Journal of Computational and Applied Mathematics
Geometric constraint solver using multivariate rational spline functions
Proceedings of the sixth ACM symposium on Solid modeling and applications
On the combinatorial complexity of euclidean Voronoi cells and convex hulls of d-dimensional spheres
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
On the Local Form and Transitions of Symmetry Sets, Medial Axes, and Shocks
International Journal of Computer Vision - Special Issue on Computational Vision at Brown University
Voronoi diagrams of semi-algebraic sets
Voronoi diagrams of semi-algebraic sets
Precise Voronoi cell extraction of free-form rational planar closed curves
Proceedings of the 2005 ACM symposium on Solid and physical modeling
The Voronoi Diagram of Curved Objects
Discrete & Computational Geometry
The predicates of the Apollonius diagram: algorithmic analysis and implementation
Computational Geometry: Theory and Applications - Special issue on robust geometric algorithms and their implementations
The predicates for the Voronoi diagram of ellipses
Proceedings of the twenty-second annual symposium on Computational geometry
Proceedings of the 2007 ACM symposium on Solid and physical modeling
An exact, complete and efficient computation of arrangements of Bézier curves
Proceedings of the 2007 ACM symposium on Solid and physical modeling
EXACUS: efficient and exact algorithms for curves and surfaces
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Experimental evaluation and cross-benchmarking of univariate real solvers
Proceedings of the 2009 conference on Symbolic numeric computation
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
A generic algebraic kernel for non-linear geometric applications
Proceedings of the twenty-seventh annual symposium on Computational geometry
Exact medial axis computation for circular arc boundaries
Proceedings of the 7th international conference on Curves and Surfaces
Computer Aided Geometric Design
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We study the Voronoi diagram, under the Euclidean metric, of a set of ellipses, given in parametric representation. The article concentrates on the InCircle predicate, which is the hardest to compute, and describes an exact and complete solution. It consists of a customized subdivision-based method that achieves quadratic convergence, leading to a real-time implementation for non-degenerate inputs. Degenerate cases are handled using exact algebraic computation. We conclude with experiments showing that most instances run in less than 0.1 s, on a 2.6 GHz Pentium-4, whereas degenerate cases may take up to 13 s. Our approach readily generalizes to smooth convex objects.