Vertex Normals and Face Curvatures of Triangle Meshes

Xiang Sun; Caigui Jiang; Johannes Wallner; Helmut Pottmann

doi:10.1007/978-3-662-50447-5_8

Vertex Normals and Face Curvatures of Triangle Meshes

Xiang Sun, Caigui Jiang, Johannes Wallner, Helmut Pottmann

Research output: Chapter in Book/Report/Conference proceeding › Chapter

3 Scopus citations

Abstract

This study contributes to the discrete differential geometry of triangle meshes, in combination with discrete line congruences associated with such meshes. In particular we discuss when a congruence defined by linear interpolation of vertex normals deserves to be called a ŉormal’ congruence. Our main results are a discussion of various definitions of normality, a detailed study of the geometry of such congruences, and a concept of curvatures and shape operators associated with the faces of a triangle mesh. These curvatures are compatible with both normal congruences and the Steiner formula.

Original language	English (US)
Title of host publication	Advances in Discrete Differential Geometry
Publisher	Springer Nature
Pages	267-286
Number of pages	20
ISBN (Print)	9783662504468
DOIs	https://doi.org/10.1007/978-3-662-50447-5_8
State	Published - Aug 13 2016

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: The authors are grateful to Alexander Bobenko for fruitful discussions and to the anonymous reviewers for their suggestions. This research was supported by the DFG Collabo- rative Research Center, TRR 109, “Discretization in Geometry and Dynamics” through grants I705 and I706 of the Austrian Science Fund (FWF)

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10.1007/978-3-662-50447-5_8

https://repository.kaust.edu.sa/bitstream/10754/622686/1/chp3A10.10072F978-3-662-50447-5_8.pdf

Cite this

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title = "Vertex Normals and Face Curvatures of Triangle Meshes",

abstract = "This study contributes to the discrete differential geometry of triangle meshes, in combination with discrete line congruences associated with such meshes. In particular we discuss when a congruence defined by linear interpolation of vertex normals deserves to be called a ŉormal{\textquoteright} congruence. Our main results are a discussion of various definitions of normality, a detailed study of the geometry of such congruences, and a concept of curvatures and shape operators associated with the faces of a triangle mesh. These curvatures are compatible with both normal congruences and the Steiner formula.",

author = "Xiang Sun and Caigui Jiang and Johannes Wallner and Helmut Pottmann",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: The authors are grateful to Alexander Bobenko for fruitful discussions and to the anonymous reviewers for their suggestions. This research was supported by the DFG Collabo- rative Research Center, TRR 109, “Discretization in Geometry and Dynamics” through grants I705 and I706 of the Austrian Science Fund (FWF)",

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AU - Sun, Xiang

AU - Jiang, Caigui

AU - Wallner, Johannes

AU - Pottmann, Helmut

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: The authors are grateful to Alexander Bobenko for fruitful discussions and to the anonymous reviewers for their suggestions. This research was supported by the DFG Collabo- rative Research Center, TRR 109, “Discretization in Geometry and Dynamics” through grants I705 and I706 of the Austrian Science Fund (FWF)

PY - 2016/8/13

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N2 - This study contributes to the discrete differential geometry of triangle meshes, in combination with discrete line congruences associated with such meshes. In particular we discuss when a congruence defined by linear interpolation of vertex normals deserves to be called a ŉormal’ congruence. Our main results are a discussion of various definitions of normality, a detailed study of the geometry of such congruences, and a concept of curvatures and shape operators associated with the faces of a triangle mesh. These curvatures are compatible with both normal congruences and the Steiner formula.

AB - This study contributes to the discrete differential geometry of triangle meshes, in combination with discrete line congruences associated with such meshes. In particular we discuss when a congruence defined by linear interpolation of vertex normals deserves to be called a ŉormal’ congruence. Our main results are a discussion of various definitions of normality, a detailed study of the geometry of such congruences, and a concept of curvatures and shape operators associated with the faces of a triangle mesh. These curvatures are compatible with both normal congruences and the Steiner formula.

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ER -

Vertex Normals and Face Curvatures of Triangle Meshes

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