The predicates for the Voronoi diagram of ellipses

This paper examines the computation of the Voronoi diagram of a set of ellipses in the Euclidean plane. We propose the first complete algorithms, under the exact computation paradigm, for the predicates of an incremental algorithm: κ1 decides which one of 2 given ellipses is closest to a given exterior point; κ2 decides the position of a query ellipse relative to an external bitangent line of 2 given ellipses; κ3 decides the position of a query ellipse relative to a Voronoi circle of 3 given ellipses; κ4 determines the type of conflict between a Voronoi edge, defined by 4 given ellipses, and a query ellipse. The paper is restricted to non-intersecting ellipses, but the extension to arbitrary ones is possible. The ellipses are input in parametric representation or constructively in terms of their axes, center and rotation. For κ1 and κ2 we derive optimal algebraic conditions, solve them exactly and provide efficient implementations in C++. For κ3 we compute a tight bound on t...

• Type: Conference
• Year: 2006
• Where: COMPGEOM
• Authors: Ioannis Z. Emiris, Elias P. Tsigaridas, George M. Tzoumas
• Keywords: COMPGEOM 2006, Non-intersecting Ellipses, Query Ellipse, Voronoi