Voronoi diagram of orthogonal polyhedra in two and three dimensions

by   Ioannis Z. Emiris, et al.
University of Athens

Voronoi diagrams are a fundamental geometric data structure for obtaining proximity relations. We consider collections of axis-aligned orthogonal polyhedra in two and three-dimensional space under the max-norm, which is a particularly useful scenario in certain application domains. We construct the exact Voronoi diagram inside an orthogonal polyhedron with holes defined by such polyhedra. Our approach avoids creating full-dimensional elements on the Voronoi diagram and yields a skeletal representation of the input object. We introduce a complete algorithm in 2D and 3D that follows the subdivision paradigm relying on a bounding-volume hierarchy; this is an original approach to the problem. The complexity is adaptive and comparable to that of previous methods, namely linear in the number of sites, namely edges or facets resp. We also provide a numerically stable, open-source implementation in Julia, illustrating the practical nature of our algorithm.


page 1

page 2

page 3

page 4


Orthogonal Voronoi Diagram and Treemap

In this paper, we propose a novel space partitioning strategy for implic...

Stable-Matching Voronoi Diagrams: Combinatorial Complexity and Algorithms

We study algorithms and combinatorial complexity bounds for stable-match...

Farthest-point Voronoi diagrams in the presence of rectangular obstacles

We present an algorithm to compute the geodesic L_1 farthest-point Voron...

Kinetic Geodesic Voronoi Diagrams in a Simple Polygon

We study the geodesic Voronoi diagram of a set S of n linearly moving si...

Efficient Inference on Generalized Fault Diagrams

The generalized fault diagram, a data structure for failure analysis bas...

Three Orthogonal Dimensions for Psychoacoustic Sonification

Objective: Three perceptually orthogonal auditory dimensions for multidi...

The EdgeConflict Predicate in the 3D Apollonius Diagram

In this paper we study one of the fundamental predicates required for th...

Please sign up or login with your details

Forgot password? Click here to reset