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
Controlled perturbation for Delaunay triangulations
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Reliable and efficient computational geometry via controlled perturbation
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Topological sweep of the complete graph
Discrete Applied Mathematics
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Reliable implementation of geometric algorithms is a notoriously difficult task. Algorithms are usually designed for the Real-RAM, capable of computing with real numbers in the sense of mathematics, and for non-degenerate inputs. But, real computers are not Real-RAMs and inputs are frequently degenerate. In the first part of the talk we illustrate the pitfalls of geometric computing by way of examples [KMP+04]. The examples demonstrate in a lucid way that standard and frequently taught algorithms can go completely astray when naively implemented with floating point arithmetic.