Circumscribed sphere of a convex polyhedron
نویسندگان
چکیده
منابع مشابه
Circumscribed sphere of a convex polyhedron
Suppose that K is a convex polyhedron in the n-dimensional Euclidean space R. Suppose that the extreme points of K are P1, P2, . . . , Pm ( m ≥ n + 1). If P is an arbitrary interior point of K, then there exist vertices Pi1 , Pi2 , . . . , Pin+1 of K and a point Q of R n and a positive number r > 0 for which ||Pik − Q|| = r for 1 ≤ k ≤ n + 1 , ||Pj − Q|| ≤ r for 1 ≤ j ≤ m and P is an interior p...
متن کاملCutting a Convex Polyhedron Out of a Sphere
Given a convex polyhedron P of n vertices inside a sphere Q, we give an O(n)-time algorithm that cuts P out of Q by using guillotine cuts and has cutting cost O(log n) times the optimal.
متن کاملApproximation Algorithms for Cutting a Convex Polyhedron Out of a Sphere
For a given convex polyhedron P of n vertices inside a sphere Q , we study the problem of cutting P out of Q by a sequence of plane cuts. The cost of a plane cut is the area of the intersection of the plane with Q , and the objective is to find a cutting sequence that minimizes the total cost. We present three approximation solutions to this problem: an O(n log n) time O(log2 n)-factor approxim...
متن کاملHow to Cut out a Convex Polyhedron
It is known that one can fold a convex polyhedron from a non-overlapping face unfolding, but the complexity of the algorithm in [MP] remains an open problem. In this paper we show that every convex polyhedron P ⊂ R can be obtained in polynomial time, by starting with a cube which contains P and sequentially cutting out the extra parts of the surface. Our main tool is of independent interest. We...
متن کاملA Topologically Convex Vertex-Ununfoldable Polyhedron
We construct a polyhedron that is topologically convex (i.e., has the graph of a convex polyhedron) yet has no vertex unfolding: no matter how we cut along the edges and keep faces attached at vertices to form a connected (hinged) surface, the surface necessarily unfolds with overlap.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Applied Mathematics Letters
سال: 2005
ISSN: 0893-9659
DOI: 10.1016/j.aml.2005.02.008