TY - JOUR
AB - The order-k Voronoi tessellation of a locally finite set đť‘‹âŠ†â„ťđť‘› decomposes â„ťđť‘› 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.
AU - Edelsbrunner, Herbert
AU - Nikitenko, Anton
ID - 5678
IS - 4
JF - Discrete and Computational Geometry
SN - 01795376
TI - Poissonâ€“Delaunay Mosaics of Order k
VL - 62
ER -