Surrounds in partitions

Abstract

Surrounds is a topological relation that can exist between two regions or between collections of regions in R2. This paper provides an algebraic construction for surrounds within a partition and provides a complementary graph-theoretic approach for the detection of the surrounds conditions created by the operations within the algebra. These two approaches are contrasted to one another. Constraints are placed upon surrounds to maintain certain algebraic benefits and the consequences of their relaxations are assessed.