Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Algorithms
Topological models for boundary representation: a comparison with n-dimensional generalized maps
Computer-Aided Design - Beyond solid modelling
Algebraic specification of a 3D-modeler based on hypermaps
CVGIP: Graphical Models and Image Processing
Algorithmic geometry
Introduction to algorithms
Journal of Automated Reasoning
Formalizing Convex Hull Algorithms
TPHOLs '01 Proceedings of the 14th International Conference on Theorem Proving in Higher Order Logics
The Design and Implementation of Planar Maps in CGAL
WAE '99 Proceedings of the 3rd International Workshop on Algorithm Engineering
Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Interactive Theorem Proving and Program Development
Interactive Theorem Proving and Program Development
Proceedings of the 2007 ACM symposium on Applied computing
GWB: A Solid Modeler with Euler Operators
IEEE Computer Graphics and Applications
Classroom examples of robustness problems in geometric computations
Computational Geometry: Theory and Applications
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
Polyhedra genus theorem and Euler formula: A hypermap-formalized intuitionistic proof
Theoretical Computer Science
Edge-Based Data Structures for Solid Modeling in Curved-Surface Environments
IEEE Computer Graphics and Applications
Journal of Automated Reasoning
Certified exact real arithmetic using co-induction in arbitrary integer base
FLOPS'08 Proceedings of the 9th international conference on Functional and logic programming
Mechanical theorem proving in computational geometry
ADG'04 Proceedings of the 5th international conference on Automated Deduction in Geometry
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This 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.