3D spherical kernel
swMATH ID:  11156 
Software Authors:  de Castro, Pedro M.M.; Cazals, Fr'ed'eric; Loriot, S'ebastien; Teillaud, Monique 
Description:  Design of the CGAL 3D spherical kernel and application to arrangements of circles on a sphere. We present a CGAL kernel for algorithms manipulating 3D spheres, circles, and circular arcs. The paper makes three contributions. First, the mathematics underlying two nontrivial 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 3D Spherical Kernel 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. 
Homepage:  http://doc.cgal.org/latest/Circular_kernel_3/index.html#Chapter_3D_Spherical_Geometry_Kernel 
Dependencies:  CGAL 
Keywords:  robustness; curved objects; generic programming; spheres; predicates; constructions; geometric kernels; numerical example; CGAL kernel; algorithms; circular arcs 
Related Software:  2D Arrangement; CGAL; 3D envelopes; Powercrust; Qsplat; 3D Convex Hulls; LEDA; 2D Regularized Boolean SetOperations; 2D Minkowski sums; Halfedge Data Structures; MAPC; LOOK 
Cited in:  5 Documents 
Standard Articles
1 Publication describing the Software, including 1 Publication in zbMATH  Year 

Design of the CGAL 3D spherical kernel and application to arrangements of circles on a sphere. Zbl 1169.65021 de Castro, Pedro M. M.; Cazals, Frédéric; Loriot, Sébastien; Teillaud, Monique 
2009

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top 5
Cited by 11 Authors
Cited in 3 Serials
2  Computational Geometry 
2  Mathematics in Computer Science 
1  Geometry and Computing 
Cited in 4 Fields
3  Numerical analysis (65XX) 
2  Algebraic geometry (14XX) 
2  Computer science (68XX) 
1  Convex and discrete geometry (52XX) 