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Vertex Normals and Face Curvatures of Triangle Meshes

In: Advances in Discrete Differential Geometry

Author

Listed:
  • Xiang Sun

    (King Abdullah Univ. of Science and Technology)

  • Caigui Jiang

    (King Abdullah Univ. of Science and Technology)

  • Johannes Wallner

    (Graz University of Technology)

  • Helmut Pottmann

    (Vienna University of Technology)

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 ‘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.

Suggested Citation

  • Xiang Sun & Caigui Jiang & Johannes Wallner & Helmut Pottmann, 2016. "Vertex Normals and Face Curvatures of Triangle Meshes," Springer Books, in: Alexander I. Bobenko (ed.), Advances in Discrete Differential Geometry, pages 267-286, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-50447-5_8
    DOI: 10.1007/978-3-662-50447-5_8
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