@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 & Computational Geometry},
  pages        = {490--499},
  publisher    = {Springer Nature},
  title        = {{Average and expected distortion of Voronoi paths and scapes}},
  doi          = {10.1007/s00454-024-00660-y},
  volume       = {73},
  year         = {2025},
}