Abstract
AbstractThis 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. It performs a recursive traversal of the existing convex hull to compute the new hull each time a new point is inserted. This requires using well-founded recursion in Coq. A concrete implementation in Ocaml is then automatically extracted and an efficient C++ program is derived (by hand) from the specification.KeywordsConvex HullComputational GeometryFormal ProofIncremental AlgorithmCollinear PointThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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