Folding Flat Crease Patterns with Thick Materials

TL;DR

This paper introduces a new algorithm to convert flat-foldable crease patterns into thick material foldings, ensuring feasible, intersection-free structures with bounds on material thickness.

Contribution

It presents a systematic, broadly applicable method for thickening crease patterns while maintaining foldability and avoiding self-intersection, with theoretical bounds and practical validation.

Findings

Algorithm successfully thickens crease patterns without intersections

Provides bounds on maximum feasible thickness for given patterns

Validated through numerical simulations and physical models

Abstract

Modeling folding surfaces with nonzero thickness is of practical interest for mechanical engineering. There are many existing approaches that account for material thickness in folding applications. We propose a new systematic and broadly applicable algorithm to transform certain flat-foldable crease patterns into new crease patterns with similar folded structure but with a facet-separated folded state. We provide conditions on input crease patterns for the algorithm to produce a thickened crease pattern avoiding local self intersection, and provide bounds for the maximum thickness that the algorithm can produce for a given input. We demonstrate these results in parameterized numerical simulations and physical models.