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
Generalized earthquake frequency–magnitude distribution described by asymmetric Laplace mixture modelling
Arnaud Mignan,Arnaud Mignan +1 more
TL;DR: In this paper, an asymmetric Laplace mixture model (GFMD-ALMM) is proposed with its parameters (detection parameter kappa, Gutenberg-Richter beta-value, mc distribution, as well as number K and weight w of eFMD components) estimated using a semi-supervised hard expectation maximization approach including BIC penalties for model complexity.
Journal ArticleDOI
Planning for a Tight Squeeze: Navigation of Morphing Soft Robots in Congested Environments
TL;DR: In this article, a path-planning method for morphing soft robots in congested environments is presented, which is suitable for all scales of robots and environments, from intra-organ biomedical navigation to search-and-rescue operations in cave networks.
Dissertation
Extended mortar method for contact and mesh-tying applications
TL;DR: A set of methods to handle tying and contact problems along real and virtual (embedded) surfaces in the framework of the finite element method to treat frictional contact problems is developed and implemented in the in-house finite element suite Z-set.
Journal ArticleDOI
Single-step creation of localized Delaunay triangulations
Filipe Araujo,Luís Rodrigues +1 more
TL;DR: Two localized algorithms are presented that build a graph called planar localized Delaunay triangulation, PLDel, known to be a good spanner of the Unit Disk Graph, UDG, that improve previous algorithms with similar theoretical bounds in the following aspects.
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.