A Topological Map-Based Kernel for Polyhedron Modelers: Algebraic Specification and Logic Prototyping

Abstract

This paper deals with the topology of surfaces, in the boundary representation of three dimensional objects. Orientable, not orientable, closed or open surfaces are efficiently described and handled when considered as combinatorial generalized maps. An algebra of such maps is first described. Using this algebra, operations to build polyhedra step by step are next defined. That is the basis of a graphical modeler presently under consideration. The presentation uses algebraic software specification techniques in an abstract way. Finally, a systematical validation of the specification by logic prototyping is described.