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Fast Discovery of Voronoi Vertices in the Construction of Voronoi Diagram of 3D Balls

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2 Author(s)
Manák, M. ; Fac. of Appl. Sci., Univ. of West Bohemia, Pilsen, Czech Republic ; Kolingerová, I.

Solving geometrical problems on a set of 3D balls is a challenging task in computational geometry. They can be solved effectively when the Voronoi diagram for the set is available. The diagram is usually constructed by the edge-tracing or similar algorithms based on finding Voronoi vertices along edges. However, its expected quadratic time complexity makes it impractical. This can be improved significantly by our new approach. Whenever a vertex needs to be found, Delaunay triangulation of ball centers is searched through to find one specific ball. The search is kept inside a spatial filter, which can be reduced in size during the search. The improvement is demonstrated on protein data (a set of balls represents atoms in a molecule), because this is our intended application.

Published in:

Voronoi Diagrams in Science and Engineering (ISVD), 2010 International Symposium on

Date of Conference:

28-30 June 2010