Vertex normals and face curvatures of triangle meshes

X. Sun; C. Jiang; Johannes Wallner; H. Pottmann

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

Vertex normals and face curvatures of triangle meshes

X. Sun, C. Jiang, Johannes Wallner, H. Pottmann

Institute of Geometry (5070)

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

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 ‘normal’ 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
Title of host publication	Advances in Discrete Differential Geometry
Editors	Alexander I. Bobenko
Publisher	Springer Verlag
Pages	267-286
ISBN (Electronic)	978-3-662-50447-5
ISBN (Print)	978-3-662-50446-8
DOIs	https://doi.org/10.1007/978-3-662-50447-5_8
Publication status	Published - 2016

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10.1007/978-3-662-50447-5_8Licence: CC BY-NC 4.0

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 {\textquoteleft}normal{\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.",

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AU - Sun, X.

AU - Jiang, C.

AU - Wallner, Johannes

AU - Pottmann, H.

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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 ‘normal’ 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 ‘normal’ 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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DO - 10.1007/978-3-662-50447-5_8

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EP - 286

BT - Advances in Discrete Differential Geometry

A2 - Bobenko, Alexander I.

PB - Springer Verlag

ER -

Vertex normals and face curvatures of triangle meshes

Abstract

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