Let S be a set S of n points on a polyhedral terrain T in R, and let ε > 0 be a fixed constant. We prove that S admits a (2 + ε)-spanner with O(n log n) edges with respect to the geodesic distance. This is the first spanner with constant spanning ratio and a near-linear number of edges for points on a terrain. On our way to this result, we prove that any set of n weighted points in R admits an ...

Tantalum polyhedral oligosilsesquioxane (POSS) complexes have been synthesised and characterized. X-ray structures of these complexes revealed that the coordination number of the tantalum center greatly affects the cube-like silsesquioxane framework.

Given a polyhedral terrain with n vertices, the shortest monotone descent path problem deals with finding the shortest path between a pair of points, called source (s) and destination (t) such that the path is constrained to lie on the surface of the terrain, and for every pair of points p = (x(p), y(p), z(p)) and q = (x(q), y(q), z(q)) on the path, if dist(s,p) < dist(s, q) then z(p) z(q), whe...

The paper describes the properties of boundedness and unboundedness of outer polyhedral (parallelepiped-valued) estimates for reachable sets of linear differential systems with stable matrices over the infinite time interval. New results concerning tight estimates are presented.

Recently the light-field and lumigraph systems have been proposed as general methods of representing the visual information present in a scene. These methods represent this information as a 4D function of light over the domain of directed lines. These systems use the intersection points of the lines on two planes to parameterize the lines in space. This paper explores the structure of the two-p...

of the Dissertation Embeddings of Polytopes and Polyhedral Complexes

We present three types of polyhedral surfaces, which are continuously flexible and have not only an initial pose, where all faces are coplanar, but pass during their self-motion through another pose with coplanar faces (“flat pose”). These surfaces are examples of so-called rigid origami, since we only admit exact flexions, i.e., each face remains rigid during the motion; only the dihedral angl...