Examinando por Materia "Spheres"

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  • Miniatura
    PublicaciónAcceso abierto
    A literature review of bounding volumes hierarchy focused on collision detection
    (Universidad del Valle, 2015-06-19) Dinas, Simena; Bañón, José M.
    (Eng) A bounding volume is a common method to simplify object representation by using the composition of geometrical shapes that enclose the object; it encapsulates complex objects by means of simple volumes and it is widely useful in collision detection applications and ray tracing for rendering algorithms. They are popular in computer graphics and computational geometry. Most popular bounding volumes are spheres, Oriented-Bounding Boxe s (OBB’ s), Axis-Align ed Bound ing Boxes (AABB’ s); moreover , the literature review includes ellipsoids, cylinders, sphere packing, sphere shells , k-DOP’ s, convex hulls, cloud of points, and minimal bounding boxe s, among others. A Bounding Volume Hierarchy is ussualy a tree in which the complete object is represented thigter fitting every level of the hierarchy. Additionally, each bounding volume has a cost associated to construction, update, and interference te ts. For instance, spheres are invariant to rotation and translations, then they do not require being updated ; their constructions and interference tests are more straightforward then OBB’ s; however, their tightness is lower than other bounding volumes. Finally , three comparisons between two polyhedra; seven different algorithms were used, of which five are public libraries for collision detection.
  • Miniatura
    PublicaciónAcceso abierto
    Another proof for the rigidity of Clifford minimal hypersurfaces of [S.sup.n]
    (2011-10-13) Perdomo, Oscar
    Let M [subset] [S.sup.n] be a minimal hypersurface, and let us denote by A the shape operator of M. In this paper we give an alternative proof of the theorem that states that if [[absolute value of A].sup.2] = n - 1, then M is a Clifford minimal hypersurface.