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.
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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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Karpenkov, O., Wallner, J. On offsets and curvatures for discrete and semidiscrete surfaces. Beitr Algebra Geom 55, 207–228 (2014). https://doi.org/10.1007/s13366-013-0146-6
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DOI: https://doi.org/10.1007/s13366-013-0146-6