Small Strictly Convex Quadrilateral Meshes of Point Sets

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 n/2 internal Steiner points are always sufficient for a convex quadrilateral mesh of n points in the plane. Furthermore, for any given n 4, there are point sets for which (n - 3)/2 - 1 Steiner points are necessary for a convex quadrilateral mesh. Key Words. Quadrilateral mesh, Convex, Quadrangulation, Bounded size, Finite elements, Interpolation.

• Type: Journal
• Year: 2002
• Where: CORR
• Authors: David Bremner, Ferran Hurtado, Suneeta Ramaswami, Vera Sacristan
• Keywords: Convex Quadrilateral Mesh, CORR 2002, Education, Internal Steiner Points, Steiner Points