Verifiable implementation of geometric algorithms using finite precision arithmetic
Artificial Intelligence - Special issue on geometric reasoning
Towards implementing robust geometric computations
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Epsilon geometry: building robust algorithms from imprecise computations
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Efficient Delaunay triangulation using rational arithmetic
ACM Transactions on Graphics (TOG)
Numerical stability of algorithms for line arrangements
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Static analysis yields efficient exact integer arithmetic for computational geometry
ACM Transactions on Graphics (TOG)
Towards exact geometric computation
Computational Geometry: Theory and Applications - Special issue: computational geometry, theory and applications
Handbook of discrete and 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
Interval arithmetic yields efficient dynamic filters for computational geometry
Discrete Applied Mathematics - Special issue 14th European workshop on computational geometry CG'98 Selected papers
High-Level Filtering for Arrangements of Conic Arcs
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
A Computational Basis for Conic Arcs and Boolean Operations on Conic Polygons
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Algebraic methods and arithmetic filtering for exact predicates on circle arcs
Computational Geometry: Theory and Applications
Controlled perturbation for Delaunay triangulations
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Iterated snap rounding with bounded drift
Computational Geometry: Theory and Applications
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
Reliable and efficient geometric computing
CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
| Hi-index | 0.00 |
Given a collection C of circles in the plane, we wish to construct the arrangement A(C) (namely the subdivision of the plane into vertices, edges and faces induced by C) using floating point arithmetic. We present an efficient scheme, controlled perturbation, that perturbs the circles in C slightly to form a collection C', so that all the predicates that arise in the construction of A(C') are computed accurately and A(C') is degeneracy free.We introduced controlled perturbation several years ago, and already applied it to certain types of arrangements. The major contribution of the current work is the derivation of a good (small) resolution bound, that is, a bound on the minimum separation of features of the arrangement that is required to guarantee that the predicates involved in the construction can be safely computed with the given (limited) precision arithmetic. A smaller resolution bound leads to smaller perturbation of the original input.We present the scheme, describe how the resolution bound is determined and how it effects the perturbation magnitude. We implemented the perturbation scheme and the construction of the arrangement and we report on experimental results.