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
Controlled perturbation for arrangements of circles
Proceedings of the nineteenth annual symposium on Computational geometry
Dynamic maintenance of molecular surfaces under conformational changes
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Controlled perturbation for Delaunay triangulations
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Controlled Perturbation of sets of line segments in R2 with smart processing order
Computational Geometry: Theory and Applications
Reliable and efficient computational geometry via controlled perturbation
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Technical note: Robust cascading of operations on polyhedra
Computer-Aided Design
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Transforming geometric algorithms into effective computer programs is a difficult task. This transformation is particularly made hard by the basic assumptions of most theoretical geometric algorithms concerning the handling of robustness issues, namely issues related to arithmetic precision and degenerate input. Controlled perturbation, an approach to robust implementation of geometric algorithms we introduced in the late 1990's, aims at removing degeneracies and certifying correct predicate-evaluation, while using fixed-precision arithmetic. After exposing the key ideas underlying the scheme, we review the development of the approach over the past decade including variations and extensions, software implementation and applications. We conclude by pointing out directions for further development and major challenges.