Efficient exact geometric computation made easy
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
A core library for robust numeric and geometric computation
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Fundamental problems of algorithmic algebra
Fundamental problems of algorithmic algebra
A new constructive root bound for algebraic expressions
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Exact geometric computation: theory and applications
Exact geometric computation: theory and applications
The design of core 2: a library for exact numeric computation in geometry and algebra
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
| Hi-index | 5.23 |
Guaranteeing accuracy is the critical capability in exact geometric computation, an important paradigm for constructing robust geometric algorithms. Constructive root bounds is the fundamental technique needed to achieve such guaranteed accuracy. Current bounds are overly pessimistic in the presence of general rational input numbers. In this paper, we introduce a method which greatly improves the known bounds for k-ary rational input numbers. Since a majority of input numbers in scientific and engineering applications are either binary (k = 2) or decimal (k = 10), our results could lead to a significant speedup for a large class of applications. We apply our method to two of the best available constructive root bounds, the BFMSS Bound and the Degree-Measure Bound. Implementation and experimental results based on the Core Library are reported.