Fast triangulation of the plane with respect to simple polygons
Information and Control
Ray shooting and other applications of spanning trees with low stabbing number
SIAM Journal on Computing
A pedestrian approach to ray shooting: shoot a ray, take a walk
SODA '93 Selected papers from the fourth annual ACM SIAM symposium on Discrete algorithms
Counting convex polygons in planar point sets
Information Processing Letters
On a partition into convex polygons
Discrete Applied Mathematics
Triangulations, visibility graph and reflex vertices of a simple polygon
Computational Geometry: Theory and Applications
Angle-restricted tours in the plane
Computational Geometry: Theory and Applications
The crust and the &Bgr;-Skeleton: combinatorial curve reconstruction
Graphical Models and Image Processing
Curve reconstruction: connecting dots with good reason
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
The angular-metric traveling salesman problem
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
A simple provable algorithm for curve reconstruction
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Computational geometry and convexity
Computational geometry and convexity
Approximation algorithms for the minimum convex partition problem
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
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We introduce a new measure for planar point sets S. Intuitively, it describes the combinatorial distance from a convex set: The reflexivity ρ(S) of S is given by the smallest number of reflex vertices in a simple polygonalization of S. We prove various combinatorial bounds and provide efficient algorithms to compute reflexivity, both exactly (in special cases) and approximately (in general). Our study naturally takes us into the examination of some closely related quantities, such as the convex cover number ϰ1(S) of a planar point set, which is the smallest number of convex chains that cover S, and the convex partition number ϰ2(S), which is given by the smallest number of disjoint convex chains that cover S. We prove that it is NP-complete to determine the convex cover or the convex partition number, and we give logarithmic-approximation algorithms for determining each.