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.
CITATION STYLE
Sun, X., Jiang, C., Wallner, J., & Pottmann, H. (2016). Vertex normals and face curvatures of triangle meshes. In Advances in Discrete Differential Geometry (pp. 267–286). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-662-50447-5_8
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