TY - GEN
T1 - Controlled perturbation for certified geometric computing with fixed-precision arithmetic
AU - Halperin, Dan
N1 - Funding Information:
This work has been supported in part by the Israel Science Foundation (grant no. 236/06), by the German-Israeli Foundation (grant no. 969/07), and by the Hermann Minkowski–Minerva Center for Geometry at Tel Aviv University.
PY - 2010
Y1 - 2010
N2 - 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.
AB - 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.
UR - https://www.scopus.com/pages/publications/78149250909
U2 - 10.1007/978-3-642-15582-6_19
DO - 10.1007/978-3-642-15582-6_19
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AN - SCOPUS:78149250909
SN - 3642155812
SN - 9783642155819
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 92
EP - 95
BT - Mathematical Software, ICMS 2010 - Third International Congress on Mathematical Software, Proceedings
T2 - 3rd International Congress on Mathematical Software, ICMS 2010
Y2 - 13 September 2010 through 17 September 2010
ER -