Issue using RegionFunction with ListContourPlot

Question

I've hit a problem using RegionFunction with ListContourPlot and am hoping someone can help.

I'm trying to use RegionFunction with ListContourPlot to suppress the rendering of contours outside a prescribed polygon.

The first example in this notebook works as I'd expect. The second does not, in that the contours are drawn outside the specified polygon.

Any suggestions/advice would be much appreciated.

Answer 1

First, precompute RegionMemberFunction for better performance. Second, increase MaxPlotPoints.

regMem = RegionMember[Polygon[...]];

Show[ListContourPlot[..., 
   RegionFunction -> Function[{x, y, z}, regMem[{x, y}]], 
   MaxPlotPoints -> 50]
]

Alternatively, if you don't want all of your points to get additionally resampled at a grid (which is what increasing MaxPlotPoints does and can be observed with Mesh -> All), you can trick Mathematica by providing RegionFunction of a region which is very slightly smaller than your actual region of datapoints. This will trigger finer resampling only at the boundary (observe with mesh). I do not know whether this can also be achieved in any other way ...

reg = Polygon[...];
smallerReg = 
  GeometricTransformation[reg, 
   ScalingTransform[{1 - 1/100000, 1 - 1/100000}, RegionCentroid[reg]]];
regMem = RegionMember[smallerReg];

Show[ListContourPlot[..., 
   RegionFunction -> Function[{x, y, z}, regMem[{x, y}]]
]

Answer 2

The resolution of the "ListContourPlot" is too small. Add e.g.: "MaxPlotPoints->30"