Tessellations

Schoenberg, Frederic Paik

doi:10.1002/9780470057339.vat004

Cited by 1 publication

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“…A tessellation is a partition of a space into convex polytopes; tessellation of the plane (into convex polygons) is the most frequently studied case (Schoenberg (2002)). Given 2 ≤ n < ∞ distinct points in R 2 , we associate all points in the space with the closest member(s) of the point set with respect to the Euclidean distance.…”

Section: Voronoi Diagrams and Delaunay Tessellationsmentioning

confidence: 99%

Extension of one-dimensional proximity regions to higher dimensions

Ceyhan

2010

Computational Geometry

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Proximity maps and regions are defined based on the relative allocation of points from two or more classes in an area of interest and are used to construct random graphs called proximity catch digraphs (PCDs) which have applications in various fields. The simplest of such maps is the spherical proximity map which maps a point from the class of interest to a disk centered at the same point with radius being the distance to the closest point from the other class in the region. The spherical proximity map gave rise to class cover catch digraph (CCCD) which was applied to pattern classification. Furthermore for uniform data on the real line, the exact and asymptotic distribution of the domination number of CCCDs were analytically available. In this article, we determine some appealing properties of the spherical proximity map in compact intervals on the real line and use these properties as a guideline for defining new proximity maps in higher dimensions. Delaunay triangulation is used to partition the region of interest in higher dimensions. Furthermore, we introduce the auxiliary tools used for the construction of the new proximity maps, as well as some related concepts that will be used in the investigation and comparison of them and the resulting graphs. We characterize the geometry invariance of PCDs for uniform data. We also provide some newly defined proximity maps in higher dimensions as illustrative examples.

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Section: Voronoi Diagrams and Delaunay Tessellationsmentioning

confidence: 99%

Extension of one-dimensional proximity regions to higher dimensions

Ceyhan

2010

Computational Geometry

View full text Add to dashboard Cite

show abstract

Tessellations

Cited by 1 publication

References 12 publications

Extension of one-dimensional proximity regions to higher dimensions

Extension of one-dimensional proximity regions to higher dimensions

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