Vertex Normals and Face Curvatures of Triangle Meshes

Xiang Sun, Caigui Jiang, Johannes Wallner, Helmut Pottmann

Research output: Chapter in Book/Report/Conference proceedingChapter

2 Scopus citations


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 languageEnglish (US)
Title of host publicationAdvances in Discrete Differential Geometry
PublisherSpringer Nature
Number of pages20
ISBN (Print)9783662504468
StatePublished - 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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