Surface reconstruction from unorganized points
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
An optimal algorithm for approximate nearest neighbor searching fixed dimensions
Journal of the ACM (JACM)
QSplat: a multiresolution point rendering system for large meshes
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Voronoi diagram of a circle set from Voronoi diagram of a point set: topology
Computer Aided Geometric Design
Voronoi diagram of a circle set from Voronoi diagram of a point set: geometry
Computer Aided Geometric Design
Pointshop 3D: an interactive system for point-based surface editing
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Proceedings of the conference on Visualization '01
Efficient simplification of point-sampled surfaces
Proceedings of the conference on Visualization '02
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
On the normal vector estimation for point cloud data from smooth surfaces
Computer-Aided Design
A survey of point-based techniques in computer graphics
Computers and Graphics
Some properties of the planar Euclidean relative neighbourhood graph
Pattern Recognition Letters
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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 @a. Our algorithm is based on the observation that a candidate point which may define an edge of an EGG with a given point p@?P is always in the scaled Voronoi region of p with a scale factor 2/@a^2 when the parameter @a=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.