Search results for "curved objects"
showing 4 items of 4 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…
Bi-2212 and Y123 highly curved single-crystal-like objects: whiskers, bows and ring-like structures
2012
High-temperature superconducting objects of Bi2Sr2CaCu2O8 and Y Ba2Cu3O7 highly curved in the ab-plane, such as curved/kinked whiskers, bows and ring-like structures, were obtained within a solid?liquid?solid (SLS) grass-like growth mechanism. As-grown objects are crystals with three-dimensional epitaxy similar to conventional single crystals: they can be viewed as crystal parts ?cut? from a conventional rectangular crystal. Between our curved objects and conventional crystals, whiskers or thin films there are some differences in the superconducting properties induced only by the shape factors and no new physics is observed. Some details of the growth mechanism are discussed, emphasizing cu…
Arrangements de cercles sur une sphère: Algorithmes et Applications aux modèles moléculaires representés par une union de boules
2008
Since the early work of Richard et al., geometric constructions havebeen paramount for the description of macromolecules and macro-molecularassemblies. In particular, Voronoï and related constructions have beenused to describe the packing properties of atoms, to compute molecularsurfaces, to find cavities. This thesis falls in this realm, andafter a brief introduction to protein structure, makes fourcontributions.First, using the sweep line paradigm of Bentley and Ottmann, wepresent the first effective algorithm able to construct the exactarrangement of circles on a sphere. Moreover, assuming the circlesstem from the intersection between spheres, we present a strategy to reportthe covering …