Applications of random sampling in computational geometry, II
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
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
Four results on randomized incremental constructions
Computational Geometry: Theory and Applications
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
Controlled perturbation for arrangements of circles
Proceedings of the nineteenth annual symposium on Computational geometry
Smoothed analysis of algorithms: Why the simplex algorithm usually takes polynomial time
Journal of the ACM (JACM)
Dynamic maintenance of molecular surfaces under conformational changes
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Out-of-order event processing in kinetic data structures
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Classroom examples of robustness problems in geometric computations
Computational Geometry: Theory and Applications
Robust Minkowski sums of polyhedra via controlled linear perturbation
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
Controlled perturbation for certified geometric computing with fixed-precision arithmetic
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
Algorithm engineering: bridging the gap between algorithm theory and practice
Algorithm engineering: bridging the gap between algorithm theory and practice
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
Reliable and efficient computational geometry via controlled perturbation
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Stability of Delaunay-type structures for manifolds: [extended abstract]
Proceedings of the twenty-eighth annual symposium on Computational geometry
Controlled linear perturbation
Computer-Aided Design
Analytical aspects of tie breaking
Theoretical Computer Science
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Most geometric algorithms are idealistic in the sense that they are designed for the Real-RAM model of computation and for inputs in general position. Real inputs may be degenerate and floating point arithmetic is only an approximation of real arithmetic. Perturbation replaces an input by a nearby input which is (hopefully) in general position and on which the algorithm can be run with floating point arithmetic. Controlled perturbation as proposed by Halperin et al. calls for more: control over the amount of perturbation needed for a given precision of the floating point system. Or conversely, a control over the precision needed for a given amount of perturbation. Halperin et al. gave controlled perturbation schemes for arrangements of polyhedral surfaces, spheres, and circles.We extend their work and point out that controlled perturbation is a general scheme for converting idealistic algorithms into algorithms which can be executed with floating point arithmetic. We also show how to use controlled perturbation in the context of randomized geometric algorithms without deteriorating the running time. Finally, we give concrete schemes for planar Delaunay triangulations and convex hulls and Delaunay triangulations in arbitrary dimensions. We analyze the relation between the perturbation amount and the precision of the floating point system. We also report about experiments with a planar Delaunay diagram algorithm.