Ball-Polyhedra
نویسندگان
چکیده
We study two notions. One is that of lens-convexity. A set of circumradius not greater than one is lens-convex if, for any pair of its points, it contains every shorter unit circular arc connecting them. The other objects of study are bodies obtained as an intersection of finitely many balls of the same radius, called ball-polyhedra. We find analogues of several results on convex polyhedral sets for ball-polyhedra.
منابع مشابه
Ball-polyhedra By
We study two notions. One is that of spindle convexity. A set of circumradius not greater than one is spindle convex if, for any pair of its points, it contains every short circular arc of radius at least one, connecting them. The other objects of study are bodies obtained as intersections of finitely many balls of the same radius, called ball-polyhedra. We find analogues of several results on ...
متن کاملRigidity of ball-polyhedra in Euclidean 3-space
In this paper we introduce ball-polyhedra as finite intersections of congruent balls in Euclidean 3-space. We define their duals and study their face-lattices. Our main result is an analogue of Cauchy’s rigidity theorem. © 2004 Elsevier Ltd. All rights reserved.
متن کاملGlobally Rigid Ball-Polyhedra in Euclidean 3-Space
The rigidity theorems of Alexandrov (1950) and Stoker (1968) are classical results in the theory of convex polyhedra.We prove analogues of them for ball-polyhedra, which are intersections of finitely many congruent balls in Euclidean 3-space.
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A ball-polyhedron is the intersection with non-empty interior of finitely many (closed) unit balls in Euclidean 3-space. One can represent the boundary of a ballpolyhedron as the union of vertices, edges, and faces defined in a rather natural way. A ball-polyhedron is called a simple ball-polyhedron if at every vertex exactly three edges meet. Moreover, a ball-polyhedron is called a standard ba...
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A very fundamental geometric problem on finite systems of spheres was independently phrased by Kneser (1955) and Poulsen (1954). According to their well-known conjecture if a finite set of balls in Euclidean space is repositioned so that the distance between the centers of every pair of balls is decreased, then the volume of the union (resp., intersection) of the balls is decreased (resp., incr...
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ورودعنوان ژورنال:
- Discrete & Computational Geometry
دوره 38 شماره
صفحات -
تاریخ انتشار 2007