On convex decompositions of a planar point set
نویسندگان
چکیده
منابع مشابه
Planar Point Sets With Large Minimum Convex Decompositions
We show the existence of sets with n points (n > 4) for which every convex decomposition contains more than f§« — § polygons, which refutes the conjecture that for every set of n points there is a convex decomposition with at most n + C polygons. For sets having exactly three extreme points we show that more than n + s/2(n 3) 4 polygons may be necessary to form a convex decomposition.
متن کاملComputing the convex hull of a planar point set
In Figure 1, the set S consists of thirteen points. The output of a convex hull algorithm should be the list (p1, p2, p3, p4, p5, p6). We remark that the list storing the vertices of CH (S) can start with an arbitrary vertex. In the example, the list (p3, p4, p5, p6, p1, p2) would also be a valid output. ∗School of Computer Science, Carleton University, Ottawa, Ontario, Canada K1S 5B6. E-mail: ...
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For a given planar point set P , consider a partition of P into disjoint convex polygons. In this paper, we estimate the maximum number of convex quadrilaterals in all partitions. 2001 Elsevier Science B.V. All rights reserved.
متن کاملOn the convex layers of a planar set
Let S be a set of n points in the Euclidean plane. The convex layers of S are the convex polygons obtained by iterating on the following procedure: compute the convex hull of S and remove its vertices from S. This process of peeling a planar point set is central in the study of robust estimators in statistics. It also provides valuable information on the morphology of a set of sites and has pro...
متن کاملOn the Rectilinear Convex Layers of a Planar Set
In this paper we give an optimal O(n log n) time and O(n) space algorithm to compute the rectilinear convex layers of a set S of n points on the plane. We also compute the rotation of S that minimizes the number of rectilinear convex layers in O(n log n) time and O(n) space.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2009
ISSN: 0012-365X
DOI: 10.1016/j.disc.2008.02.008