On Flips in Polyhedral Surfaces: a new development

Lyuba Alboul; Ruud van Damme

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 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.

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	http://ewcg2002.mimuw.edu.pl/

Keywords

Triangulations
diagonal flips
polyhedral surfaces

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1 Oral presentation

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

Cite this

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title = "On Flips in Polyhedral Surfaces: a new development",

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 theoperation of diagonal flip for 2:5D triangulations by omitting the usual restriction that the flip operation should notproduce a self-intersecting triangulation. We denote this flip operation by EDF (extended diagonal flip). Among allpossible 2:5D triangulations with the vertex set V we first single out those that are topologically equivalent to the 2Dsphere. We show that any two such 2:5D triangulations (if V is situated in general position), are equivalent underEDF, i.e., they can be transformed into each other via a finite sequence of EDF.",

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author = "Lyuba Alboul and {van Damme}, Ruud",

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TY - CONF

T1 - On Flips in Polyhedral Surfaces: a new development

AU - Alboul, Lyuba

AU - van Damme, Ruud

N1 - Conference code: 18

PY - 2002/4/11

Y1 - 2002/4/11

N2 - 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 theoperation of diagonal flip for 2:5D triangulations by omitting the usual restriction that the flip operation should notproduce a self-intersecting triangulation. We denote this flip operation by EDF (extended diagonal flip). Among allpossible 2:5D triangulations with the vertex set V we first single out those that are topologically equivalent to the 2Dsphere. We show that any two such 2:5D triangulations (if V is situated in general position), are equivalent underEDF, i.e., they can be transformed into each other via a finite sequence of EDF.

AB - 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 theoperation of diagonal flip for 2:5D triangulations by omitting the usual restriction that the flip operation should notproduce a self-intersecting triangulation. We denote this flip operation by EDF (extended diagonal flip). Among allpossible 2:5D triangulations with the vertex set V we first single out those that are topologically equivalent to the 2Dsphere. We show that any two such 2:5D triangulations (if V is situated in general position), are equivalent underEDF, i.e., they can be transformed into each other via a finite sequence of EDF.

KW - Triangulations

KW - diagonal flips

KW - polyhedral surfaces

M3 - Abstract

T2 - 18th European Workshop on Computational Geometry 2002

Y2 - 10 April 2002 through 12 April 2002

ER -