Voronoi diagrams and arrangements
Discrete & Computational Geometry
Advanced programming techniques applied to Cgal's arrangement package
Computational Geometry: Theory and Applications
Robust, generic and efficient construction of envelopes of surfaces in three-dimensional spaces
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Exact arrangements on tori and Dupin cyclides
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Sweeping and maintaining two-dimensional arrangements on surfaces: a first step
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Constructing two-dimensional Voronoi diagrams via divide-and-conquer of envelopes in space
Transactions on computational science IX
Constructing two-dimensional Voronoi diagrams via divide-and-conquer of envelopes in space
Transactions on computational science IX
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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.