check if a point exists in given area containing 4 vertices

Question

refering to http://www.weather.gov/directives/sym/pd01008006curr.pdf, page 8, we are given an area with four vertices in geographic coordinate system(lat and long system). I

Answer 1

This is a point-in-polygon problem on a sphere with a coordinate system, which has several subtleties that make it harder than the "regular" point-in-polygon problem in the X-Y plane:

1) what's inside and outside? (e.g. if I have a small "square" 1 miles on a side, does it enclose the 1 square mile, or the remainder of the earth's surface? This is a trivial example but for very large polygons it may be unclear which should be inside and which should be outside, unless specified explicitly)

2) are the segments of the polygons great-circle segments? If so, then those do not represent straight lines in a lat-long coordinate system unless they are meridian lines or the equator -- and you need to deal with curves rather than lines in your geometry. Spherical geometry is the way to go.

3) "edges" of the coordinate system (international date line and the poles) -- the "square" delimited by longitudes +179.9 degrees, -179.9 degrees, and latitudes +0.1degree, -0.1degree would not usually be considered to contain the point 0 N, 0 W, and would be considered to contain the point 0 N, 180 W. But if you naively check inequalities with lat/long points, you'll get the opposite answer.

So I don't have an answer but those are subtle issues to consider. (read this as "make sure you include them as test cases"!)

edit: I found the spheres package which has the method SphericalPolygon.contains that may do what you are looking for. However I have not personally used this package, and it's GPL, not LGPL, so it will "contaminate" the rest of your source if you wish to use this in a proprietary product.