A neural poly-vector based non-orthogonal frame field generation method for quad meshing

Recent breakthroughs in artificial intelligence have revolutionized the automation of frame-field-driven quad mesh generation, a critical surface representation paradigm in computer-aided engineering. However, existing neural frame-field generation methods, limited by the orthogonality of fields, struggle to preserve the geometric fidelity as well as quad quality around sharp features. To address these limitations, we propose NeuralPoly, an intelligent non-orthogonal frame-field generation method. We design a poly-vector encoding of the non-orthogonal field to leverage the representation power of neural network in capturing geometric features without manual tuning. Furthermore, we introduce a Hessian-based neural weighting scheme that autonomously resolves ambiguous alignments in flat and spherical regions. We then incorporates the poly-vector encoding and the proposed weighting scheme into the loss functions of a unified neural network architecture consists of a SIREN module for neural implicit representation and a ResUNet module for field prediction. Finally, we compare our method with state-of-the-art techniques in field-guided quad mesh generation. Quantitative and qualitative evaluations demonstrate that our approach achieves superior performance in both geometric fidelity and quad mesh quality.