Crystal-Growth-Driven 3D Generative Modeling: A Framework for Incremental Spatial Construction Under Local Structural Constraints
Abstract
Three-dimensional generative modeling has developed through several major approaches, including volumetric generation, point-cloud generation, neural radiance fields, 3D Gaussian splatting, diffusion models, and autoregressive structure generation. Although these approaches differ substantially in representation and implementation, they provide alternative mechanisms for constructing, refining, or representing three-dimensional objects. This paper proposes Crystal-Growth-Driven 3D Generative Modeling (CG3D), a conceptual framework that treats three-dimensional generation as an incremental spatial construction process inspired by crystal growth. Instead of generating an entire object in a single operation or primarily transforming a global latent representation, CG3D constructs an object through successive local growth events. At each step, a growth controller evaluates candidate structural units, local geometric compatibility, neighborhood constraints, global objectives, and the consequences of adding, modifying, or removing structural elements. Although motivated by the ordered accumulation of atoms, ions, and molecules during crystallization, the framework is not restricted to physical crystals. It can potentially support periodic materials, irregular geometric objects, hybrid regular–irregular structures, and other three-dimensional representations. The paper formalizes the growth state, candidate selection, local constraint satisfaction, adaptive growth policies, structural revision, and stopping criteria. It also introduces a proposed optimization objective and an experimental protocol for comparing CG3D with existing generative approaches. The framework is conceptual and has not yet been empirically validated. Its potential contribution lies in treating locally governed structural growth as an explicit and generalizable generative mechanism, while identifying the conditions under which this mechanism provides advantages over existing incremental and iterative generation methods.
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BibTeX
@misc{zhang2026crystalgrowthdriven,
title = {{Crystal-Growth-Driven 3D Generative Modeling: A Framework for Incremental Spatial Construction Under Local Structural Constraints}},
author = {Jincheng Zhang},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23635834},
url = {https://zenodo.org/records/23635834},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Crystal-Growth-Driven 3D Generative Modeling: A Framework for Incremental Spatial Construction Under Local Structural Constraints
AU - Jincheng Zhang
PY - 2026
DA - 2026/10/25
PB - Zenodo
DO - 10.5281/zenodo.23635834
UR - https://zenodo.org/records/23635834
AB - Three-dimensional generative modeling has developed through several major approaches, including volumetric generation, point-cloud generation, neural radiance fields, 3D Gaussian splatting, diffusion models, and autoregressive structure generation. Although these approaches differ substantially in representation and implementation, they provide alternative mechanisms for constructing, refining, or representing three-dimensional objects. This paper proposes Crystal-Growth-Driven 3D Generative Modeling (CG3D), a conceptual framework that treats three-dimensional generation as an incremental spatial construction process inspired by crystal growth. Instead of generating an entire object in a single operation or primarily transforming a global latent representation, CG3D constructs an object through successive local growth events. At each step, a growth controller evaluates candidate structural units, local geometric compatibility, neighborhood constraints, global objectives, and the consequences of adding, modifying, or removing structural elements. Although motivated by the ordered accumulation of atoms, ions, and molecules during crystallization, the framework is not restricted to physical crystals. It can potentially support periodic materials, irregular geometric objects, hybrid regular–irregular structures, and other three-dimensional representations. The paper formalizes the growth state, candidate selection, local constraint satisfaction, adaptive growth policies, structural revision, and stopping criteria. It also introduces a proposed optimization objective and an experimental protocol for comparing CG3D with existing generative approaches. The framework is conceptual and has not yet been empirically validated. Its potential contribution lies in treating locally governed structural growth as an explicit and generalizable generative mechanism, while identifying the conditions under which this mechanism provides advantages over existing incremental and iterative generation methods.
ER -