Centroid Triangulations from k-Sets

k-set Polygons and Centroid Triangulations

Flip Graphs of Degree-Bounded (Pseudo-)Triangulations⋆

We study flip graphs of (pseudo-)triangulations whose maximum vertex degree is bounded by a constant k. In particular, we consider (pseudo-)triangulations of sets of n points in convex position in the plane and prove that their flip graph is connected if and only if k > 6; the diameter of the flip graph is O(n). We also show that for general point sets flip graphs of minimum pseudo-triangulatio...

Flip Graphs of Bounded-Degree Triangulations

We study flip graphs of triangulations whose maximum vertex degree is bounded by a constant k. In particular, we consider triangulations of sets of n points in convex position in the plane and prove that their flip graph is connected if and only if k > 6; the diameter of the flip graph is O(n). We also show that, for general point sets, flip graphs of pointed pseudo-triangulations can be discon...

Approaches to High Aspect Ratio Triangulations

In aerospace computational uid dynamics calculations, high aspect ratio, or stretched, triangulations are often used to adequately resolve the features of a viscous ow around bodies. In this paper, we explore alternatives to the Delaunay triangulation which can be used to generate high aspect ratio triangulations of point sets. The method is based on a variation of the lifting map concept which...

Flipping Edges on Triangulations

In this paper we study the problem of flipping edges in triangulations of polygons and point sets. We prove that if a polygon Qn has k reflex vertices, then any triangulation of Qn can be transformed to another triangulation of Qn with at most O(n + k 2 ) flips. We produce examples of polygons with two triangulations T and T such that to transform T to T requires O(n ) flips. These results are ...