$ Commented Nov 20, 2015 at 20:00
  • $\begingroup$ With version 10.2, there is a simple modification for the visualization which eliminates the test function f. For example, region=BoundaryDiscretizeGraphics[curve,MaxCellMeasure->0.01], followed by p=RandomPoint[region,5000], and Graphics[{{Red,AbsolutePointSize[1],Point[p]},{FaceForm[],EdgeForm[Black],curve}}]. $\endgroup$ Commented Dec 25, 2015 at 1:11