Structures of Triangulations of Points
Summary :
Triangulations have been one of main research topics in computational geometry and have many applications in computer graphics, finite element methods, mesh generation, etc. This paper surveys properties of triangulations in the two- or higher-dimensional spaces. For triangulations of the planar point set, we have a good triangulation, called the Delaunay triangulation, which satisfies several optimality criteria. Based on Delaunay triangulations, many properties of planar triangulations can be shown, and a graph structure can be constructed for all planar triangulations. On the other hand, triangulations in higher dimensions are much more complicated than in planar cases. However, there does exist a subclass of triangulations, called regular triangulations, with nice structure, which is also touched upon.
- Publication
- IEICE TRANSACTIONS on Information Vol.E83-D No.3 pp.428-437
- Publication Date
- 2000/03/25
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- INVITED SURVEY PAPER
- Category
- Algorithms for Geometric Problems
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Keiko IMAI, "Structures of Triangulations of Points" in IEICE TRANSACTIONS on Information,
vol. E83-D, no. 3, pp. 428-437, March 2000, doi: .
Abstract: Triangulations have been one of main research topics in computational geometry and have many applications in computer graphics, finite element methods, mesh generation, etc. This paper surveys properties of triangulations in the two- or higher-dimensional spaces. For triangulations of the planar point set, we have a good triangulation, called the Delaunay triangulation, which satisfies several optimality criteria. Based on Delaunay triangulations, many properties of planar triangulations can be shown, and a graph structure can be constructed for all planar triangulations. On the other hand, triangulations in higher dimensions are much more complicated than in planar cases. However, there does exist a subclass of triangulations, called regular triangulations, with nice structure, which is also touched upon.
URL: https://global.ieice.org/en_transactions/information/10.1587/e83-d_3_428/_p
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@ARTICLE{e83-d_3_428,
author={Keiko IMAI, },
journal={IEICE TRANSACTIONS on Information},
title={Structures of Triangulations of Points},
year={2000},
volume={E83-D},
number={3},
pages={428-437},
abstract={Triangulations have been one of main research topics in computational geometry and have many applications in computer graphics, finite element methods, mesh generation, etc. This paper surveys properties of triangulations in the two- or higher-dimensional spaces. For triangulations of the planar point set, we have a good triangulation, called the Delaunay triangulation, which satisfies several optimality criteria. Based on Delaunay triangulations, many properties of planar triangulations can be shown, and a graph structure can be constructed for all planar triangulations. On the other hand, triangulations in higher dimensions are much more complicated than in planar cases. However, there does exist a subclass of triangulations, called regular triangulations, with nice structure, which is also touched upon.},
keywords={},
doi={},
ISSN={},
month={March},}
Copy
TY - JOUR
TI - Structures of Triangulations of Points
T2 - IEICE TRANSACTIONS on Information
SP - 428
EP - 437
AU - Keiko IMAI
PY - 2000
DO -
JO - IEICE TRANSACTIONS on Information
SN -
VL - E83-D
IS - 3
JA - IEICE TRANSACTIONS on Information
Y1 - March 2000
AB - Triangulations have been one of main research topics in computational geometry and have many applications in computer graphics, finite element methods, mesh generation, etc. This paper surveys properties of triangulations in the two- or higher-dimensional spaces. For triangulations of the planar point set, we have a good triangulation, called the Delaunay triangulation, which satisfies several optimality criteria. Based on Delaunay triangulations, many properties of planar triangulations can be shown, and a graph structure can be constructed for all planar triangulations. On the other hand, triangulations in higher dimensions are much more complicated than in planar cases. However, there does exist a subclass of triangulations, called regular triangulations, with nice structure, which is also touched upon.
ER -
English
