On Sweep-plane Analysis of Laguerre Voronoi Diagram

We discuss application of the sweep-plane technique for the construction of weighted Voronoi diagram in Laguerre geometry (or Laguerre Voronoi diagram). It is shown that the attempt to construct Laguerre Voronoi diagram utilizing the sweep-plane approach transforms the original problem for a given set of weighted sites to the problem of constructing Laguerre diagram for a different set of sites. It follows that the weighted Voronoi diagram in Laguerre geometry is an invariant of a family of all input sets of sites.