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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Proceedings ArticleDOI
Weighed ℓ 1 on the Simplex: Compressive Sensing Meets Locality
TL;DR: In this paper, the authors propose weighted l 0 and weighted l 1 regularizations that encourage representation via neighborhood atoms suited for dictionary based manifold learning, assuming that the data is generated from Delaunay triangulation.
Polynomial-size nonobtuse triangulation
Marshall Bern,David Eppstein +1 more
TL;DR: The main result is that a polygon with n sides can be triangulated with O(n 2 ) nonobtuse triangles, and it is shown that any triangulation (without Steiner points) of a simple polygon has a reflnement with O-shaped triangles.
Dissertation
Algorithms for Multiple Ground Target Tracking
TL;DR: A novel visual tracking algorithm that has high speed and better or comparable performance to state-of-the-art trackers is proposed that alleviates issues like the track impurity and coalescence problem and achieves better performance comparing to standard trackers assuming state independence.
Journal ArticleDOI
A dynamic data structure suitable for adaptive mesh refinement in finite element method
TL;DR: A dynamic data structure and its implementation, used for an optimum mesh generator, which takes advantage of the Delaunay algorithm, which maximizes the summation of the smallest angles in all triangles and thus creates a mesh that is proved to be an optimumMesh for use in the finite element method.
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.