10.1007/s00454-018-0049-2
Edelsbrunner, Herbert
Herbert
Edelsbrunner0000-0002-9823-6833
Nikitenko, Anton
Anton
Nikitenko
Poisson–Delaunay Mosaics of Order k
Springer
2018
2018-12-16T22:59:20Z
2019-08-13T08:31:21Z
journal_article
https://research-explorer.app.ist.ac.at/record/5678
https://research-explorer.app.ist.ac.at/record/5678.json
01795376
599339 bytes
application/pdf
The order-k Voronoi tessellation of a locally finite set 𝑋⊆ℝ𝑛 decomposes ℝ𝑛 into convex domains whose points have the same k nearest neighbors in X. Assuming X is a stationary Poisson point process, we give explicit formulas for the expected number and total area of faces of a given dimension per unit volume of space. We also develop a relaxed version of discrete Morse theory and generalize by counting only faces, for which the k nearest points in X are within a given distance threshold.