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
Voronoi diagrams—a survey of a fundamental geometric data structure
TL;DR: The Voronoi diagram as discussed by the authors divides the plane according to the nearest-neighbor points in the plane, and then divides the vertices of the plane into vertices, where vertices correspond to vertices in a plane.
Journal ArticleDOI
The Quadtree and Related Hierarchical Data Structures
TL;DR: L'accentuation est mise sur la representation de donnees dans les applications de traitement d'images, d'infographie, les systemes d'informations geographiques and the robotique.
Book ChapterDOI
Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator
TL;DR: Triangle as discussed by the authors is a robust implementation of two-dimensional constrained Delaunay triangulation and Ruppert's Delaunayer refinement algorithm for quality mesh generation, and it is shown that the problem of triangulating a planar straight line graph (PSLG) without introducing new small angles is impossible for some PSLGs.
Journal ArticleDOI
A sweepline algorithm for Voronoi diagrams
TL;DR: A geometric transformation is introduced that allows Voronoi diagrams to be computed using a sweepline technique and is used to obtain simple algorithms for computing the Vor onoi diagram of point sites, of line segment sites, and of weighted point sites.
References
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Journal ArticleDOI
Location in Space: A Theoretical Approach to Economic Geography
Journal ArticleDOI
Two Dimensional Interpolation from Random Data
TL;DR: A method is described for smooth interpolation between random data points in two or more dimensions that gives a smooth surface passing exactly through the given data points, and is suitable for graphical applications.
Book
Location in space: A theoretical approach to economic geography
Peter E. Lloyd,Peter Dicken +1 more
Proximity and reachability in the plane.
TL;DR: The method is applicable for the construction of the Voronoi diagram for a set of more complex figures, e.g., polygons and circles in the Euclidean plane, if the given line segments from a simple polygon, O(NlogN) time is sufficient.
Proceedings ArticleDOI
On triangulations of a set of points in the plane
TL;DR: It is shown that the problem of determining the existence of a triangulation, in a given subset of the line segments whose endpoints are in V, is NP-Complete.