Modeling polyhedral meshes with affine maps

We offer a framework for editing and modeling of planar meshes, focusing on planar quad, and hexagonal-dominant 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.