24 citations · 42 across the 6 of their papers we have counts for
7 papers
Average and Expected Distortion of Voronoi Paths and Scapes
Herbert Edelsbrunner, Anton Nikitenko
The approximation of a circle with the edges of a fine square grid distorts the perimeter by a factor about . We prove that this factor is the same on average (in the e…
The Beauty of Random Polytopes Inscribed in the 2-sphere
Arseniy Akopyan, Herbert Edelsbrunner, Anton Nikitenko
Consider a random set of points on the unit sphere in , which can be either uniformly sampled or a Poisson point process. Its convex hull is a random inscribed polyto…
Integrating by Spheres: Summary of Blaschke-Petkantschin Formulas
Anton Nikitenko
In some applications, like some areas in stochastic geometry, a convenient change of variables involves spheres. In this review we summarize formulas of Blaschke-Petkantschin type,…
Poisson-Delaunay Mosaics of Order
Herbert Edelsbrunner, Anton Nikitenko
The order- Voronoi tessellation of a locally finite set decomposes into convex domains whose points have the same nearest neighbors…
Random Inscribed Polytopes Have Similar Radius Functions as Poisson-Delaunay Mosaics
Herbert Edelsbrunner, Anton Nikitenko
Using the geodesic distance on the -dimensional sphere, we study the expected radius function of the Delaunay mosaic of a random set of points. Specifically, we consider the par…
Weighted Poisson-Delaunay Mosaics
Herbert Edelsbrunner, Anton Nikitenko
Slicing a Voronoi tessellation in with a -plane gives a -dimensional weighted Voronoi tessellation, also known as power diagram or Laguerre tessellation. Mappi…