On the definition and computation of rectilinear convex hulls
References (14)
- et al.
Maintenance of configurations in the plane
J. Comput. System Sci.
(1981) Multidimensional divide-and-conquer
Comm. ACM
(1980)Convex Polytopes
(1967)- et al.
Combinatorial Geometry in the Plane
(1964) - et al.
The ultimate planar convex hull algorithm
- D. G. Kirkpatrick and R. Seidel, An O(n log h) algorithm for computing a staircase, to...
- D. G. Kirkpatrick and R. Seidel, An O(n log h) algorithm for computing a three-dimensional staircase, to...
Cited by (67)
A fast and efficient algorithm for determining the connected orthogonal convex hulls
2022, Applied Mathematics and ComputationA modified Graham's convex hull algorithm for finding the connected orthogonal convex hull of a finite planar point set
2021, Applied Mathematics and ComputationSet-valued games and mixed-strategy equilibria in discounted supergames
2019, Discrete Applied MathematicsCitation Excerpt :We note that this is not the standard definition since these sets need not be connected in general. These sets are also called rectilinear convex, orthogonal convex, or restricted-orientation convex [23,31,32]. The monotonicity guarantees that the extrema are found in the extreme points of the X-Y convex sets.
On the O<inf>β</inf>-hull of a planar point set
2018, Computational Geometry: Theory and ApplicationsSeparability of imprecise points
2017, Computational Geometry: Theory and ApplicationsCovering points with minimum/maximum area orthogonally convex polygons
2016, Computational Geometry: Theory and ApplicationsCitation Excerpt :It can be employed, for instance, in constructing 2D floor layouts with area constraints, and also as a finer grain substitute for bounding boxes of graphical objects as well as being theoretically interesting in its own right. As stated in [9], orthogonal convex hulls, studied in [10], may be disconnected or degenerate. The orthogonally convex cover, however, is a balanced representation and may be useful where the bounding box is too simple and the orthogonal convex hull is disconnected.
- ∗
The work of the second author was supported partially by the Academy of Finland and partially by the Alexander von Humboldt Foundation, while that of the third author was supported under Natural Sciences and Engineering Research Council of Canada Grant No. A-5692.