Boolean operations on general planar polygons

Computing boolean operations between general planar polygons is one of the fundamental problems in geometric and solid modeling. In this work we present a new algorithm to calculate intersection, union and difference, valid for general planar polygons (manifold and non-manifold, with and without holes), based on a formal representation system. This formal model is based on the concept of simplicial chain, developed by Feito and Rivero (Computers & Graphics 22(5) (1998)). Using algebraic operations between simplicial chains we can obtain any general polygon and the Boolean operations between them. The fact of that our algorithm is based on simplicial chains and their operations, reduces the study of special cases, and allows us to develop a robust and efficient algorithm to calculate the intersection between general polygons.