NASM: Neural Anisotropic Surface Meshing

Hongbo Li1, Haikuan Zhu1, Sikai Zhong1, Ningna Wang2, Cheng Lin4, Xiaohu Guo2, Shiqing Xin3, Wenping Wang5, Jing Hua1, Zichun Zhong1
1Wayne State University, 2The University of Texas at Dallas, 3Shandong University, 4The University of Hong Kong 5Texas A&M University
SIGGRAPH Asia 2024 (Conference Track)
Paper Supplementary Code arXiv

Fig. 1. A gallery of anisotropic surface meshes generated by our NASM method. These results are selected from our testing models in Thingi10K dataset, including complicated organic surfaces, and surfaces with sharp and weak features as well as varying anisotropic metrics.

Abstract

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.

Results in Thingi10K

Fig. 2. Our anisotropic surface meshing results on smooth surfaces (top two rows) and surfaces with sharp or weak features (bottom row) from Thingi10K dataset. (left to right: curvature tensors with corresponding stretching ratios denoted in colors, anisotropic meshing, and a zoom-in illustration).

Results in MGN

Fig. 3. Our anisotropic surface meshing results on an unseen testing dataset, e.g., MGN dataset. The examples of our results can well capture the open boundaries and detailed cloth wrinkles and folds from tops and pants models.

Results in FAUST

Fig. 4. Our anisotropic surface meshing results on an unseen testing dataset, e.g., FAUST dataset. Several human subject meshes in different poses are shown to well capture geometric anisotropies and features around hands, arms, legs, and thin clothes wrinkles on 3D human models.

Video Presentation

Overview Pipeline

Fig. 5. The overview pipeline of NASM. Our method includes two main components: neural high-d Euclidean embedding and high-d normal metric CVT for feature-sensitive anisotropic meshing.

Additional Applications: Anisotropic RVD

Fig. 6. Anisotropic RVD results generated on some complicated surfaces from Thingi10K dataset, which are computed by our high-d normal metric CVT optimization.

Additional Applications: Surface Mesh Simplification

Fig. 7. NASM can be used for surface mesh simplification. An example of Candycane with different resolutions.

BibTeX

Coming soon