DL-Polycube: deep learning enhanced generalized polycube method for high-quality hexahedral mesh generation and volumetric spline construction

In this paper, we present a novel algorithm that integrates deep learning with the generalized polycube method (DL-Polycube) to generate high-quality hexahedral (hex) meshes, which are then used to construct volumetric splines for isogeometric analysis. Our DL-Polycube algorithm begins by establishing a connection between surface triangular meshes and polycube structures. We employ a deep neural network to classify surface triangular meshes into their corresponding polycube structures. Following this, we combine the acquired polycube structural information with unsupervised learning to perform surface segmentation of triangular meshes. In this way, it ensures the validity of polycube structures, eliminating the need for heuristic adjustments. Quality hex meshes are then generated using the polycube structures, together with octree subdivision, parametric mapping and quality improvement techniques. Through the use of deep learning for predicting polycube structures and unsupervised learning for segmenting surface triangular meshes, hex mesh generation becomes more efficient. Finally, truncated hierarchical B-splines are constructed on the generated hex meshes. We extract trivariate Bézier elements from these splines and apply them directly in isogeometric analysis. We offer several examples to demonstrate the robustness of our DL-Polycube algorithm.