Search results for "cgal"
showing 3 items of 3 documents
Design of the CGAL Spherical Kernel and application to arrangements of circles on a sphere
2009
International audience; 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 …
Design of the CGAL 3D Spherical Kernel and application to arrangements of circles on a sphere
2009
AbstractThis 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 3D Spherical Kernel is made through the calculation of the exact arrangement of circles on a sphere. On average w…
Exact Voronoi diagram of smooth convex pseudo-circles: General predicates, and implementation for ellipses
2013
International audience; We examine the problem of computing exactly the Voronoi diagram (via the dual Delaunay graph) of a set of, possibly intersecting, smooth convex \pc in the Euclidean plane, given in parametric form. Pseudo-circles are (convex) sites, every pair of which has at most two intersecting points. The Voronoi diagram is constructed incrementally. Our first contribution is to propose robust and efficient algorithms, under the exact computation paradigm, for all required predicates, thus generalizing earlier algorithms for non-intersecting ellipses. Second, we focus on \kcn, which is the hardest predicate, and express it by a simple sparse $5\times 5$ polynomial system, which a…