On offsets and curvatures for discrete and semidiscrete surfaces

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.