Robust ray intersection with interval arithmetic
Proceedings on Graphics interface '90
Interval analysis for computer graphics
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Rasterizing Algebraic Curves and Surfaces
IEEE Computer Graphics and Applications
Efficient isolation of polynomial's real roots
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on linear algebra and arithmetic, Rabat, Morocco, 28-31 May 2001
Isotopic approximation of implicit curves and surfaces
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
On the topology of planar algebraic curves
Proceedings of the twenty-fifth annual symposium on Computational geometry
Exact numerical computation in algebra and geometry
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
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
Discrete & Computational Geometry - Special Issue: 25th Annual Symposium on Computational Geometry; Guest Editor: John Hershberger
A simple but exact and efficient algorithm for complex root isolation
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Non-local isotopic approximation of nonsingular surfaces
Computer-Aided Design
Near optimal tree size bounds on a simple real root isolation algorithm
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
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We provide an empirical study of subdivision algorithms for isolating the simple roots of a polynomial in any desired box region B0 of the complex plane. One such class of algorithms is based on Newton-like interval methods (Moore, Krawczyk, Hansen-Sengupta). Another class of subdivision algorithms is based on function evaluation. Here, Yakoubsohn discussed a method that is purely based on an exclusion predicate. Recently, Sagraloff and Yap introduced another algorithm of this type, called Ceval. We describe the first implementation of Ceval in Core Library. We compare its performance to the above mentioned algorithms, and also to the well-known MPSolve software from Bini and Florentino. Our results suggest that certified evaluation-based methods such as Ceval are encouraging and deserve further exploration.