Boolean representation of general planar polygons
F. R. Feito, M. Rivero, A. Rueda

Departamento de Informática
Universidad de Jaén


  There are many applications of the geometric modelling in which it is necessary to accomplish decompositions of the geometric objects that intervene in the model, to facilitate the analysis and design of the algorithms implicated in the resolution of particular problems. Triangulations, trapezoidations, convex decompositions and BSP (binary space partitioning trees) are some of the methods used for the polygon representation. In this work we present a new type of decomposition, based on triangles, valid for closed polygons, manifold and non-manifold, with or without holes. The structure as, well as the necessary algorithms for the calculation of the representation, is easy to implement. The resulting formula can be seen as a particular case of CSG representation of polygons, in  which the primitives are triangles.

 Keywords: polygons, Boolean expresions, decomposition of polygons, triangles, CSG