International audienceThis article presents the formal design of a functional algorithm which computes the convex hull of a finite set of points incrementally. This algorithm, specified in Coq, is then automatically extracted into an OCaml-program which can be plugged into an interface for data input (point selection) and graphical visualization of the output. A formal proof of total correctness, relying on structural induction, is also carried out. This requires to study many topologic and geometric properties. We use a combinatorial structure, namely hypermaps, to model planar subdivisions of the plane. Formal specifications and proofs are carried out in the Calculus of Inductive Constructions and its implementation: the Coq system

This article deals with a method to build programs in computational geometry from their specifications. It focuses on a case study namely computing incrementally the convex hull of a set of points in the plane using hypermaps. Our program to compute convex hulls is specified and proved correct using the Coq proof assistant. A concrete implementation in Ocaml is then automatically extracted and an efficient C++ program is derived (by hand) from the specification.