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
Incremental and Enhanced Scanline-Based Segmentation Method for Surface Reconstruction of Sparse LiDAR Data
TL;DR: An incremental scheme—the Incremental Recursive Segmentation (IRIS) that can be easily applied to any segmentation method is proposed, that is achieved by combining the segments of newly added point clouds and the previously segmented results.
Journal ArticleDOI
Localization in Unstructured Environments: Towards Autonomous Robots in Forests with Delaunay Triangulation
TL;DR: A novel approach where local observations are matched to a general tree map using the Delaunay triangularization as the representation format instead of point cloud based matching methods, which is realistic during forest operations.
Journal ArticleDOI
Navigation path planning for autonomous aircraft - Voronoi diagram approach
Jimmy Krozel,Dominick Andrisani +1 more
TL;DR: The present technique for generating a search graph depicting topologically unique paths around mountain boundaries at constant altitudes involves a description of mountain boundaries as polygons; the search graph is then generated on the basis of a geometric construct.
Phase space ray tracing for illumination optics
TL;DR: A submitted manuscript is the version of the article upon submission and before peer-review as discussed by the authors, while a published version is the final layout of the paper including the volume, issue and page numbers.
Journal ArticleDOI
Digital Three-Dimensional Modelling of Donatello's David by Frequency-Modulated Laser Radar
TL;DR: In this article, a laser scanner based on the operation principle of continuous-wave frequency-modulated (CWFM) radar is applied to the acquisition of a digital three-dimensional model of the well-known David by Donatello.
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.