Efficient Delaunay triangulation using rational arithmetic
ACM Transactions on Graphics (TOG)
Efficient exact arithmetic for computational geometry
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Exact geometric predicates using cascaded computation
Proceedings of the fourteenth annual symposium on Computational geometry
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
LEDA: a platform for combinatorial and geometric computing
LEDA: a platform for combinatorial and geometric computing
Computational Geometry: Theory and Applications
How to Compute the Voronoi Diagram of Line Segments: Theoretical and Experimental Results
ESA '94 Proceedings of the Second Annual European Symposium on Algorithms
Controlled perturbation for Delaunay triangulations
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Snap rounding of Bézier curves
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Reliable and efficient geometric computing
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Exact and efficient 2D-arrangements of arbitrary algebraic curves
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Controlled perturbation for certified geometric computing with fixed-precision arithmetic
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
Controlled Perturbation of sets of line segments in R2 with smart processing order
Computational Geometry: Theory and Applications
A general approach to the analysis of controlled perturbation algorithms
Computational Geometry: Theory and Applications
Reliable and efficient geometric computing
CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
| Hi-index | 0.00 |
Most algorithms of computational geometry are designed for the Real-RAM and non-degenerate input. We call such algorithms idealistic. Executing an idealistic algorithm with floating point arithmetic may fail. Controlled perturbation replaces an input x by a random nearby $\tilde{x}$ in the δ-neighborhood of x and then runs the floating point version of the idealistic algorithm on $\tilde{x}$. The hope is that this will produce the correct result for $\tilde{x}$ with constant probability provided that δ is small and the precision L of the floating point system is large enough. We turn this hope into a theorem for a large class of geometric algorithms and describe a general methodology for deriving a relation between δ and L. We exemplify the usefulness of the methodology by examples.