منابع مشابه
Complexity in Surfaces of Densest Packings for Families of Polyhedra
Elizabeth R. Chen, Daphne Klotsa, Michael Engel, Pablo F. Damasceno, and Sharon C. Glotzer School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA Applied Physics Program, University of Michigan, Ann Arbor, Michigan 48109, USA Department of Materials Science and...
متن کاملNormals of subdivision surfaces and their control polyhedra
For planar spline curves and bivariate box-spline functions, the cone of normals of a polynomial spline piece is enclosed by the cone of normals of its spline control polyhedron. This note collects some concrete examples to show that this is not true for subdivision surfaces, both at extraordinary points and in the regular, box-spline setting. A larger set, the cross products of families of con...
متن کاملIsoptic curves of conic sections in constant curvature geometries
In this paper, we consider the isoptic curves in 2-dimensional geometries of constant curvature E, H, E. The topic is widely investigated in the Euclidean plane E, see for example [1] and [15] and the references given there. In the hyperbolic and elliptic plane (according to [18]), there are few results in this topic (see [3] and [4]). In this paper, we give a review of the known results on iso...
متن کاملGraphs of polyhedra; polyhedra as graphs
Relations between graph theory and polyhedra are presented in two contexts. In the first, the symbiotic dependence between 3-connected planar graphs and convex polyhedra is described in detail. In the second, a theory of nonconvex polyhedra is based on a graph-theoretic foundation. This approach eliminates the vagueness and inconsistency that pervade much of the literature dealing with polyhedr...
متن کاملOn the Isoptic Hypersurfaces in the n-Dimensional Euclidean Space
The theory of the isoptic curves is widely studied in the Euclidean plane E2 (see [1] and [13] and the references given there). The analogous question was investigated by the authors in the hyperbolic H2 and elliptic E2 planes (see [3], [4]), but in the higher dimensional spaces there is no result according to this topic. In this paper we give a natural extension of the notion of the isoptic cu...
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ژورنال
عنوان ژورنال: Computer Aided Geometric Design
سال: 2016
ISSN: 0167-8396
DOI: 10.1016/j.cagd.2016.03.001