TY - JOUR
AB - The Voronoi tessellation in Rd is defined by locally minimizing the power distance to given weighted points. Symmetrically, the Delaunay mosaic can be defined by locally maximizing the negative power distance to other such points. We prove that the average of the two piecewise quadratic functions is piecewise linear, and that all three functions have the same critical points and values. Discretizing the two piecewise quadratic functions, we get the alpha shapes as sublevel sets of the discrete function on the Delaunay mosaic, and analogous shapes as superlevel sets of the discrete function on the Voronoi tessellation. For the same non-critical value, the corresponding shapes are disjoint, separated by a narrow channel that contains no critical points but the entire level set of the piecewise linear function.
AU - Biswas, Ranita
AU - Cultrera Di Montesano, Sebastiano
AU - Edelsbrunner, Herbert
AU - Saghafian, Morteza
ID - 10773
JF - Discrete and Computational Geometry
SN - 0179-5376
TI - Continuous and discrete radius functions on Voronoi tessellations and Delaunay mosaics
VL - 67
ER -