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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Online product configuration in e-commerce with 3d web viewing technology
TL;DR: A novel idea for online 3D product configuration in e-Commerce and its prototyping system using the Web viewing technology that collects the customer preference and feedback of the product by transferring the information over to and stored in a backend PDM system.
Guarantees Concerning Geometric Objects with Imprecise Points
TL;DR: It is argued that in some cases, it may be desirable for geometric algorithms to treat this imprecision as an explicit component of the input, and to reflect this imp recursion in the output.
Proceedings ArticleDOI
Retrieving cross-sectional contours from tunnel point clouds
TL;DR: For the tunnel point clouds acquired by 3-d laser scanner, a method of automatically retrieving cross-sectional contours of tunnels is proposed by the use of abundant normal vectors embedded in point clouds, and an improved 2-d Delaunay triangulation algorithm is employed.
Journal ArticleDOI
Horizontal Expanding Method—A Quick Algorithm for Generating Delaunay Triangulation from Points in the Plane: Horizontal Expanding Method—A Quick Algorithm for Generating Delaunay Triangulation from Points in the Plane
Proceedings ArticleDOI
Efficient Communication in Large Multi-robot Networks
TL;DR: The proposed communication model is generic to any type of message and guarantees a low hop routing between any pair of robots in this network and easily scales up to 1000 robots while drastically reducing the space complexity for maintaining the network information.
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.