TY - JOUR
AB - 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.
AU - Edelsbrunner, Herbert
AU - Nikitenko, Anton
ID - 17149
JF - Discrete and Computational Geometry
SN - 0179-5376
TI - Average and expected distortion of Voronoi paths and scapes
ER -