Vertex Normals and Face Curvatures of Triangle Meshes

Xiang Sun (), Caigui Jiang (), Johannes Wallner () and Helmut Pottmann ()
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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

A chapter in Advances in Discrete Differential Geometry, 2016, pp 267-286 from Springer

Abstract: 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.

Keywords: Principal Curvature; Shape Operator; Triangle Mesh; Quadratic Cone; Focal Surface (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-662-50447-5_8

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DOI: 10.1007/978-3-662-50447-5_8

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