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Voronoi tiling and circle packing on spiral lattices with rotational symmetry
It is shown that the bifurcation diagram of circle packings on logarithmic spiral lattices with rotational symmetry is graph-theoretically dual to...
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Voronoi Cells
Every real algebraic variety X determines aVoronoi decomposition of its ambient Euclidean space...
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Unbounded Regions of High-Order Voronoi Diagrams of Lines and Line Segments in Higher Dimensions
We study the behavior at infinity of the farthest and the higher-order Voronoi diagram of n line segments or lines in a d -dimensional Euclidean...
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An Optimal Deterministic Algorithm for Geodesic Farthest-Point Voronoi Diagrams in Simple Polygons
Given in the plane a set S of m point sites in a simple polygon P of n vertices, we consider the problem of computing the geodesic farthest-point...
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Tropical Bisectors and Voronoi Diagrams
In this paper we initiate the study of tropical Voronoi diagrams. We start out with investigating bisectors of finitely many points with respect to...
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A boundary-partition-based Voronoi diagram of d-dimensional balls: definition, properties, and applications
In computational geometry, different ways of space partitioning have been developed, including the Voronoi diagram of points and the power diagram of...
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Dispersing facilities on planar segment and circle amidst repulsion
In this paper, we study restricted variations of the following obnoxious facility location problem in the plane: locate k new obnoxious facilities...
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Non-Simplicial Delaunay Meshing via Approximation by Radical Partitions
AbstractWe consider the construction of a polyhedral Delaunay partition as a limit of the sequence of power diagrams (in Russian traditionally called
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Hybrid Voronoi Mesh Generation: Algorithms and Unsolved Problems
AbstractWe consider problem of constructing Voronoi mesh where the union of Voronoi cells approximates the computational domain with a piecewise...
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An Optimal and Practical Algorithm for the Planar 2-Center Problem
The 2-center problem for a set S of n points in the plane asks for two congruent circular disks of the minimum radius...
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A System of Hamilton-Jacobi Equations Characterizing Geodesic Centroidal Tessellations
We introduce a class of systems of Hamilton-Jacobi equations characterizing geodesic centroidal tessellations, i.e., tessellations of domains with...
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Laguerre Voronoi Diagram as a Model for Generating the Tessellation Patterns on the Sphere
We propose a model for generating tessellation patterns on the sphere using the spherical Laguerre Voronoi diagram which satisfies the real-world...
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Approximation Algorithms for Solving the 1-Line Minimum Steiner Tree of Line Segments Problem
We address the 1-line minimum Steiner tree of line segments (1L-MStT-LS) problem. Specifically, given a set S of n disjoint line segments in
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Randomized incremental construction for the Hausdorff Voronoi diagram revisited and extended
The Hausdorff Voronoi diagram of clusters of points in the plane is a generalization of Voronoi diagrams based on the Hausdorff distance function....
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On the Structure of Higher Order Voronoi Cells
The classic Voronoi cells can be generalized to a higher order version by considering the cells of points for which a given k -element subset of the...
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Voronoi Diagrams for a Moderate-Sized Point-Set in a Simple Polygon
Given a set of sites in a simple polygon, a geodesic Voronoi diagram of the sites partitions the polygon into regions based on distances to sites...
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Polygonal and Polyhedral Delaunay Meshing
We consider construction of a polyhedral Delaunay partition as a limit of the sequence of radical partitions (power diagrams), while the dual Voronoi...