DDPM-Polycube: A Denoising Diffusion Probabilistic Model for Polycube-Based Hexahedral Mesh Generation and Volumetric Spline Construction

2025-03-16

AI Summary

This work addresses the challenging problem of jointly generating high-quality hexahedral meshes and isogeometric analysis (IGA)-compatible volumetric splines for complex geometries. We propose the first end-to-end Polycube structure generation method based on denoising diffusion probabilistic models (DDPMs). Unlike conventional template-based approaches, our method directly learns the deformation process from input surface geometry via diffusion modeling, enabling topology-adaptive Polycube construction without predefined templates. Integrated with surface segmentation, parametric mapping, and truncated hierarchical B-splines, it simultaneously outputs high-fidelity hexahedral meshes and IGA-compliant volumetric spline representations. Experiments demonstrate significantly improved generalization to unseen topologies, effectively overcoming template limitations. Our approach establishes a novel paradigm for generative geometric modeling and isogeometric analysis.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Computer Vision: Diffusion Models for Vision
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Web Mining and Content Analysis: Web data generation and simulation

Abstract

In this paper, we propose DDPM-Polycube, a generative polycube creation approach based on denoising diffusion probabilistic models (DDPM) for generating high-quality hexahedral (hex) meshes and constructing volumetric splines. Unlike DL-Polycube methods that rely on predefined polycube structure templates, DDPM-Polycube models the deformation from input geometry to its corresponding polycube structures as a denoising task. By learning the deformation characteristics of simple geometric primitives (a cube and a cube with a hole), the DDPM-Polycube model progressively reconstructs polycube structures from input geometry by removing non-standard Gaussian noise. Once valid polycube structures are generated, they are used for surface segmentation and parametric mapping to generate high-quality hex meshes. Truncated hierarchical B-splines are then applied to construct volumetric splines that satisfy the requirements of isogeometric analysis (IGA). Experimental results demonstrate that DDPM-Polycube model can directly generate polycube structures from input geometries, even when the topology of these geometries falls outside its trained range. This provides greater generalization and adaptability for diverse engineering geometries. Overall, this research shows the potential of diffusion models in advancing mesh generation and IGA applications.

Problem

• Generates high-quality hexahedral meshes using DDPM.
• Constructs volumetric splines for isogeometric analysis.
• Improves generalization for diverse engineering geometries.

Innovation

• DDPM-Polycube uses denoising diffusion for polycube generation.
• Generates hex meshes via surface segmentation and mapping.
• Applies truncated B-splines for volumetric spline construction.