Modeling planar 3-valence meshes

Abstract

In architectural and sculptural practice, the eventual goal is constructing the shapes that have been designed. Due to fabrication considerations, shapes with planar faces are in demand for these practices. In this thesis, a novel computational modeling approach to design constructible shapes is introduced. This method guarantees that the resulting shapes are planar meshes with 3-valence vertices, which can always be physically constructed using planar or developable materials such as glass, sheet metal or plywood. The method introduced is inspired by the traditional sculpture and is based on the idea of carving a mesh by using slicing planes. The process of determining the slicing planes can either be interactive or automated. A framework is developed which allows user to sculpt shapes by using the in- teractive and automated processes. The framework allows user to cut a source mesh based on its edges, faces or vertices. The user can sculpt various kinds of developable surfaces by cutting the parallel edges of the mesh. The user can also introduce in- teresting conical patterns by cutting dierent vertex, edge, face combinations of the mesh.