Optimization of Constrained Quasiconformal Mapping for Origami Design

2026-04-21

AI Summary

This work proposes a high-precision method for designing Miura-ori origami structures that accurately conform to target surfaces. Addressing the challenge of aligning Miura-ori patterns with arbitrary curved geometries, the approach constructs developable Miura folds within a narrow-band approximation of the target surface and maps them parametrically onto a planar domain. A joint optimization framework is employed to simultaneously satisfy geometric constraints and minimize an energy functional, yielding a quasi-conformal mapping that ensures precise surface alignment. The method substantially enhances both the approximation accuracy and design flexibility of Miura-ori patterns for complex surfaces, as demonstrated through extensive experiments across diverse surface types.

Technology Category

• Machine Learning: Learning with Manifolds
• Search and Optimization: Sampling/Simulation-based Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

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.

Problem

• constrained quasiconformal mapping
• origami design
• Miura-ori
• surface approximation
• deployable structures

Innovation

• constrained optimization
• quasiconformal mapping
• Miura-ori
• surface approximation
• origami design