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Abstract
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 dened 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 selfintersecting 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.
operation of diagonal flip for 2:5D triangulations by omitting the usual restriction that the flip operation should not
produce a selfintersecting 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.
Original language  English 

Number of pages  4 
Publication status  Published  11 Apr 2002 
Event  18th European Workshop on Computational Geometry 2002  Warsaw University, Warschaw, Poland Duration: 10 Apr 2002 → 12 Apr 2002 Conference number: 18 http://ewcg2002.mimuw.edu.pl/ 
Conference
Conference  18th European Workshop on Computational Geometry 2002 

Abbreviated title  EWCG 2002 
Country  Poland 
City  Warschaw 
Period  10/04/02 → 12/04/02 
Internet address 
Keywords
 Triangulations
 diagonal flips
 polyhedral surfaces
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Activities
 1 Oral presentation

On Flips in Polyhedral Surfaces: a new development
Lyuba Alboul (Speaker)
11 Apr 2002Activity: Talk or presentation › Oral presentation