Minimal Enclosing Hyperbolas of Line Sets
نویسنده
چکیده
We prove the following theorem: If H is a slim hyperbola that contains a closed set S of lines in the Euclidean plane, there exists exactly one hyperbola Hmin of minimal volume that contains S and is contained in H. The precise concepts of “slim”, the “volume of a hyperbola” and “straight lines or hyperbolas being contained in a hyperbola” are defined in the text.
منابع مشابه
Number of Minimal Path Sets in a Consecutive-k-out-of-n: F System
In this paper the combinatorial problem of determining the number of minimal path sets of a consecutive-k-out-of-n: F system is considered. For the cases where k = 2, 3 the explicit formulae are given and for k ≥ 4 a recursive relation is obtained. Direct computation for determining the number of minimal path sets of a consecutive-k-out-of-n: F system for k ≥ 4 remains a difficult task. ...
متن کاملGamRec: A Clustering Method Using Geometrical Background Knowledge for GPR Data Preprocessing
GPR is a nondestructive method to scan the subsurface. On the resulting radargrams, originally interpreted manually in a time consuming process, one can see hyperbolas corresponding to buried objects. For accelerating the interpretation a machine shall be enabled to recognize hyperbolas on radargrams autonomously. One possibility is the combination of clustering with an expectation maximization...
متن کاملUniqueness results for minimal enclosing ellipsoids
We prove uniqueness of the minimal enclosing ellipsoid with respect to strictly eigenvalue convex size functions. Special examples include the classic case of minimal volume ellipsoids (Löwner ellipsoids), minimal surface area ellipsoids or, more generally, ellipsoids that are minimal with respect to quermass integrals.
متن کاملSmallest Enclosing Ball for a Point Set with Strictly Convex Level Sets
Let the center point be the point that minimizes the maximum distance from a point of a given point set to the center point. Finding this center point is referred to as the smallest enclosing ball problem. In case of points with Euclidean distance functions, the smallest enclosing ball is actually the center of a geometrical ball. We consider point sets with points that have distance functions ...
متن کاملApproximate Minimum Volume Enclosing Ellipsoids Using Core Sets
We study the problem of computing the minimum volume enclosing ellipsoid containing a given point set S = {p1, p2, . . . , pn} ⊆ R. Using “core sets” and a column generation approach, we develop a (1 + )-approximation algorithm. We prove the existence of a core set X ⊆ S of size at most |X| = α = O ( d ( log d + 1 )) . We describe an algorithm that computes the set X and a (1 + )-approximation ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006