Rewriting-based Derivation of Eecient Algorithms to Build Planar Subdivisions

Algebraic speciications allied to rewriting are used more and more often in design and logical prototyping of programs. We show how these techniques can be applied to a basic problem in computational geometry, namely the construction of planar subdivisions. We build up a simple, complete and convergent system of rules to cope with this problem and show how it is transformed to describe concrete and eecient algorithms such as plane-sweep ones.