Boolean Algebra on Physically Meaningful Regions in the Plane

Physically meaningful regions can be modeled by regular open semianalytic sets with bounded boundaries. These sets are named as Yin sets and they form a topological space called the Yin space. Due to the regularity, the Yin sets can be represented by a collection of particular sets of oriented Jordan curves; this collection is referred to as the Jordan space. After defining a meet operation, a join operation, and a complementation operation on the Jordan space, we show that the Yin space and the Jordan space are isomorphic Boolean algebras. The isomorphism is a mapping that sends sets of one-dimensional Jordan curves to two-dimensional regular open semianalytic sets. As one of its distinguishing features, the proposed algorithm is able to handle arbitrarily complex topology of two-dimensional regions.