How to determine if a point (x, y) is inside a polygon defined by a list of boundary points

Question

I have a large list of points that define the boundary of some (not necessarily convex) shape. Then I have a query point (x, y) , and I want to determine if (x, y) is within the area defined by my point boundary.

So, a fairly simple question. How to determine if the request point will be inside the form formed by my boundary points? And is there a good enhancement module for this? I am looking through boost::geometry but haven't found anything.

Answer 1

It seems that you are looking within , no?

http://www.boost.org/libs/geometry/doc/html/geometry/reference/algorithms/within/within_2.html

The example they give on the page is, in fact, point-in-polygon:

 #include <iostream> #include <list> #include <boost/geometry.hpp> #include <boost/geometry/geometries/point_xy.hpp> #include <boost/geometry/geometries/polygon.hpp> #include <boost/geometry/domains/gis/io/wkt/wkt.hpp> int main() { typedef boost::geometry::model::d2::point_xy<double> point_type; typedef boost::geometry::model::polygon<point_type> polygon_type; polygon_type poly; boost::geometry::read_wkt( "POLYGON((2 1.3,2.4 1.7,2.8 1.8,3.4 1.2,3.7 1.6,3.4 2,4.1 3,5.3 2.6,5.4 1.2,4.9 0.8,2.9 0.7,2 1.3)" "(4.0 2.0, 4.2 1.4, 4.8 1.9, 4.4 2.2, 4.0 2.0))", poly); point_type p(4, 1); std::cout << "within: " << (boost::geometry::within(p, poly) ? "yes" : "no") << std::endl; return 0; } 

UPDATE: as @ildjarn points out, you can use covered_by if you need points that lie at the very edge of the polygon to count:

http://www.boost.org/libs/geometry/doc/html/geometry/reference/algorithms/covered_by/covered_by_2.html

The behavior within wrt edges is "dependent", so pay attention to this nuance in the documentation.