Small Strictly Convex Quadrilateral Meshes of Point Sets

Details Small Strictly Convex Quadrilateral Meshes of Point Sets Small Strictly Convex Quadrilateral Meshes of Point Sets

2002-02-12

arxiv.org/abs/cs/0202011v1

Computer Science

Computational Geometry

25 pages, 23 figures. A preliminary version appeared in ISAAC 2001, Christchurch NZ

Scientific paper

In this paper, we give upper and lower bounds on the number of Steiner points required to construct a strictly convex quadrilateral mesh for a planar point set. In particular, we show that $3{\lfloor\frac{n}{2}\rfloor}$ internal Steiner points are always sufficient for a convex quadrilateral mesh of $n$ points in the plane. Furthermore, for any given $n\geq 4$, there are point sets for which $\lceil\frac{n-3}{2}\rceil-1$ Steiner points are necessary for a convex quadrilateral mesh.

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