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

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 languageEnglish (US)
Title of host publicationAdvances in Discrete Differential Geometry
PublisherSpringer Nature
Pages267-286
Number of pages20
ISBN (Print)9783662504468
DOIs
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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