Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms
ACM Transactions on Graphics (TOG)
Computer graphics: principles and practice (2nd ed.)
Computer graphics: principles and practice (2nd ed.)
Introduction to HOL: a theorem proving environment for higher order logic
Introduction to HOL: a theorem proving environment for higher order logic
On degeneracy in geometric computations
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
LEDA: a platform for combinatorial and geometric computing
LEDA: a platform for combinatorial and geometric computing
Formalization of Planar Graphs
Proceedings of the 8th International Workshop on Higher Order Logic Theorem Proving and Its Applications
Formalizing Convex Hull Algorithms
TPHOLs '01 Proceedings of the 14th International Conference on Theorem Proving in Higher Order Logics
Three-valued logic in bounded model checking
MEMOCODE '05 Proceedings of the 2nd ACM/IEEE International Conference on Formal Methods and Models for Co-Design
Hazard detection in combinational and sequential switching circuits
IBM Journal of Research and Development
Dependable polygon-processing algorithms for safety-critical embedded systems
EUC'05 Proceedings of the 2005 international conference on Embedded and Ubiquitous Computing
Formalizing Desargues' theorem in Coq using ranks
Proceedings of the 2009 ACM symposium on Applied Computing
Dependable polygon-processing algorithms for safety-critical embedded systems
EUC'05 Proceedings of the 2005 international conference on Embedded and Ubiquitous Computing
A case study in formalizing projective geometry in Coq: Desargues theorem
Computational Geometry: Theory and Applications
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Many safety-critical systems deal with geometric objects. Reasoning about the correctness of such systems is mandatory and requires the use of basic definitions of geometry for the specification of these systems. Despite the intuitive meaning of such definitions, their formalisation is not at all straightforward: In particular, degeneracies lead to situations where none of the Boolean truth values adequately defines a geometric primitive. Therefore, we use a three-valued logic for the definition of geometric primitives to explicitly handle such degenerate cases. We have implemented a three-valued library of linear geometry in an interactive theorem prover for higher order logic which allows us to specify and verify entire algorithms of computational geometry.