This paper details a robust and efficient algorithm for point classification with respect to a polygon in 2D real number domain. The concept of tolerance makes this algorithm robust and consistent. It enables to define‘on-boundary’ , which can be interpreted as either‘in-’or‘out-’side region, and to manage rounding errors in floating point computation. Also the tolerance is used as a measure of reliability of point classifications. The proposed algorithm is based on a ray-intersection technique known as the most efficient, in which intersections between a ray originating from a given test point and the boundary of a region are counted. An odd number of intersections indicates that the point is inside region. For practical examples the algorithm is most efficient because most edges of the polygon region are processed by simple bit operations.