Set Boolean Operat ions on 2 D Objects

Abstrac t Set boolean operations between 2-dlmensional geometric objects are crucial in computational geometry and deserve rigorous treatments. We build up a simple and convergent system of rewrite rules modulo equations to cope with their design. This system is complete is the sense that it gives a detailed description for all particular cases. This specification leans on a new operation of labeling serf-refinement of planar subdivisions. Starting from these abstract descriptions, we design concrete algorithms with a new method. The rewrite system is successively transformed in specialized ones from which we derive efficient treatments, like plane-sweep algorithms.