Name
Abstract | ||
|---|---|---|
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. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1016/j.comgeo.2009.02.006 | Comput. Geom. |
Keywords | Field | DocType |
fixed orientations change combinatorially,staircases,extremal points,computing minimum-area rectilinear convex,l-shape,n point,extremal point,rectilinear convex hull,efficient algorithm,minimum area,time complexity,enclosing shapes,extreme point,convex hull,coordinate system | Coordinate system,Discrete mathematics,Minimum bounding box algorithms,Combinatorics,Convex combination,Convex hull,Convex set,Point set,Time complexity,Mathematics | Journal |
Volume | Issue | ISSN |
42 | 9 | Computational Geometry: Theory and Applications |
Citations | PageRank | References |
3 | 0.40 | 8 |
Authors | ||
5 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Sang Won Bae | 1 | 189 | 31.53 |
| Chunseok Lee | 2 | 51 | 3.54 |
| Hee-kap Ahn | 3 | 219 | 42.92 |
| Sunghee Choi | 4 | 671 | 40.52 |
| Kyung-Yong Chwa | 5 | 919 | 97.10 |