Meshes are ubiquitous in visual computing and simulation, yet most existing machine learning techniques represent meshes only indirectly, e.g. as the level set of a scalar field or deformation of a template, or as a disordered triangle soup lacking local structure. This work presents a scheme to directly generate manifold, polygonal meshes of complex connectivity as the output of a neural network. Our key innovation is to define a continuous latent connectivity space at each mesh vertex, which implies the discrete mesh. In particular, our vertex embeddings generate cyclic neighbor relationships in a halfedge mesh representation, which gives a guarantee of edge-manifoldness and the ability to represent general polygonal meshes. This representation is well-suited to machine learning and stochastic optimization, without restriction on connectivity or topology. We first explore the basic properties of this representation, then use it to fit distributions of meshes from large datasets. The resulting models generate diverse meshes with tessellation structure learned from the dataset population, with concise details and high-quality mesh elements. In applications, this approach not only yields high-quality outputs from generative models, but also enables directly learning challenging geometry processing tasks such as mesh repair.

翻译：网格在视觉计算与仿真中无处不在，然而现有大多数机器学习技术仅以间接方式表示网格，例如作为标量场的等值面或模板的变形，或作为缺乏局部结构的无序三角形集合。本研究提出一种方案，能够直接生成具有复杂连接性的流形多边形网格作为神经网络的输出。我们的核心创新在于为每个网格顶点定义连续的潜在连接空间，该空间隐式定义了离散网格。具体而言，我们的顶点嵌入在半边网格表示中生成循环邻接关系，这保证了边缘流形特性，并能表示一般多边形网格。该表示非常适合机器学习和随机优化，且不受连接性或拓扑结构的限制。我们首先探究该表示的基本性质，随后利用其从大型数据集中拟合网格分布。所得模型能够生成具有从数据集群体学习到的细分结构的多样化网格，其细节简洁且网格单元质量高。在应用层面，该方法不仅能够从生成模型中产生高质量输出，还能直接学习具有挑战性的几何处理任务，例如网格修复。