Optimizing Constrained Offset and Scaled Polygonal Annuli

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1663)


Aicholzer et al. recently presented a new geometric construct called the straight skeleton of a simple polygon and gave several combinatorial bounds for it. Independently, the current authors defined in companion papers a distance function based on the same offsetting function for convex polygons. In particular, we explored the nearest- and furthest- neighbor Voronoi diagrams of this function and presented algorithms for constructing them. In this paper we give solutions to some constrained annulus placement problems for offset polygons. The goal is to find the smallest annulus region of a polygon containing a set of points. We fix the inner (resp.,outer) polygon of the annulus and minimize the annulus region by minimizing the outer offset (resp., maximizing the inner offset. We also solve a a special case of the first problem: finding the smallest translated offset of a polygon containing an entire point set. We extend our results for the standard polygon scaling function as well


Distance Function Feasible Region Voronoi Diagram Convex Polygon Medial Axis 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  1. 1.Faculty of Computer ScienceThe Technion—IITHaifaIsrael
  2. 2.Center for Geometric Computing, Dept. of Computer ScienceJohns Hopkins UniversityBaltimore
  3. 3.School of Computer ScienceCarleton UniversityOttawaCanada

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