On the computation of foldings

Abstract

The process of determining the development (or net) of a polyhedron or of a developable surface is called unfolding and has a unique result, apart from the placement of different components in the plane. The reverse process called folding is much more complex. In the case of polyhedra it leads to a system of algebraic equations. A given development can correspond to several or even to infinitely many incongruent polyhedra. The same holds also for smooth surfaces. In the paper two examples of such foldings are presented. In both cases the spatial realisations bound solids, for which mathematical models are required. In the first example, the cylinders with curved creases are given. In this case the involved curves can be exactly described. In the second example, even the ruling of the involved developable surface is unknown. Here, the obtained model is only an approximation.

Keywords

• folding
• curved folding
• developable surfaces
• revolute surfaces of constant curvature