Geometric modeling of developable surfaces is an actively researched topic, with important practical applications
ranging from manufacturing and architecture, to art and paper-craft or origami. In particular, there
still exists a demand for an intuitive design paradigm for composite piecewise C2-smooth developable surfaces,
which decompose into ruled pieces and planar patches. Such a type of surface can be equivalently characterized
in several forms, such as:
• defined as torsal ruled surfaces; that is, surfaces containing at least one parametric family of lines, with
constant tangent planes along such lines;
• through the theory of isometric mappings, by being mapped to local planar domains;
• surfaces with a singular shape operator; or, equivalently, exhibiting zero Gaussian curvature.
Each of these definitions has been the motivation for new classes of discrete developable meshes in recent
work [1, 2]. We review some of these, propose a novel one, and explore related tools for interactive manipulation,
such as handle deformation, curve folding, cutting and gluing, and others.

Joint work with: Florian Rist, Johannes Wallner, Helmut Pottmann