Polygonnet

Polygonnet is a class of geometric deep learning models designed to operate directly on polygonal meshes and polygon networks. It extends graph neural networks to irregular polygons, enabling learning on faces and edges in addition to vertices. Polygonnet aims to capture local and global mesh structure while preserving geometric properties such as edge orientation and face adjacency.

Core mechanisms include polygon-level message passing, where feature vectors attach to vertices, edges, and polygon faces; a dual graph representation that alternates between primal and dual meshes; and differentiable pooling and unpooling operations to coarsen or refine mesh resolution. Kernel functions may be designed to align with mesh geometry, using edge-aware or face-aware aggregations, and attention mechanisms to weigh contributions from neighboring polygons.

Inputs are typically polygon meshes from 3D scans or CAD data. Preprocessing may involve ensuring manifoldness, repairing holes, and normalizing coordinates. Polygonnet models can operate on mixed-polygon meshes including triangles, quadrilaterals, and higher-order polygons; some variants treat polygons as sets of sub-edges with shared vertices.

Applications include 3D shape classification and segmentation, surface reconstruction, mesh denoising, finite element analysis, and geographic information systems that use polygonal maps. It is also used in computer graphics for texture mapping and parameterization.

Challenges include computational cost, memory consumption for large meshes, and sensitivity to mesh quality. Development is ongoing, with multiple research groups proposing different variants and evaluation benchmarks; there is no single standardized framework for Polygonnet, and practical use often requires careful data preprocessing and hardware considerations.