Voronoi diagrams and arrangements
Discrete & Computational Geometry
A linear-time algorithm for computing the Voronoi diagram of a convex polygon
Discrete & Computational Geometry
Applications of random sampling in computational geometry, II
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
On the computational geometry of pocket machining
On the computational geometry of pocket machining
On the construction of abstract Voronoi diagrams
Discrete & Computational Geometry
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Randomized incremental construction of abstract Voronoi diagrams
Computational Geometry: Theory and Applications
Voronoi diagrams and Delaunay triangulations
Handbook of discrete and computational geometry
Voronoi diagrams based on convex distance functions
SCG '85 Proceedings of the first annual symposium on Computational geometry
Combinatorial Properties of Abstract Voronoi Diagrams
WG '89 Proceedings of the 15th International Workshop on Graph-Theoretic Concepts in Computer Science
Abstract Voronoi Diagrams and their Applications
CG '88 Proceedings of the International Workshop on Computational Geometry on Computational Geometry and its Applications
Hamiltonian Abstract Voronoi Diagrams in Linear Time
ISAAC '94 Proceedings of the 5th International Symposium on Algorithms and Computation
Casting a polyhedron with directional uncertainty
Computational Geometry: Theory and Applications
Abstract Voronoi diagram in 3-space
Journal of Computer and System Sciences
SFCS '75 Proceedings of the 16th Annual Symposium on Foundations of Computer Science
Link distance and shortest path problems in the plane
Computational Geometry: Theory and Applications
The ordered anti-median problem with distances derived from a strictly convex norm
Discrete Applied Mathematics
On the complexity of higher order abstract voronoi diagrams
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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Abstract Voronoi diagrams [R. Klein, Concrete and Abstract Voronoi Diagrams, Lecture Notes in Computer Science, vol. 400, Springer-Verlag, 1987] were designed as a unifying concept that should include as many concrete types of diagrams as possible. To ensure that abstract Voronoi diagrams, built from given sets of bisecting curves, are finite graphs, it was required that any two bisecting curves intersect only finitely often; this axiom was a cornerstone of the theory. In [A.G. Corbalan, M. Mazon, T. Recio, Geometry of bisectors for strictly convex distance functions, International Journal of Computational Geometry and Applications 6 (1) (1996) 45-58], Corbalan et al. gave an example of a smooth convex distance function whose bisectors have infinitely many intersections, so that it was not covered by the existing AVD theory. In this paper we give a new axiomatic foundation of abstract Voronoi diagrams that works without the finite intersection property.