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

TL;DR

A novel algorithm that integrates deep learning with the polycube method (DL-Polycube) to generate high-quality hexahedral (hex) meshes, which are then used to construct volumetric splines for isogeometric analysis.

Abstract

In this paper, we present a novel algorithm that integrates deep learning with the 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 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. This step addresses the issue of segmentation not corresponding to a polycube while reducing manual intervention. Quality hex meshes are then generated from the polycube structures, with employing octree subdivision, parametric mapping and quality improvement techniques. The incorporation of deep learning for creating polycube structures, combined with unsupervised learning for segmentation of surface triangular meshes, substantially accelerates hex mesh generation. 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.

Figures (15)

• Figure 1: The DL-Polycube pipeline using deep learning and the polycube method. (a) The CAD geometry and converting it into a triangular mesh; (b) a pretrained deep learning model to generate a polycube structure from the triangular mesh; (c) the polycube structure predicted by the deep learning model; (d) surface segmentation using the polycube structure information with K-means segmentation; (e) the polycube structure and surface segmentation are used to create an all-hex mesh through octree subdivision, parametric mapping and quality improvement techniques; and (f) volumetric spline with IGA simulation results using ANSYS-DYNA.
• Figure 2: Overview of the DL-Polycube algorithm. Step 1: Training dataset generation and curation: A cage is created around the target mesh to generate a diverse set of models with random transformations and deformations. Step 2: GCN-Polycube recognition: The GCN-Polycube classification enables the automatic conversion of complex geometries into polycube structures. Step 3: K-means surface segmentation: Segment the surface of CAD geometry to ensure a one-to-one correspondence with the surface of the polycube structure.
• Figure 3: Procedural geometric modeling process of GCN-Polycube model architecture. Step 1: Initial polycube structure created using Boolean operations. Step 2: Surface subdivision applied using the Catmull-Clark algorithm and triangulation of the subdivided surface. Step 3: Free-form deformation applied to the triangulated and subdivided polycube structure. These steps generate input and output geometries for deep learning model training.
• Figure 4: Feature extraction and data integration process for GCN-Polycube classification and K-means surface segmentation. $A_{ij}=1$ indicating that two triangular elements $i$ and $j$ are adjacent. The node feature vectors $N$ include vertex coordinates (red points), centroid coordinates (yellow points), and normal vectors (dashed arrows) of each face.
• Figure 5: Hierarchical overview of the GCN-Polycube model architecture. (a) The input features from the CAD geometry. (b) The four GCN-Polycube layers capture local and global geometric structures. (c) The pooling layer aggregates node-level information into graph-level representations. (d) The fully connected layers map the features of complex topological structures to the target space, i.e., the polycube structure. (e) The output predicts the suggest corresponding polycube structures.