Hexahedral mesh generation via the dual
Proceedings of the eleventh annual symposium on Computational geometry
Linear complexity hexahedral mesh generation
Proceedings of the twelfth annual symposium on Computational geometry
Characterizing and efficiently computing quadrangulations of planar point sets
Computer Aided Geometric Design
Converting triangulations to quadrangulations
Computational Geometry: Theory and Applications
Decomposing polygonal regions into convex quadrilaterals
SCG '85 Proceedings of the first annual symposium on Computational geometry
Quadrangulations of Planar Sets
WADS '95 Proceedings of the 4th International Workshop on Algorithms and Data Structures
Hamilton Triangulations for Fast Rendering
ESA '94 Proceedings of the Second Annual European Symposium on Algorithms
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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 quadrangulation 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 quadrangulation.