Smallest Enclosing Ellipses -
An Exact and Generic Implementation

Bernd Gärtner
Institut für Theoretische Informatik
ETH Zentrum, IFW
CH-8092 Zürich, Switzerland

Sven Schönherr
Institut für Informatik
Freie Universität Berlin
Takustr. 9, D-14195 Berlin, Germany

Report B 98-05
April 1998

We present a C++ implementation of an optimisation algorithm for computing the smallest (w.r.t. area) enclosing ellipse of a finite point set in the plane. We obtain an exact solution by using Welzl's method together with the primitives as described in report B 97-03. The algorithm is implemented as a semi-dynamic data structure, thus allowing to insert points while maintaining the smallest enclosing ellipse. Following the generic programming paradigm, we use the template feature of C++ to provide generic code. The data structure is parameterized with a traits class, that defines the abstract interface between the optimisation algorithm and the primitives it uses. The interface of the data structure is compliant with the STL.

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