Article

Regular meshes

Authors:

Jianer ChenAuthors Info & Claims

SPM '05: Proceedings of the 2005 ACM symposium on Solid and physical modeling

Pages 213 - 219

https://doi.org/10.1145/1060244.1060268

Published: 13 June 2005 Publication History

Abstract

This paper presents our preliminary results on regular meshes in which all faces have the same size and all vertices have the same valence. A regular mesh is denoted by (n, m, g) where n is the number of the sides of faces, m is the valence of vertices and g is the genus of the mesh. For g = 0, regular meshes include regular platonic solids, all two sided polygons. For g = 1 regular meshes include regular tilings of infinite plane. Our work shows that there exist infinitely many regular meshes for g > 1. Moreover, we have constructive proofs that describe how to create high genus regular meshes that consist of triangles and quadrilaterals (3, m, g) and (4, m, g).

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Cited By

Crutison JRoyston T(2022)The design and application of a diffusion tensor informed finite-element model for exploration of uniaxially prestressed muscle architecture in magnetic resonance imagingEngineering with Computers10.1007/s00366-022-01690-x38:5(3893-3908)Online publication date: 30-Jun-2022
https://doi.org/10.1007/s00366-022-01690-x
Séquin C(2019)Turning Hild’s Sculptures into Single-Sided SurfacesMathematics10.3390/math70201257:2(125)Online publication date: 25-Jan-2019
https://doi.org/10.3390/math7020125
Lombardo PVanhavere FLebacq AStruelens LBogaerts R(2018)Development and Validation of the Realistic Anthropomorphic Flexible (RAF) PhantomHealth Physics10.1097/HP.0000000000000805114:5(486-499)Online publication date: May-2018
https://doi.org/10.1097/HP.0000000000000805
Show More Cited By

Regular meshes
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
2. Theory of computation
  1. Randomness, geometry and discrete structures

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cover image ACM Conferences

SPM '05: Proceedings of the 2005 ACM symposium on Solid and physical modeling

June 2005

287 pages

ISBN:1595930159

DOI:10.1145/1060244

Program Chairs:
Leif Kobbelt
RWTH Aachen University, Germany
,
Vadim Shapiro
University of Wisconsin--Madison, USA

Copyright © 2005 ACM.

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Published: 13 June 2005

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SPM05: 2005 ACM Symposium on Solid and Physical Modeling

June 13 - 15, 2005

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Cited By

Crutison JRoyston T(2022)The design and application of a diffusion tensor informed finite-element model for exploration of uniaxially prestressed muscle architecture in magnetic resonance imagingEngineering with Computers10.1007/s00366-022-01690-x38:5(3893-3908)Online publication date: 30-Jun-2022
https://doi.org/10.1007/s00366-022-01690-x
Séquin C(2019)Turning Hild’s Sculptures into Single-Sided SurfacesMathematics10.3390/math70201257:2(125)Online publication date: 25-Jan-2019
https://doi.org/10.3390/math7020125
Lombardo PVanhavere FLebacq AStruelens LBogaerts R(2018)Development and Validation of the Realistic Anthropomorphic Flexible (RAF) PhantomHealth Physics10.1097/HP.0000000000000805114:5(486-499)Online publication date: May-2018
https://doi.org/10.1097/HP.0000000000000805
Vidal VLavoué GDupont F(2015)Low budget and high fidelity relaxed 567-remeshingComputers and Graphics10.1016/j.cag.2014.10.00447:C(16-23)Online publication date: 1-Apr-2015
https://dl.acm.org/doi/10.1016/j.cag.2014.10.004
Akleman EChen JGross J(2015)Block meshesComputers and Graphics10.1016/j.cag.2014.09.02046:C(306-326)Online publication date: 1-Feb-2015
https://dl.acm.org/doi/10.1016/j.cag.2014.09.020
Akleman EChen J(2006)Regular Mesh Construction Algorithms using Regular HandlesProceedings of the IEEE International Conference on Shape Modeling and Applications 200610.1109/SMI.2006.28Online publication date: 14-Jun-2006
https://dl.acm.org/doi/10.1109/SMI.2006.28
Landreneau EOzener OPak BAkleman EKeyser J(2006)Interactive Rule-Based DesignInnovations in Design & Decision Support Systems in Architecture and Urban Planning10.1007/978-1-4020-5060-2_28(433-445)Online publication date: 2006
https://doi.org/10.1007/978-1-4020-5060-2_28
Akleman ESrinivasan VMandal E(2005)Remeshing Schemes for Semi-Regular TilingsProceedings of the International Conference on Shape Modeling and Applications 200510.1109/SMI.2005.40(44-50)Online publication date: 13-Jun-2005
https://dl.acm.org/doi/10.1109/SMI.2005.40

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