Algorithms
Introduction to algorithms
Algorithmic geometry
Using Reflection to Build Efficient and Certified Decision Procedures
TACS '97 Proceedings of the Third International Symposium on Theoretical Aspects of Computer Software
Formal Specification and Theorem Proving Breakthroughs in Geometric Modeling
Proceedings of the 11th International Conference on Theorem Proving in Higher Order Logics
Formalizing the Trading Theorem for the Classification of Surfaces
TPHOLs '02 Proceedings of the 15th International Conference on Theorem Proving in Higher Order Logics
Dependent Types, Theorem Proving, and Applications for a Verifying Compiler
Verified Software: Theories, Tools, Experiments
Formalizing projective plane geometry in Coq
ADG'08 Proceedings of the 7th international conference on Automated deduction in geometry
Using three-valued logic to specify and verify algorithms of computational geometry
ICFEM'05 Proceedings of the 7th international conference on Formal Methods and Software Engineering
Dependable polygon-processing algorithms for safety-critical embedded systems
EUC'05 Proceedings of the 2005 international conference on Embedded and Ubiquitous Computing
Mechanical theorem proving in computational geometry
ADG'04 Proceedings of the 5th international conference on Automated Deduction in Geometry
Formal study of plane delaunay triangulation
ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
Designing and proving correct a convex hull algorithm with hypermaps in Coq
Computational Geometry: Theory and Applications
Consistency analysis of decision-making programs
Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
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We study the development of formally proved algorithms for computational geometry. The result of this work is a formal description of the basic principles that make convex hull algorithms work and two programs that implement convex hull computation and have been automatically obtained from formally verified mathematical proofs. A special attention has been given to handling degenerate cases that are often overlooked by conventional algorithm presentations.