Epsilon geometry: building robust algorithms from imprecise computations
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Polyhedral perturbations that preserve topological form
Computer Aided Geometric Design
A perturbation scheme for spherical arrangements with application to molecular modeling
Computational Geometry: Theory and Applications - special issue on applied 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
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Combinatorial algorithms for feedback problems in directed graphs
Information Processing Letters
Controlled perturbation for Delaunay triangulations
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Ordering by weighted number of wins gives a good ranking for weighted tournaments
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Approximation algorithms for spreading points
Journal of Algorithms
Classroom examples of robustness problems in geometric computations
Computational Geometry: Theory and Applications
Aggregating inconsistent information: Ranking and clustering
Journal of the ACM (JACM)
Reliable and efficient computational geometry via controlled perturbation
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Controlled perturbation for certified geometric computing with fixed-precision arithmetic
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
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Controlled Perturbation is a framework for perturbing geometric sets to make the processes that use them more robust for fixed-precision manipulation. We present a Controlled Perturbation scheme for sets of line segments in R^2 (CPLS, for short). CPLS iteratively perturbs the endpoints of the line segments to eliminate potential degeneracies that may cause round-off errors when using fixed-precision arithmetic. We implemented CPLS and provide experimental results. In the core of this work, we present a novel method for decreasing the perturbation magnitude. The main idea behind our method is that different endpoint processing orders yield different perturbation quality. We devise several heuristics for deciding smart endpoint processing to decrease the perturbation. We implemented and experimented with them. Our experiments show a significant decrease in the perturbation magnitude.