5,243 research outputs found
Gap Processing for Adaptive Maximal Poisson-Disk Sampling
In this paper, we study the generation of maximal Poisson-disk sets with
varying radii. First, we present a geometric analysis of gaps in such disk
sets. This analysis is the basis for maximal and adaptive sampling in Euclidean
space and on manifolds. Second, we propose efficient algorithms and data
structures to detect gaps and update gaps when disks are inserted, deleted,
moved, or have their radius changed. We build on the concepts of the regular
triangulation and the power diagram. Third, we will show how our analysis can
make a contribution to the state-of-the-art in surface remeshing.Comment: 16 pages. ACM Transactions on Graphics, 201
Bregman Voronoi Diagrams: Properties, Algorithms and Applications
The Voronoi diagram of a finite set of objects is a fundamental geometric
structure that subdivides the embedding space into regions, each region
consisting of the points that are closer to a given object than to the others.
We may define many variants of Voronoi diagrams depending on the class of
objects, the distance functions and the embedding space. In this paper, we
investigate a framework for defining and building Voronoi diagrams for a broad
class of distance functions called Bregman divergences. Bregman divergences
include not only the traditional (squared) Euclidean distance but also various
divergence measures based on entropic functions. Accordingly, Bregman Voronoi
diagrams allow to define information-theoretic Voronoi diagrams in statistical
parametric spaces based on the relative entropy of distributions. We define
several types of Bregman diagrams, establish correspondences between those
diagrams (using the Legendre transformation), and show how to compute them
efficiently. We also introduce extensions of these diagrams, e.g. k-order and
k-bag Bregman Voronoi diagrams, and introduce Bregman triangulations of a set
of points and their connexion with Bregman Voronoi diagrams. We show that these
triangulations capture many of the properties of the celebrated Delaunay
triangulation. Finally, we give some applications of Bregman Voronoi diagrams
which are of interest in the context of computational geometry and machine
learning.Comment: Extend the proceedings abstract of SODA 2007 (46 pages, 15 figures
Voronoi Particle Merging Algorithm for PIC Codes
We present a new particle-merging algorithm for the particle-in-cell method.
Based on the concept of the Voronoi diagram, the algorithm partitions the phase
space into smaller subsets, which consist of only particles that are in close
proximity in the phase space to each other. We show the performance of our
algorithm in the case of the two-stream instability and the magnetic shower.Comment: 11 figure
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