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.
Bibliographical noteKAUST 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)