## Mar 26, 2014

### Geospatial function: Point in Ploygon Test

There is an excellent post on point in polygon test from Mathematica Stackexchange.

Point in polygon test is one of the most useful functions when processing Geospatial data. Unfortunately, there is no official built-in function from Mathematica yet. Here is an example of showing usefulness of this function.
We have some data on Greenland icesheet thickness in format of {lon,lat, thickness}.

Our goal is to make a map to show the thickness of icesheet.
First try with ListDensityPlot:

You can see it is not working well, we need to limit the plot region inside the boundary of Greenland. Here is the place we can use the point-in-polygon test. In this example, I use inPolyQ2 from the answer by Simon Woods:

Still not right? What's wrong? The trick is to increase MaxPlotPoints  to 100 at least:
ListDensityPlot[data, PlotRange -> All,
ColorFunction -> (ColorData["Rainbow"][1 - #] &),
RegionFunction -> (inPolyQ2[greenland_ploygon[[1, 1]], #1, #2] &),
MaxPlotPoints -> 150, MeshFunctions -> {#3 &}, Mesh -> 10]

It looks like a real map now.

Armin Vollmer said...

This is very easy now with Mathematica V10:

In[1]:= poly = CountryData["Germany", "Polygon"];

In[2]:= coord = CityData["Berlin", "Coordinates"]

Out[2]= {52.52, 13.38}

In[3]:= RegionMember[poly /. GeoPosition -> Sequence, coord]

Out[3]= True

Kind regards, Armin

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