ITECH 2014-2015 Master Thesis

Annie Locke Scherer

Tutors: Oliver David Krieg, David Correa, Benjamin Felbrich


One does not normally design leftover waste material. More commonly, one designs and what is left over is discarded. Programmable Folding is centered around strategic cuts. Careful design of removed material has the ability to imbue a flat sheet with intrinsic curvature. 

The aim of this thesis is to create parametrically-derived folding patterns that approximate irregular, doubly-curved surfaces when assembled. Looking at fundamentals of cut patterns, this thesis investigates the relatively unexplored world of origami’s lesser-known cousin: kirigami. This, like origami, is the art of folding sheets but also utilizes simple cuts to program inherent curvature into a flat material. 

Programmable Folding analyzes the basic geometrical rules of kirigami folding, identifying which parameters are flexible and which ones must be followed. The resulting geometrical pattern encodes a sheet material with an inherent assembly logic and provides the necessary information to fold the material into a complex, 3-dimensional surface. 

This project builds upon research from much of the origami world, particularly referencing the work of Tomohiro Tachi (University of Tokyo), Daniel Piker (Foster + Partners), and Toen Castle (University of Pennsylvania). Grasshopper and Kangaroo for Rhino are the primary design tools to realize the geometrical complexities within double-curvature folding. These tools allow for easy manipulation of areas and degrees of curvature, quick generation of a cut and tabbing pattern, and simulation of the final folded geometry.

Programmable Folding explores design possibilities of geometry on multiple levels and delivers a final product whose design is embedded in the generated folding pattern. This thesis simplifies complex geometrical problems of approximating an irregular surface, while simultaneously investigating typology, assembly logic and structural performance.

The final booklet is available here.

Classic kirigami paper folding

Kirigami cut fundamentals

Creating curvature with kirigami and basic Gaussian curvature principles


Computational model

Study of geometric possibilities

Full thesis booklet