geography - How to test if a GeoPosition is inside a geographic Polygon?

I have tried the following:

usentity = Entity["Country", "UnitedStates"];
uspoly = usentity["Polygon"];
stdpoly = uspoly /. GeoPosition -> Identity;
RegionQ[stdpoly]

[1] True

RegionMember[stdpoly, {35, -90}]

returns unevaluated.

Is there a better approach?

Answer

If you look at the structure of the Polygon, it seems there is an extra level of {} that needs to be removed

Short@stdpoly
(* Polygon[{{{49.0021,-122.758},<<2620>>}}] *)

So you can use FlattenAt to remove that layer of brackets,

stdpoly2=FlattenAt[stdpoly,{1,1}];
Short@stdpoly
(* Polygon[{{{49.0021,-122.758},<<2620>>}}] *)

The polygons appear the same

RegionPlot /@ {stdpoly, stdpoly2}

Mathematica graphics

and now you can use RegionMember all you like

RegionMember[stdpoly2, {35, -90}]

(* True *)

There is also the fact that for some reason, geographic polygons have their coordinates reversed, as I learned here. This is what I did there,

stdpoly = Polygon @@ First@First@uspoly // Map[Reverse, #, {-2}] &;
Graphics@stdpoly
RegionMember[stdpoly, {-90, 35}]

Mathematica graphics

(* True  *)

As rcollyer points out, you can use the built-in GeoWithinQ to test this as well,

GeoWithinQ[Entity["Country", "UnitedStates"], GeoPosition[{35, -90}]]
(* True *)

Comments

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