Arrangements of geodesic arcs on the sphere

This movie illustrates exact construction and maintenance of arrangements induced by arcs of great circles embedded on the sphere, also known as geodesic arcs, and exact computation of Voronoi diagrams on the sphere, the bisectors of which are geodesic arcs. This class of Voronoi diagrams includes the subclass of Voronoi diagrams of points and its generalization, power diagrams, also known as Laguerre Voronoi diagrams. The resulting diagrams are represented as arrangements, and can be passed as input to consecutive operations supported by the Arrangement 2 package of Cgal and its derivatives. The implementation handles well degenerate input and produces exact results. Categories and Subject Descriptors F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems--Geometrical problems and computations General Terms Algorithms, Experimentation, Performance

• Type: Conference
• Year: 2008
• Where: COMPGEOM
• Authors: Efi Fogel, Ophir Setter, Dan Halperin
• Keywords: COMPGEOM 2008, Discrete Geometry, Geodesic Arcs, Laguerre Voronoi Diagrams, Voronoi Diagrams