Optimization of Constrained Quasiconformal Mapping for Origami Design

TL;DR

This paper presents an optimization algorithm for designing surface-aligned Miura-ori origami patterns using constrained quasiconformal mapping, enabling advanced surface approximation and deployable structures.

Contribution

It introduces a novel constrained mapping optimization method specifically tailored for Miura-ori origami design on complex surfaces.

Findings

The method effectively designs surface-aligned Miura-ori patterns.

Experiments demonstrate the flexibility and significance of the proposed approach.

Abstract

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.