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Design of the CGAL Spherical Kernel and application to arrangements of circles on a sphere

Pedro M. M. de Castro 1 Frédéric Cazals 2 Sebastien Loriot 2, 3 Monique Teillaud 1 
1 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée
2 ABS - Algorithms, Biology, Structure
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : This paper presents a CGAL kernel for algorithms manipulating 3D spheres, circles, and circular arcs. The paper makes three contributions. First, the mathematics underlying two non trivial predicates are presented. Second, the design of the kernel concept is developed, and the connexion between the mathematics and this design is established. In particular, we show how two different frameworks can be combined: one for the general setting, and one dedicated to the case where all the objects handled lie on a reference sphere. Finally, an assessment about the efficacy of the \sk\ is made through the calculation of the exact arrangement of circles on a sphere. On average while computing arrangements with few degeneracies (on sample molecular models), it is shown that certifying the result incurs a modest factor of two with respect to calculations using a plain double arithmetic.
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Submitted on : Tuesday, November 25, 2008 - 3:17:45 PM
Last modification on : Friday, November 25, 2022 - 10:12:06 AM
Long-term archiving on: : Tuesday, October 9, 2012 - 2:42:48 PM


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  • HAL Id : inria-00335865, version 1


Pedro M. M. de Castro, Frédéric Cazals, Sebastien Loriot, Monique Teillaud. Design of the CGAL Spherical Kernel and application to arrangements of circles on a sphere. Computational Geometry, 2009. ⟨inria-00335865⟩



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