Set Membership Classification: A Unified Approach to Geometric Intersection Problems

Abstract

Many practically important problems in computational geometry may be regarded as a generalization of "clipping," and may be formulated precisely in terms of a function called "membership classification." This function operates on a pair of point sets called the reference and candidate sets; it segments the candidate into three subsets which are "inside," "outside," and "on the boundary of" the reference. Examples of classification problems include clipping, polygon intersection, point inclusion, and solid interference.