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.

翻译：本文提出了一种新的基于学习的方法NASM，用于各向异性表面网格生成。我们的核心思想是采用图神经网络将输入网格嵌入高维欧几里得嵌入空间，通过高维边向量之间的点积损失来保持基于曲率的各向异性度量。这能显著减少计算时间并提高可扩展性。随后，我们在生成的高维嵌入上提出了一种新颖的特征敏感重网格化方法，以自动捕捉尖锐的几何特征。我们定义了高维法向量度量，并推导了基于该法向量度量的高维质心Voronoi细分（CVT）优化自动微分方法，从而同时保持原始三维形状中呈现的几何特征与曲率各向异性。据我们所知，这是首次提出采用深度学习框架和大规模数据集来构建用于三维各向异性表面网格生成的高维欧几里得嵌入空间。实验结果在Thingi10K数据集的大量表面模型上进行了评估，并与各向异性表面网格生成领域的最先进方法进行了比较，同时在Multi-Garment Network数据集和FAUST人体数据集的大量未见三维形状上进行了测试。