@article{17149,
abstract = {The approximation of a circle with the edges of a fine square grid distorts the perimeter by a factor about 4/Pi. We prove that this factor is the same on average (in the ergodic sense) for approximations of any rectifiable curve by the edges of any non-exotic Delaunay mosaic (known as Voronoi path), and extend the results to all dimensions, generalizing Voronoi paths to Voronoi scapes.},
author = {Edelsbrunner, Herbert and Nikitenko, Anton},
issn = {1432-0444},
journal = {Discrete and Computational Geometry},
publisher = {Springer Nature},
title = {{Average and expected distortion of Voronoi paths and scapes}},
doi = {10.1007/s00454-024-00660-y},
year = {2024},
}