ABSTRACT
This chapter presents some useful properties of B-coded restricted domains that will be used in later proofs. Line drawings have been commonly used to represent the boundaries of two-dimensional objects. Restricted domains can be represented in terms of the intersections of discrete half-planes. The half-planes that are not redundant and form the sides of the polygon will be called primary. If the input restricted domains are in their B-code representations or if the output restricted domains are needed in their B-code representation, the results can be used for the interconversion between representations. The algorithms for opening and closing can be easily obtained by applying the dilation and erosion algorithms in the appropriate order. The algorithm for opening consists of two stages—an erosion stage followed by a dilation stage. Since erosion and dilation algorithms are constant in time, the algorithm for opening is also constant in time.
