This is a Point Location Algorithm. Given a polygon on a plane, an answer should be given for any point located on the plane, whether it lies inside the polygon or not.
Krkpatrick's algorithm works in O(logn) time and requires O(n) of memory, where n is the number of vertices on the polygon.
A good description of how the algorithm works can be found here.
The original paper is Optimal Search in Planar Subdivisions by D.Kirkpatrick.