We consider the problem of obtaining “nice” quadrangulations of planar sets of points. For many applications “nice” means that the quadrilaterals obtained are convex if po...
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 sh...
David Bremner, Ferran Hurtado, Suneeta Ramaswami, ...
We extend Schaeffer's bijection between rooted quadrangulations and welllabeled trees to the general case of Eulerian planar maps with prescribed face valences to obtain a bi...
Schnyder woods are decompositions of simple triangulations into three edge-disjoint spanning trees crossing each other in a specific way. In this article, we define a generalizatio...