Vertex normals and face curvatures of triangle meshes

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

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


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 languageEnglish
Title of host publicationAdvances in Discrete Differential Geometry
EditorsAlexander I. Bobenko
PublisherSpringer Verlag
ISBN (Electronic)978-3-662-50447-5
ISBN (Print)978-3-662-50446-8
Publication statusPublished - 2016

Fields of Expertise

  • Information, Communication & Computing

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