ORCID

0000-0002-7145-8831

Keywords

Unfolding, Compact refolding, Tessellation, Topological defects, Reinforcement learning, Distortion minimization

Abstract

Unfolding and folding are related geometric and mechanical transformations fundamental to structural applications. Particularly, unfolding curved surfaces is important for deployable structures, garment pattern generation, etc. A central challenge is minimizing geometric distortion between a surface and its unfolded counterpart avoiding overlaps. As regions of lower Gaussian curvature typically produce less distortion during flattening, identifying curvature distribution becomes essential. Topological defects in a particle assembly on a surface in its minimum interaction-energy configuration indicate regions of concentrated curvature. In this work, an unfolding method is proposed that segments the surface using defects' location. Cutlines connecting the defects isolate lower curvature regions. Segmented patches are sequentially unfolded using an energy-based distortion minimization formulated as a hyperelastic membrane problem. To control the unfolded template geometry, the segmented surface is represented as graph where candidate unfolding paths correspond to spanning trees. Graph-based exploratory search identifies unfolding sequences that optimize different criteria. The framework introduces strategy to generate templates for compact refolding through alternate folding pattern for efficient stacking. As the combinatorial space of possible unfolding paths grows with geometric complexity, reinforcement learning is introduced for efficient exploration. Using Proximal Policy Optimization, an agent constructs unfolding paths that satisfy geometric objectives while reducing overlaps. The method is first applied to unfold simple geometries with varying Gaussian curvature. Distortion levels are computed, and compactly refoldable templates are demonstrated. Finally, the framework is applied to a torso-based model for garment applications to illustrate its capability for complex geometries and demonstrate the effectiveness of the PPO-based strategy.

Completion Date

2026

Semester

Spring

Committee Chair

Luigi E. Perotti

Degree

Doctor of Philosophy (Ph.D.)

College

College of Engineering and Computer Science

Department

Mechanical and Aerospace Engineering

Format

PDF

Document Type

Dissertation

Identifier

DP0053227

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