Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10327625 | Computational Geometry | 2005 | 15 Pages |
Abstract
We address a number of extremal point query problems when P is a set of n points in Rd, d⩾3 a constant, including the computation of the farthest point from a query line and the computation of the farthest point from each of the lines spanned by the points in P. In R3, we give a data structure of size O(n1+É), that can be constructed in O(n1+É) time and can report the farthest point of P from a query line segment in O(n2/3+É) time, where É>0 is an arbitrarily small constant. Applications of our results also include: (1) Sub-cubic time algorithms for fitting a polygonal chain through an indexed set of points in Rd, d⩾3 a constant, and (2) A sub-quadratic time and space algorithm that, given P and an anchor point q, computes the minimum (maximum) area triangle defined by q with Pâ{q}.
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Ovidiu Daescu, Robert Serfling,