Fold-and-Deploy Generative Modeling: A Material-Centric Framework for Three-Dimensional Shape Generation Through Folding, Bending, and Deployment
Abstract
Three-dimensional shape generation has advanced through neural implicit representations, point-cloud generative models, diffusion-based methods, and Gaussian splatting. However, generating a geometrically plausible three-dimensional surface does not necessarily produce a physically realizable structure that can be obtained from a flat sheet through folding and deployment. This paper proposes Fold-and-Deploy Generative Modeling (FDGM), a material-centric framework for generating three-dimensional structures by modeling the transformation of a two-dimensional sheet into a three-dimensional configuration. Instead of treating the final surface as the sole generative target, FDGM jointly represents a planar material domain, a crease-and-hinge graph, a continuous deformation field, a time-dependent deployment trajectory, and a final three-dimensional geometry. The proposed framework combines topology-aware crease generation, material deformation, geometric compatibility, collision avoidance, and deployment reversibility within a unified objective. A hybrid representation distinguishes discrete structural decisions, such as crease placement and panel connectivity, from continuous variables, such as fold angles, vertex positions, and bending fields. The framework accommodates rigid origami, flexible-sheet folding, and selected deployable structures through material-dependent constraint configurations. We formulate the learning problem, define the optimization objectives, present a training algorithm, and propose an evaluation protocol based on geometric accuracy, foldability, collision frequency, deployment continuity, and reconstruction consistency. The framework is a research proposal, and its performance and comparative advantages remain to be established experimentally. Its central hypothesis is that generating a shape through a constrained material transformation can provide better control over foldability and deployability than optimizing the final geometry alone.
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BibTeX
@misc{zhang2026foldanddeploy,
title = {{Fold-and-Deploy Generative Modeling: A Material-Centric Framework for Three-Dimensional Shape Generation Through Folding, Bending, and Deployment}},
author = {Jincheng Zhang},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23636304},
url = {https://zenodo.org/records/23636304},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fold-and-Deploy Generative Modeling: A Material-Centric Framework for Three-Dimensional Shape Generation Through Folding, Bending, and Deployment
AU - Jincheng Zhang
PY - 2026
DA - 2026/10/25
PB - Zenodo
DO - 10.5281/zenodo.23636304
UR - https://zenodo.org/records/23636304
AB - Three-dimensional shape generation has advanced through neural implicit representations, point-cloud generative models, diffusion-based methods, and Gaussian splatting. However, generating a geometrically plausible three-dimensional surface does not necessarily produce a physically realizable structure that can be obtained from a flat sheet through folding and deployment. This paper proposes Fold-and-Deploy Generative Modeling (FDGM), a material-centric framework for generating three-dimensional structures by modeling the transformation of a two-dimensional sheet into a three-dimensional configuration. Instead of treating the final surface as the sole generative target, FDGM jointly represents a planar material domain, a crease-and-hinge graph, a continuous deformation field, a time-dependent deployment trajectory, and a final three-dimensional geometry. The proposed framework combines topology-aware crease generation, material deformation, geometric compatibility, collision avoidance, and deployment reversibility within a unified objective. A hybrid representation distinguishes discrete structural decisions, such as crease placement and panel connectivity, from continuous variables, such as fold angles, vertex positions, and bending fields. The framework accommodates rigid origami, flexible-sheet folding, and selected deployable structures through material-dependent constraint configurations. We formulate the learning problem, define the optimization objectives, present a training algorithm, and propose an evaluation protocol based on geometric accuracy, foldability, collision frequency, deployment continuity, and reconstruction consistency. The framework is a research proposal, and its performance and comparative advantages remain to be established experimentally. Its central hypothesis is that generating a shape through a constrained material transformation can provide better control over foldability and deployability than optimizing the final geometry alone.
ER -