Trash removal algorithm for fast construction of the elliptic Gabriel graph using Delaunay triangulation

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Given a set of points P, finding near neighbors among the points is an important problem in many applications in CAD/CAM, computer graphics, computational geometry, etc. In this paper, we propose an efficient algorithm for constructing the elliptic Gabriel graph (EGG), which is a generalization of the well-known Gabriel graph and parameterized by a non-negative value alpha. Our algorithm is based on the observation that a candidate point which may define an edge of an EGG with a given point p E P is always in the scaled Voronoi region of p with a scale factor 2/alpha(2) when the parameter alpha < 1. From this observation, we can reduce the search space for locating neighbors of p in the EGG. For the case of alpha >= 1, due to the fact that EGG is a subgraph of the Delaunay graph of P, EGG can be efficiently computed by watching the validity of each edge in the Delaunay graph. The proposed algorithm is shown to have its time complexity as O(n(3)) in the worst case and O(n) in the average case when a is moderately close to unity. The idea presented in this paper may similarly apply to other problems for the proximity search for point sets. (c) 2008 Elsevier Ltd. All rights reserved.
Publisher
ELSEVIER SCI LTD
Issue Date
2008-08
Language
English
Article Type
Article
Keywords

NORMAL VECTOR ESTIMATION; POINT SET; VORONOI DIAGRAM; CIRCLE SET; DIMENSIONS

Citation

COMPUTER-AIDED DESIGN, v.40, pp.852 - 862

ISSN
0010-4485
DOI
10.1016/j.cad.2008.05.002
URI
http://hdl.handle.net/10203/89820
Appears in Collection
IE-Journal Papers(저널논문)
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