A Simple Algorithm for Higher-order Delaunay Mosaics and Alpha Shapes

We present a simple algorithm for computing higher-order Delaunay mosaics that works in Euclidean spaces of any finite dimensions. The algorithm selects the vertices of the order-\(k\) mosaic from incrementally constructed lower-order mosaics and uses an algorithm for weighted first-order Delaunay m...

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Bibliographic Details
Published inarXiv.org
Main Authors Edelsbrunner, Herbert, Osang, Georg
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 06.11.2020
Subjects
Algorithms
Alpha shapes
Apexes
Combinatorial analysis
Euclidean geometry
Mosaics
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Summary:We present a simple algorithm for computing higher-order Delaunay mosaics that works in Euclidean spaces of any finite dimensions. The algorithm selects the vertices of the order-\(k\) mosaic from incrementally constructed lower-order mosaics and uses an algorithm for weighted first-order Delaunay mosaics as a black-box to construct the order-\(k\) mosaic from its vertices. Beyond this black-box, the algorithm uses only combinatorial operations, thus facilitating easy implementation. We extend this algorithm to compute higher-order \(\alpha\)-shapes and provide open-source implementations. We present experimental results for properties of higher-order Delaunay mosaics of random point sets.
ISSN:2331-8422