Journal ArticleDOI
Two algorithms for constructing a Delaunay triangulation
Der-Tsai Lee,Bruce Schachter +1 more
TLDR
This paper provides a unified discussion of the Delaunay triangulation and two algorithms are presented for constructing the triangulations over a planar set ofN points.Abstract:
This paper provides a unified discussion of the Delaunay triangulation. Its geometric properties are reviewed and several applications are discussed. Two algorithms are presented for constructing the triangulation over a planar set ofN points. The first algorithm uses a divide-and-conquer approach. It runs inO(N logN) time, which is asymptotically optimal. The second algorithm is iterative and requiresO(N
2) time in the worst case. However, its average case performance is comparable to that of the first algorithm.read more
Citations
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Journal ArticleDOI
Long-term pattern formation and maintenance for battery-powered robots
TL;DR: This paper presents a distributed, energy-aware method for the autonomous deployment and maintenance of battery-powered robots within a known or unknown region in 2D space that allows for applications in GPS-denied environments such as underwater sensing or underground monitoring.
Book ChapterDOI
Conditionality Analysis of the Radial Basis Function Matrix
Martin Cervenka,Vaclav Skala +1 more
TL;DR: Experiments made proved dependency between the shape parameter and number of RBF center points where the matrix is ill-conditioned, and the dependency can be further described as an analytical function.
Journal ArticleDOI
An incremental algorithm for simultaneous construction of 2D Voronoi diagram and Delaunay triangulation based on a face-based data structure
TL;DR: In this article , a new incremental algorithm with an overall complexity of O(n logn) for constructing both the 2D Voronoi diagram (VD) and Delaunay triangulation (DT) is proposed.
Image Reconstruction in Photoacoustic Computed Tomography with Acoustically Heterogeneous Media
TL;DR: Huang et al. as discussed by the authors developed and investigated a full-wave approach to iterative image reconstruction in PACT with acoustically heterogeneous lossy media, which is based on the exact photoacoustic (PA) wave wave.
Journal ArticleDOI
The Weber Location Problem: The Threshold Objective
Tammy Drezner,Zvi Drezner +1 more
TL;DR: An optimal algorithm is developed to solve the Weber location problem and the weights of the Weber problem are drawn form a multivariate distribution.
References
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Journal ArticleDOI
Nouvelles applications des paramètres continus à théorie des formes quadratiques. Deuxième Mémoire. Recherches sur les paralléloèdres primitifs.
Proceedings ArticleDOI
Closest-point problems
Michael Ian Shamos,Dan Hoey +1 more
TL;DR: The purpose of this paper is to introduce a single geometric structure, called the Voronoi diagram, which can be constructed rapidly and contains all of the relevant proximity information in only linear space, and is used to obtain O(N log N) algorithms for most of the problems considered.