PolycubeNet: A Dual-latent Diffusion Model for Polycube-Based Hexahedral Mesh Generation

2026-05-18

AI Summary

This work addresses the long-standing challenge of automatic hexahedral mesh generation for complex CAD models, which has been hindered by traditional polycube-based methods relying on surface segmentation and heuristic strategies that are prone to failure and computationally inefficient. The authors propose an end-to-end conditional diffusion model that directly generates polycube point clouds from input point clouds, eliminating the need for explicit segmentation or template matching. By employing a dual-latent conditional diffusion architecture, the method confines expensive self-attention operations to a low-dimensional, fixed latent space, thereby decoupling computational complexity from output resolution and enabling support for arbitrary topologies and flexible scales. Integrated with rigid and non-rigid point cloud registration and a polycube-to-hexmesh conversion pipeline, the approach achieves high-quality hexahedral mesh generation in seconds for CAD models of arbitrary genus, significantly outperforming existing learning-based methods. The dataset and code are publicly released.

Abstract

Hexahedral meshes are widely used in simulation pipelines, yet automatic generation remains challenging for complex CAD geometries. Polycube-based hexahedral meshing is a representative approach due to its regular, parameterization-friendly structure, but existing polycube construction methods often rely on intricate surface segmentation and local heuristics, which can produce artifacts or fail on difficult shapes. In this paper, we propose an end-to-end framework for polycube generation based on conditional diffusion models. Given an input geometry represented as a point cloud, our method directly produces a corresponding polycube point cloud, eliminating the need for explicit surface segmentation or predefined polycube templates. At the core of our approach is a dual-latent conditional diffusion architecture that confines computationally expensive self-attention operations to a fixed-capacity, low-dimensional latent space. This design effectively decouples computational complexity from the resolution of both the input geometry and the output polycube, thereby avoiding the quadratic cost typical of point cloud self-attention mechanisms while supporting flexible input and output resolutions. To obtain a hexahedral mesh, the generated polycube is aligned to the input shape via rigid and non-rigid point cloud registration to establish surface correspondence, followed by a polycube-to-hex pipeline. We additionally create and release a paired dataset of CAD meshes and their corresponding polycube meshes, together with the core implementation of our model. Experiments show that PolycubeNet generalizes to complex CAD models with arbitrary genus and produces high-quality polycube structures within seconds, improving robustness and efficiency over prior learning-based approaches.

Problem

• hexahedral mesh generation
• polycube construction
• CAD geometries
• automatic meshing
• surface segmentation

Innovation

• dual-latent diffusion
• polycube generation
• hexahedral meshing
• point cloud self-attention
• end-to-end learning