Shape Representation by Zippable Ribbons

Abstract

Shape fabrication from developable parts is the basis for arts such as papercraft and needlework, as well as modern architecture and CAD in general, and it has inspired much research. We observe that the assembly of complex 3D shapes created by existing methods often requires first fabricating many small flat parts and then carefully following instructions to assemble them together. Despite its significance, this error prone and tedious process is generally neglected in the discussion. We propose an approach for shape representation through a single developable part that attaches to itself and requires no assembly instructions. Our inspiration comes from the so-called zipit bags, which are made of a single, long ribbon with a zipper around its boundary. In order to "assemble" the bag, one simply needs to zip up the ribbon. Our method operates in the same fashion, but it can be used to approximate any shape. Given a 3D model, our algorithm produces plans for a single 2D shape that can be laser cut in few parts from flat fabric or paper. We can then attach a zipper along the boundary for quick assembly and disassembly, or apply more traditional approaches, such as gluing and stitching. We show physical and virtual results that demonstrate the capabilities of our method and the ease with which shapes can be assembled.