The point containment predicate which specifies if a point is part of a mathematically defined shape is one of the most elementary operations in computer graphics and is a natural way to perform the many raster calculations. It plays an essential role in several important processes such as filling, stroking, anti-aliasing, geometric modeling and volume rendering. This paper presents a generalized point containment algorithm for arbitrary dimension discrete objects whose main characteristics are low complexity, simple data structures and suitability for hardware implementation.