Functional specification and prototyping with oriented combinatorial maps

A functional specification and a prototype based on the notion of oriented combinatorial map are proposed in order to approach computational geometric problems in the plane and allow to focus on logical, topological and geometrical aspects of algorithms, before taking account efficiency in a detailed design based on suitable data structures and traversals.

Abstract

A functional specification and a prototype based on the notion of oriented combinatorial map are proposed in order to approach computational geometric problems in the plane. They allow to focus on logical, topological and geometrical aspects of algorithms, before taking account efficiency in a detailed design based on suitable data structures and traversals. All the descriptions are written into an ML dialect, namely the Ocaml language. They intensively use the notion of quasi-map, an extended version of combinatorial map well adapted to the definition of algorithms by structural induction and to the proof of their total correctness. To illustrate the power of our propositions, classical operations—segmentation of a planar image, point location in a planar subdivision and refinement of a map—are revisited, easily specified and debugged on the quasi-map structure. Finally, an interactive modeler of 3D subdivisions developed from such specifications is overviewed.