On Vertex Offsets of Polyhedral Surfaces

Planar-faced mesh surfaces, also known as polyhedral surfaces, that possess vertex-offsets are useful in architectural design for constructing supporting structures, and also of interest in discrete differential geometry. We consider the existence and computation of vertex-offset meshes of general polyhedral surfaces and, specifically, study how the existence of vertex offsets is dictated by the face shape, mesh surface geometry and mesh surface topology. This extends the study in [Pottmann et al. 2007; Pottmann and Wallner 2008] on vertex-offset meshes of simply-connected circular quad meshes.