detect if a point is inside a MKPolygon overlay

Question

I want to be able to tell if tap is within a MKPolygon.

I have a MKPolygon:

CLLocationCoordinate2D  points[4];

points[0] = CLLocationCoordinate2DMak         


        

Answer 1

Determining whether a point is in an arbitrary polygon is non-trivial and it is unsurprising that Apple doesn't supply it as part of MKPolygon. You can access the points, which allows you to iterate over the edges.

To determine whether a point p is inside a polygon s, consider each edge as a directed line segment in s. If a ray from p in any fixed direction (typically parallel to either the X or Y axis) intersects the segment, take the sign of the Z component of the cross product of the ray with that directed line segment. If the Z component is > 0, add 1 to a counter. If it is < 0, subtract 1. The trick in implementing this is to avoid issues when the edge is nearly parallel to the ray, or when the ray passes through a vertex (it has to count only once, not once for each edge).

When you have done this for all edges in s, you will have counted the number of times your ray intersects the outline of the polygon, where if the edge was going from left to right you added, and if it was going from right to left, you subtracted. If the resulting sum is zero, you are outside the polygon. Otherwise you are inside it.

There are numerous optimizations possible. One such is to do a quick bounding box test before the more complete test. Another is to have a data structure with bounds on all the edges to trivially discard edges that do not intersect the ray.

Edit: the Z component of A X B ( the cross product of A with B ) is given by:

a.x * b.y - a.y * b.x

since all you care about is the sign, you can check

a.x * b.y > a.y * b.x