Pseudotriangulations from surfaces and a novel type of edge flip

Oswin Aichholzer; Franz Aurenhammer; Hannes Krasser; Peter Brass

doi:10.1137/S0097539702411368

Pseudotriangulations from surfaces and a novel type of edge flip

Oswin Aichholzer^*, Franz Aurenhammer, Hannes Krasser, Peter Brass

^*Corresponding author for this work

Research output: Contribution to journal › Review article › peer-review

Abstract

We prove that planar pseudotriangulations have realizations as polyhedral surfaces in three-space. Two main implications are presented. The spatial embedding leads to a novel flip operation that allows for a drastic reduction of flip distances, especially between (full) triangulations. Moreover, several key results for triangulations, like flipping to optimality, (constrained) Delaunayhood, and a convex polytope representation, are extended to pseudotriangulations in a natural way.

Original language	English
Pages (from-to)	1621-1653
Number of pages	33
Journal	SIAM Journal on Computing
Volume	32
Issue number	6
DOIs	https://doi.org/10.1137/S0097539702411368
Publication status	Published - Sept 2003

Keywords

Constrained regular complex
Flip distance
Locally convex function
Polytope representation
Pseudotriangulation
Surface realization

ASJC Scopus subject areas

Computer Science(all)
Mathematics(all)

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10.1137/S0097539702411368

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title = "Pseudotriangulations from surfaces and a novel type of edge flip",

abstract = "We prove that planar pseudotriangulations have realizations as polyhedral surfaces in three-space. Two main implications are presented. The spatial embedding leads to a novel flip operation that allows for a drastic reduction of flip distances, especially between (full) triangulations. Moreover, several key results for triangulations, like flipping to optimality, (constrained) Delaunayhood, and a convex polytope representation, are extended to pseudotriangulations in a natural way.",

keywords = "Constrained regular complex, Flip distance, Locally convex function, Polytope representation, Pseudotriangulation, Surface realization, Discrete and Computational Geometry",

author = "Oswin Aichholzer and Franz Aurenhammer and Hannes Krasser and Peter Brass",

year = "2003",

month = sep,

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language = "English",

volume = "32",

pages = "1621--1653",

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TY - JOUR

T1 - Pseudotriangulations from surfaces and a novel type of edge flip

AU - Aichholzer, Oswin

AU - Aurenhammer, Franz

AU - Krasser, Hannes

AU - Brass, Peter

PY - 2003/9

Y1 - 2003/9

N2 - We prove that planar pseudotriangulations have realizations as polyhedral surfaces in three-space. Two main implications are presented. The spatial embedding leads to a novel flip operation that allows for a drastic reduction of flip distances, especially between (full) triangulations. Moreover, several key results for triangulations, like flipping to optimality, (constrained) Delaunayhood, and a convex polytope representation, are extended to pseudotriangulations in a natural way.

AB - We prove that planar pseudotriangulations have realizations as polyhedral surfaces in three-space. Two main implications are presented. The spatial embedding leads to a novel flip operation that allows for a drastic reduction of flip distances, especially between (full) triangulations. Moreover, several key results for triangulations, like flipping to optimality, (constrained) Delaunayhood, and a convex polytope representation, are extended to pseudotriangulations in a natural way.

KW - Constrained regular complex

KW - Flip distance

KW - Locally convex function

KW - Polytope representation

KW - Pseudotriangulation

KW - Surface realization

KW - Discrete and Computational Geometry

UR - http://www.scopus.com/inward/record.url?scp=0942266548&partnerID=8YFLogxK

U2 - 10.1137/S0097539702411368

DO - 10.1137/S0097539702411368

M3 - Review article

AN - SCOPUS:0942266548

SN - 0097-5397

VL - 32

SP - 1621

EP - 1653

JO - SIAM Journal on Computing

JF - SIAM Journal on Computing

IS - 6

ER -

Pseudotriangulations from surfaces and a novel type of edge flip

Abstract

Keywords

ASJC Scopus subject areas

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