Rapid Qualification of Mereotopological Relationships Using Signed Distance Fields

Abstract

Although mereotopological relationship theories and their qualification problems have been extensively studied in R^2, the qualification of mereotopological relations in R^3 remains challenging. This is due to the limited availability of topological operators and high costs of boundary intersection tests. In this paper, a novel qualification technique for mereotopological relations in R^3 is presented. Our technique rapidly computes RCC-8 base relations using precomputed signed distance fields, and makes no assumptions with regards to complexity or representation method of the spatial entities under consideration.