用深度学习生成更高效的3D曲面网格，自动保留锐利特征和曲率方向。
NASM: Neural Anisotropic Surface Meshing
- 用图神经网络将网格嵌入高维空间，通过点积损失保持曲率各向异性。
- 在高维空间中基于法向量度量优化，自动捕捉尖锐几何特征。
- 首次结合深度学习与大规模数据构建3D各向异性网格生成框架，适合工业建模与动画应用。
本文提出一种新的基于学习的各向异性表面网格化方法NASM。核心思想是使用图神经网络将输入网格嵌入高维欧氏空间，通过高维边向量间的点积损失来保留基于曲率的各向异性度量，显著降低计算时间并提升可扩展性。随后，我们在生成的高维嵌入空间中提出一种新颖的特征敏感重网格化方法，定义高维法向量度量，并对高维中心化沃罗诺伊剖分（CVT）优化进行自动微分，同时保持几何特征与原始3D形状中的曲率各向异性。据我们所知，这是首个将深度学习框架与大规模数据集结合用于构建3D各向异性表面网格化高维欧氏嵌入空间的工作。实验在Thingi10K数据集上的大量表面模型上评估并对比了当前最先进方法，且在Multi-Garment Network和FAUST人体数据集上进行了广泛未见3D形状的测试。
原文摘要 · Abstract (English)
This paper introduces a new learning-based method, NASM, for anisotropic surface meshing. Our key idea is to propose a graph neural network to embed an input mesh into a high-dimensional (high-d) Euclidean embedding space to preserve curvature-based anisotropic metric by using a dot product loss between high-d edge vectors. This can dramatically reduce the computational time and increase the scalability. Then, we propose a novel feature-sensitive remeshing on the generated high-d embedding to automatically capture sharp geometric features. We define a high-d normal metric, and then derive an automatic differentiation on a high-d centroidal Voronoi tessellation (CVT) optimization with the normal metric to simultaneously preserve geometric features and curvature anisotropy that exhibit in the original 3D shapes. To our knowledge, this is the first time that a deep learning framework and a large dataset are proposed to construct a high-d Euclidean embedding space for 3D anisotropic surface meshing. Experimental results are evaluated and compared with the state-of-the-art in anisotropic surface meshing on a large number of surface models from Thingi10K dataset as well as tested on extensive unseen 3D shapes from Multi-Garment Network dataset and FAUST human dataset.
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