Modeling Polyhedral Meshes with Affine Maps

Abstract

We offer a framework for editing and modeling of planar meshes, focusing on planar quad, and hexagonaldominant meshes, which are held in high demand in the field of architectural design. Our framework manipulates these meshes by affine maps that are assigned per-face, and which naturally ensure the planarity of these faces throughout the process, resulting in a linear subspace of compatible planar deformations for any given mesh. Our modeling metaphors include classical handle-based editing, mesh interpolation, and shape-space exploration, all of which allow for an intuitive way to produce new polyhedral and near-polyhedral meshes by editing.