Computing a ham-sandwich cut in two dimensions
Journal of Symbolic Computation
Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
A geometric consistency theorem for a symbolic perturbation scheme
Journal of Computer and System Sciences
Finite-resolution computational geometry
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
Triangulating topological spaces
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Computational geometry: a retrospective
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Polyhedral modelling with exact arithmetic
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
How good are convex hull algorithms?
Proceedings of the eleventh annual symposium on Computational geometry
Robust proximity queries: an illustration of degree-driven algorithm design
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Controlled perturbation for arrangements of polyhedral surfaces with application to swept volumes
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
On degeneracy in geometric computations
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Linear-time triangulation of a simple polygon made easier via randomization
Proceedings of the sixteenth annual symposium on Computational geometry
An Easy to Use Implementation of Linear Perturbations within CGAL
WAE '99 Proceedings of the 3rd International Workshop on Algorithm Engineering
Exact Computation of 4-D Convex Hulls with Perturbation and Acceleration
PG '99 Proceedings of the 7th Pacific Conference on Computer Graphics and Applications
Stability versus speed in a computable algebraic model
Theoretical Computer Science - Real numbers and computers
Handling degeneracies in exact boundary evaluation
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Point set stratification and Delaunay depth
Computational Statistics & Data Analysis
Sliver-free perturbation for the Delaunay tetrahedrization
Computer-Aided Design
Algorithm engineering: bridging the gap between algorithm theory and practice
Algorithm engineering: bridging the gap between algorithm theory and practice
Analytical aspects of tie breaking
Theoretical Computer Science
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Many descriptions of algorithms in computational geometry exclude degeneracies by fiat. Practitioners are left to their own devices for dealing with degeneracies when implementing such algorithms. Since degeneracies tend to be numerous and hard to enumerate exhaustively, this is often a reason against implementing such algorithms. This paper proposes a symbolic scheme for treating degeneracies. Our method is simple to use, and is applicable to a variety of problems in computational geometry. Implementation, limitations and wider issues are discussed.