Skeleton of a multi-ribbon surface

Abstract

In this paper, two-dimensional manifolds in three- dimensional Euclidian space are considered in order to single out surfaces whose skeletons fulfill the grass-fire concept. Among such surfaces we distinguish those ones that can be covered by finite number of adjacent patches. We name them multi-ribbon surfaces. We aim to calculate a multi-ribbon surface skeleton by constructing every patch Voronoi diagram in a surface parameter space and merging all Voronoi diagrams. Voronoi diagrams merging technique is proposed. The introduced approach can be applied to the problems of geographic information systems (for example, to street network modeling). © 2010 Springer-Verlag Berlin Heidelberg.