Summary: Weighted Skeletons and Fixed­Share Decomposition #
FRANZ AURENHAMMER
Institute for Theoretical Computer Science
University of Technology, Graz, Austria
auren@igi.tugraz.at
Abstract
We introduce the concept of weighted skeleton of a polygon and present various decomposition and
optimality results for this skeletal structure when the underlying polygon is convex.
1 Introduction
Polygon decomposition is a major issue in computational geometry. Its relevance stems from breaking com­
plex shapes (modeled by polygons) into sub­polygons that are easier to manipulate, and from subdividing
areas of interest into parts that satisfy certain containment requirements and/or optimality properties. We
refer to [13] for a nice survey on this topic. In particular, a rich literature exists on decomposition into
convex polygons. Convex decompositions are most natural in some sense. They have many applications
and can be computed efficiently; see e.g. [7, 14, 16].
In this paper, we focus on the problem of decomposing a convex polygon such that predefined constraints
are met. More specifically, the goal is to partition a given convex n­gon P into n convex parts, each part
being based on a single side of P and containing a specified 'share' of P . The share may relate, for
example, to the spanned area, to the number of contained points from a given point set, or to the total edge
length covered from a given set of curves. Possible applications of such fixed­share decompositions include

Source: Aurenhammer, Franz - Institute for Theoretical Computer Science, Technische Universität Graz

Collections: Computer Technologies and Information Sciences