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On offsets and curvatures for discrete and semidiscrete surfaces

  • Oleg Karpenkov
  • Johannes Wallner
Original Paper

Abstract

This paper studies semidiscrete surfaces from the viewpoint of parallelity, offsets, and curvatures. We show how various relevant classes of surfaces are defined by means of an appropriate notion of infinitesimal quadrilateral, how offset surfaces behave in the semidiscrete case, and how to extend and apply the mixed-area based curvature theory which has been developed for polyhedral surfaces.

Keywords

Semidiscrete surfaces Curvatures 

Mathematics Subject Classification (2000)

53A05 53A10 

Notes

Acknowledgments

The authors are grateful to the anonymous reviewer for many useful suggestions. This research was supported by Austrian Science Fund (grant S9209, part of the National Research Network Industrial Geometry, and grant I705, part of the SFB-Transregio Discretization in Geometry and Dynamics).

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Copyright information

© The Managing Editors 2013

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of LiverpoolLiverpoolUK
  2. 2.Institut für GeometrieTU GrazGrazAustria

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