HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Journal articles

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

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.
Complete list of metadata

Cited literature [36 references]  Display  Hide  Download

Contributor : Sebastien Loriot Connect in order to contact the contributor
Submitted on : Tuesday, November 25, 2008 - 3:17:45 PM
Last modification on : Wednesday, February 2, 2022 - 3:51:54 PM
Long-term archiving on: : Tuesday, October 9, 2012 - 2:42:48 PM


Files produced by the author(s)


  • HAL Id : inria-00335865, version 1


Pedro 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, Elsevier, 2009. ⟨inria-00335865⟩



Record views


Files downloads