CASC 2005 Poster
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TITLE
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Apollonius Circle Conflict

AUTHORS
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Ioannis Z. Emiris - National University of Athens
George M. Tzoumas - National University of Athens

ABSTRACT
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Computation of the Voronoi diagram of a set of ellipses in the plane
involves high degree polynomial equations. We have solved efficiently
several predicates, but the main operation appears to be the determination
of the relative position of a query ellipse with respect to the Apollonius
circle of three given ellipses. We avoid computations with high degree
algebraic numbers, which are often costly and inefficient operations.
Instead, we propose a subdivision-based full-precision algorithm that
exploits the geometric characteristics of the problem.