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Approximating BoundaryTriangulated Objects with Balls # O. Aichholzer + F. Aurenhammer # T. Hackl + B. Kornberger + M. Peternell H. Pottmann
 

Summary: Approximating Boundary­Triangulated Objects with Balls #
O. Aichholzer + F. Aurenhammer # T. Hackl + B. Kornberger + M. Peternell § H. Pottmann §
Abstract
We compute a set of balls that approximates a given
3D object, and we derive small additive bounds for
the overhead in balls with respect to the minimal so­
lution with the same quality. The algorithm has been
implemented and tested using the CGAL library [7].
1 Introduction
Representing a complex geometric object with prim­
itives is a fundamental task in computational geom­
etry and computer graphics. A general distinction is
between exact representation, like slab decomposition
or triangulation, and approximate representation, like
spline boundary conversion or approximate covering.
The choice of the primitives used depends on the ap­
plication, for example, whether the object is to be
processed for visualization or for subsequent manipu­
lation.
In the present note, we deal with the problem of

  

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

 

Collections: Computer Technologies and Information Sciences