Wind-Directed Abrasion Generative Models: A Framework for Three-Dimensional Shape Generation Through Directional Erosion and Localized Material Removal

Most contemporary three-dimensional (3D) generative methods construct objects through learned geometric representations, probabilistic denoising, implicit surface reconstruction, or explicit primitive-based representations. This paper proposes Wind-Directed Abrasion Generative Models (WDAG), a conceptual framework for generating 3D shapes through the computational principles of wind erosion and granular abrasion. Instead of treating erosion merely as a post-processing effect, WDAG treats directional exposure, particle-impact interactions, material-dependent removal, and local geometric evolution as components of the generative process. An initial object is represented using a signed distance field, a volumetric grid, or a polygonal surface. A directional transport field determines the trajectories and impact distributions of abrasive particles, while local material properties regulate the amount of material removed from exposed regions. Repeated erosion steps progressively transform the initial geometry into a target morphology. A conditional variant introduces shape objectives, material constraints, and spatially varying exposure fields to guide generation toward specified 3D structures. The framework also considers differentiable approximations for gradient-based optimization and hybrid integration with neural generative models. Mathematical formulations, an iterative generation algorithm, training objectives, evaluation protocols, and ablation experiments are presented. WDAG is proposed as a research framework rather than an experimentally validated system. Its potential contribution lies in the explicit use of directional, material-dependent removal as a generative mechanism, while its novelty and practical advantages remain to be established through systematic comparison with existing erosion simulation and 3D generation methods.