Interactive design of curved-crease-folding

Building on the historic work of Huffman (Demaine et al. 2011), there has been increasing recent interest in the digital design and architectural application of curved-crease folded (CCF) geometries. This is particularly timely, given the new possibilities of producing curved surfaces from flat sheet material afforded by developments in robotic technology. However there are difficulties in interactively modelling such geometries, which stem from the lack of both appropriate geometric descriptions and constructive tools available in commercial CAD software. The author’s initial survey of methods included both the iterative optimization-based methods and simple constructive methods. Most methods presented difficulties for incorporation within an intuitive, real-time, edit-and-observe exploratory method. This research overcomes attempts to overcome these difficulties through the use of Dynamic Relaxation (DR) (Day 1965) for the interactive modelling of CCF geometries. It applies discrete differential operators and their gradients(Meyer et al. 2003), within a DR framework, to perturb meshes to satisfy the geometric criteria of CCF geometries outlined in Kilian et al. (2008). This research also outlines procedural strategies for generating appropriate topologies of an initial mesh, and a novel method for applying boundary conditions. The dissertation also includes a broad overview of existing methods to model developable surfaces, simulate elasto-plastic behaviour of thin (inextensible) shells and 2D parameterization of 3D meshes.