Fiber-Network Construction: An Incremental Generative Framework for Three-Dimensional Structure Synthesis Through Path Planning, Connectivity Formation, and Topological Constraints
Abstract
Three-dimensional generative models have achieved substantial progress in synthesizing geometric structures through implicit representations, point clouds, voxels, radiance fields, Gaussian primitives, and diffusion-based processes. However, many generative pipelines primarily formulate structure synthesis as the prediction of a final geometric representation, while the sequential construction of connected structural elements can be modeled as a distinct generative process. This paper proposes Fiber-Network Construction (FNC), a conceptual framework for three-dimensional generation in which a structure emerges through the incremental placement, extension, attachment, branching, and reinforcement of fiber-like elements. Inspired by natural construction processes, including spider-web formation and bird-nest building, FNC represents a generated object as a spatially embedded graph whose edges correspond to fibers or elongated structural elements and whose vertices represent attachment points, intersections, branching locations, and endpoints. Generation is formulated as a sequence of construction actions conditioned on the current partial structure, target geometry, connectivity requirements, material constraints, and structural objectives. A construction policy selects candidate paths, determines their endpoints and curvature, evaluates possible connections, and decides whether additional elements are required. Explicit topology constraints prevent invalid connections, while geometric and mechanical objectives encourage coverage, stability, and efficient material use. The framework can operate independently or be integrated with diffusion models, neural radiance fields, point-cloud generators, and other three-dimensional representations. This paper defines the mathematical formulation, architecture, construction algorithm, training objectives, evaluation protocol, and experimental hypotheses for FNC. The framework is presented as a research proposal rather than an experimentally validated method. Its potential contribution lies in treating sequential, topology-constrained network construction as an explicit generative paradigm for three-dimensional structures.
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BibTeX
@misc{zhang2026fibernetwork,
title = {{Fiber-Network Construction: An Incremental Generative Framework for Three-Dimensional Structure Synthesis Through Path Planning, Connectivity Formation, and Topological Constraints}},
author = {Jincheng Zhang},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23636072},
url = {https://zenodo.org/records/23636072},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fiber-Network Construction: An Incremental Generative Framework for Three-Dimensional Structure Synthesis Through Path Planning, Connectivity Formation, and Topological Constraints
AU - Jincheng Zhang
PY - 2026
DA - 2026/10/25
PB - Zenodo
DO - 10.5281/zenodo.23636072
UR - https://zenodo.org/records/23636072
AB - Three-dimensional generative models have achieved substantial progress in synthesizing geometric structures through implicit representations, point clouds, voxels, radiance fields, Gaussian primitives, and diffusion-based processes. However, many generative pipelines primarily formulate structure synthesis as the prediction of a final geometric representation, while the sequential construction of connected structural elements can be modeled as a distinct generative process. This paper proposes Fiber-Network Construction (FNC), a conceptual framework for three-dimensional generation in which a structure emerges through the incremental placement, extension, attachment, branching, and reinforcement of fiber-like elements. Inspired by natural construction processes, including spider-web formation and bird-nest building, FNC represents a generated object as a spatially embedded graph whose edges correspond to fibers or elongated structural elements and whose vertices represent attachment points, intersections, branching locations, and endpoints. Generation is formulated as a sequence of construction actions conditioned on the current partial structure, target geometry, connectivity requirements, material constraints, and structural objectives. A construction policy selects candidate paths, determines their endpoints and curvature, evaluates possible connections, and decides whether additional elements are required. Explicit topology constraints prevent invalid connections, while geometric and mechanical objectives encourage coverage, stability, and efficient material use. The framework can operate independently or be integrated with diffusion models, neural radiance fields, point-cloud generators, and other three-dimensional representations. This paper defines the mathematical formulation, architecture, construction algorithm, training objectives, evaluation protocol, and experimental hypotheses for FNC. The framework is presented as a research proposal rather than an experimentally validated method. Its potential contribution lies in treating sequential, topology-constrained network construction as an explicit generative paradigm for three-dimensional structures.
ER -