On Flips in Polyhedral Surfaces: a new development
Lyuba Alboul, Ruud van Damme · University of Twente Research Information · 2002
Let V be a finite point set in 3D and let ST (V) be the set of closed triangulated polyhedral surfaces with a vertex set V. Those surfaces can be defined as 2.5D (closed) triangulations of the given discrete data set V. We generalise the operation of diagonal flip for 2.5D triangulations by omitting the usual restriction that the flip operation should not produce a self–intersecting triangulation. We denote this flip operation by EDF (extended diagonal flip). Among all possible 2.5D triangulations with the vertex set V we first single out those that are topologically equivalent to the 2D sphere. We show that any two such 2.5D triangulations (if V is situated in general position), are equivalent under EDF, i.e., they can be transformed into each other via a finite sequence of EDF.