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Summary: Computational and Structural Advantages of
Circular Boundary Representation #
O. Aichholzer 1 , F. Aurenhammer 1 , T. Hackl 1
B. J˜uttler 2 , M. Oberneder 2 , and Z. Ÿ S’r 2
1 University of Technology Graz, Austria
{oaich,thackl}@ist.tugraz.at, auren@igi.tugraz.at
2 Johannes Kepler University of Linz, Austria
{bert.juettler,margot.oberneder,zbynek.sir}@jku.at
Abstract. Boundary approximation of planar shapes by circular arcs
has quantitive and qualitative advantages compared to using straight
line segments. We demonstrate this by way of three basic and frequent
computations on shapes -- convex hull, decomposition, and medial axis. In
particular, we propose a novel medial axis algorithm that beats existing
methods in simplicity and practicality, and at the same time guarantees
convergence to the medial axis of the original shape.
1 INTRODUCTION
The plain majority of algorithms in computational geometry have been designed
for processing linear objects, like lines, planes, or polygons. On the one hand,
this is certainly due to the fact that many interesting and deep computational
and combinatorial questions do arise already for inputs of this simple form.
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