Gelation-Driven 3D Generation: A Network-Formation Framework for Constructing Three-Dimensional Structures Through Crosslinking and Liquid Confinement
Abstract
Three-dimensional generative modeling commonly represents target objects through volumetric grids, point clouds, implicit fields, explicit geometric primitives, or learned latent representations. Although these representations support flexible shape synthesis, they do not necessarily describe how a three-dimensional structure emerges from the progressive formation of an interconnected material network. This paper proposes Gelation-Driven 3D Generation (GD3G), a generative framework inspired by gelation, in which molecular or polymer-like units progressively connect, crosslink, and form a spatially distributed network that constrains an initially available volume. Instead of directly predicting a final three-dimensional object, GD3G generates a sequence of network states and derives the resulting geometry from network topology, local crosslink density, pore accessibility, and a liquid-confinement field. The framework comprises a candidate-unit initialization module, a spatially constrained connection mechanism, a crosslinking controller, a network-to-volume transformation, and a structure-aware objective function. A differentiable implementation can combine graph generation, continuous spatial representations, and learned transition operators, while a stochastic implementation can explicitly sample connection and crosslinking events. The proposed formulation supports conditional generation according to target porosity, network connectivity, spatial density, and geometric constraints. A mathematical formulation, training procedure, evaluation protocol, baseline comparisons, and ablation studies are presented. Because the framework has not yet been experimentally evaluated, its effectiveness and advantages over existing generative methods remain hypotheses to be tested. The principal research question is whether explicitly modeling network formation and liquid confinement can provide a useful alternative to direct geometry generation for porous and network-dominated three-dimensional structures.
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BibTeX
@misc{zhang2026gelationdriven,
title = {{Gelation-Driven 3D Generation: A Network-Formation Framework for Constructing Three-Dimensional Structures Through Crosslinking and Liquid Confinement}},
author = {Jincheng Zhang},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23636224},
url = {https://zenodo.org/records/23636224},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Gelation-Driven 3D Generation: A Network-Formation Framework for Constructing Three-Dimensional Structures Through Crosslinking and Liquid Confinement
AU - Jincheng Zhang
PY - 2026
DA - 2026/10/25
PB - Zenodo
DO - 10.5281/zenodo.23636224
UR - https://zenodo.org/records/23636224
AB - Three-dimensional generative modeling commonly represents target objects through volumetric grids, point clouds, implicit fields, explicit geometric primitives, or learned latent representations. Although these representations support flexible shape synthesis, they do not necessarily describe how a three-dimensional structure emerges from the progressive formation of an interconnected material network. This paper proposes Gelation-Driven 3D Generation (GD3G), a generative framework inspired by gelation, in which molecular or polymer-like units progressively connect, crosslink, and form a spatially distributed network that constrains an initially available volume. Instead of directly predicting a final three-dimensional object, GD3G generates a sequence of network states and derives the resulting geometry from network topology, local crosslink density, pore accessibility, and a liquid-confinement field. The framework comprises a candidate-unit initialization module, a spatially constrained connection mechanism, a crosslinking controller, a network-to-volume transformation, and a structure-aware objective function. A differentiable implementation can combine graph generation, continuous spatial representations, and learned transition operators, while a stochastic implementation can explicitly sample connection and crosslinking events. The proposed formulation supports conditional generation according to target porosity, network connectivity, spatial density, and geometric constraints. A mathematical formulation, training procedure, evaluation protocol, baseline comparisons, and ablation studies are presented. Because the framework has not yet been experimentally evaluated, its effectiveness and advantages over existing generative methods remain hypotheses to be tested. The principal research question is whether explicitly modeling network formation and liquid confinement can provide a useful alternative to direct geometry generation for porous and network-dominated three-dimensional structures.
ER -