Optimization of Constrained Quasiconformal Mapping for Origami Design
This addresses the challenge of creating deployable origami structures for applications in surface approximation and design, though it appears incremental as it builds on existing quasiconformal mapping techniques.
The paper tackles the problem of designing surface-aligned Miura-ori origami patterns by developing a constrained mapping optimization algorithm that approximates input surfaces via a narrow band, resulting in a method that demonstrates significance and flexibility in extensive experiments.
Origami structures, particularly Miura-ori patterns, offer unique capabilities for surface approximation and deployable designs. In this study, a constrained mapping optimization algorithm is designed for designing surface-aligned Miura-ori via a narrow band approximation of the input surface. The Miura-fold, embedded in the narrow band, is parameterized to a planar domain, and a mapping is computed on the parameter pattern by optimizing certain energy terms and constraints. Extensive experiments are conducted, showing the significance and flexibility of our methods.