Circular Separability of Polygons

Jean-Daniel Boissonnat (1) , Jurek Czyzowicz (2) , Olivier Devillers (1) , Mariette Yvinec (1)

1 PRISME - Geometry, Algorithms and Robotics
2 DII - Département d'Informatique et d'Ingénierie

Two planar sets are circularly separable if there exists a circle enclosing one of the set and whose open interior disk does not intersect the other set. This paper studies two problems related to circular separability. A linear-time algorithm is proposed to decide if two polygons are circularly separable. The algorithm outputs the smallest separating circle. The second problem asks for the largest circle included in a preprocessed, convex polygon, under some point and/or line constraints. The resulting circle must contain the query points and it must lie in the halfplanes delimited by the query lines.

Domaines: Géométrie algorithmique [cs.CG]

Jean-Daniel Boissonnat, Jurek Czyzowicz, Olivier Devillers, Mariette Yvinec. Circular Separability of Polygons. Algorithmica, 2001, 30 (1), pp.67--82. ⟨10.1007/s004530010078⟩. ⟨inria-00090667⟩