Computational geometry: an introduction
Computational geometry: an introduction
Discrete & Computational Geometry - Special issue on ACM symposium on computational geometry, North Conway
Convex hulls of finite sets of points in two and three dimensions
Communications of the ACM
Approximation of Convex Figures by Pairs of Rectangles
STACS '90 Proceedings of the 7th Annual Symposium on Theoretical Aspects of Computer Science
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
Fitting a two-joint orthogonal chain to a point set
Computational Geometry: Theory and Applications
| Hi-index | 0.00 |
We study the problems of computing two non-convex enclosing shapes with the minimum area; the L-shape and the rectilinear convex hull. Given a set of n points in the plane, we find an L-shape enclosing the points or a rectilinear convex hull of the point set with minimum area over all orientations. We show that the minimum enclosing shapes for fixed orientations change combinatorially at most O(n) times while rotating the coordinate system. Based on this, we propose efficient algorithms that compute both shapes with the minimum area over all orientations. The algorithms provide an efficient way of maintaining the set of extremal points, or the staircase, while rotating the coordinate system, and compute both minimum enclosing shapes in O(n^2) time and O(n) space. We also show that the time complexity of maintaining the staircase can be improved if we use more space.