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

arXiv: https://arxiv.org/abs/2410.18852 · HTML: https://mlsanity.com/paper/2410.18852/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 49 references that are in the map.
- First posted on arXiv 24 Oct 2024.

## Builds on (most cited first, 5 of 5)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Hex-Mesh Generation and Processing: a Survey](https://mlsanity.com/paper/2202.12670/) (2022)
- [HexGen and Hex2Spline: Polycube-based Hexahedral Mesh Generation and Spline Modeling for Isogeometric Analysis Applications in LS-DYNA](https://mlsanity.com/paper/2011.14213/) (2020)
- [HybridOctree_Hex: Hybrid Octree-Based Adaptive All-Hexahedral Mesh Generation with Jacobian Control](https://mlsanity.com/paper/2401.05984/) (2024)

## Built on by (most cited first, 2 of 2)

- [A Survey of AI Methods for Geometry Preparation and Mesh Generation in Engineering Simulation](https://mlsanity.com/paper/2512.23719/) (2025)
- [DDPM-Polycube: A Denoising Diffusion Probabilistic Model for Polycube-Based Hexahedral Mesh Generation and Volumetric Spline Construction](https://mlsanity.com/paper/2503.13541/) (2025)

## Abstract (arXiv)

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 B'ezier elements from these splines and apply them directly in isogeometric analysis. We offer several examples to demonstrate the robustness of our DL-Polycube algorithm.