Exact geometric computation in LEDA
Proceedings of the eleventh annual symposium on Computational geometry
Handbook of discrete and computational geometry
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
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
From Algorithm to Program to Software Library
Informatics - 10 Years Back. 10 Years Ahead.
Randomized Zero Testing of Radical Expressions and Elementary Geometry Theorem Proving
ADG '00 Revised Papers from the Third International Workshop on Automated Deduction in Geometry
A Separation Bound for Real Algebraic Expressions
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
High-Level Filtering for Arrangements of Conic Arcs
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Constructive root bound for k-ary rational input numbers
Proceedings of the nineteenth annual symposium on Computational geometry
Towards and open curved kernel
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Counterexamples to the uniformity conjecture
Computational Geometry: Theory and Applications - Special issue on robust geometric algorithms and their implementations
Exact, efficient, and complete arrangement computation for cubic curves
Computational Geometry: Theory and Applications
An exact, complete and efficient computation of arrangements of Bézier curves
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Constructive root bound for k-ary rational input numbers
Theoretical Computer Science
Reliable Implementation of Real Number Algorithms: Theory and Practice
Design of the CGAL 3D Spherical Kernel and application to arrangements of circles on a sphere
Computational Geometry: Theory and Applications
Lower bounds for zero-dimensional projections
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Counterexamples to the uniformity conjecture
Computational Geometry: Theory and Applications - Special issue on robust geometric algorithms and their implementations
Exact, efficient, and complete arrangement computation for cubic curves
Computational Geometry: Theory and Applications
Algorithm engineering: bridging the gap between algorithm theory and practice
Algorithm engineering: bridging the gap between algorithm theory and practice
The diamond operator: implementation of exact real algebraic numbers
CASC'05 Proceedings of the 8th international conference on Computer Algebra in Scientific Computing
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Computing effective root bounds for constant algebraic expressions is a critical problem in the Exact Geometric Computation approach to robust geometric programs. Classical root bounds are often non-constructive. Recently, various authors have proposed bounding methods which might be called constructive root bounds. For the important class of radical expressions, Burnikel et al (BFMS) have provided a constructive root bound which, in the division-free case, is an improvement over previously known bounds and is essentially tight. In the presence of division, their bound requires a quadratic blowup in root bit-bound compared to the division-free case. We present a new constructive root bound that avoids this quadratic blowup and which is applicable to a more general class of algebraic expressions. This leads to dramatically better performance in some computations. We also give an improved version of the degree-measure bound from Mignotte and BFMS. We describe our implementation in the context of the Core Library, and report on some experimental results.