Although polygon meshes have been a standard representation in geometry
processing, their irregular and combinatorial nature hinders their suitability
for learning-based applications. In this work, we introduce a novel learnable
mesh representation through a set of local 3D sample Points and their
associated Normals and Quadric error metrics (QEM) w.r.t. the underlying shape,
which we denote PoNQ. A global mesh is directly derived from PoNQ by
efficiently leveraging the knowledge of the local quadric errors. Besides
marking the first use of QEM within a neural shape representation, our
contribution guarantees both topological and geometrical properties by ensuring
that a PoNQ mesh does not self-intersect and is always the boundary of a
volume. Notably, our representation does not rely on a regular grid, is
supervised directly by the target surface alone, and also handles open surfaces
with boundaries and/or sharp features. We demonstrate the efficacy of PoNQ
through a learning-based mesh prediction from SDF grids and show that our
method surpasses recent state-of-the-art techniques in terms of both surface
and edge-based metrics.

通过本文，我们引入了一种新型的可学习网格表示方法，通过一组局部三维样本点、法线和二次误差度量（QEM）相对于底层形状的获取，我们将其称为 PoNQ。我们通过高效地利用局部二次误差的知识，直接从 PoNQ 中获取全局网格，并确保了拓扑和几何特性，使 PoNQ 网格不自相交且始终是一个边界体积。值得注意的是，我们的表示方法不依赖于正规网格，仅由目标表面进行监督，并且还能处理具有边界和 / 或锐利特征的开放表面。通过从 SDF 网格进行基于学习的网格预测，我们展示了 PoNQ 的有效性，并且在表面和边缘相关指标上超过了最近研究中的先进技术。

PoNQ: 基于神经量化嵌网的网格表示

PoNQ: a Neural QEM-based Mesh Representation

In stark contrast to the case of images, finding a concise, learnable
discrete representation of 3D surfaces remains a challenge. In particular,
while polygon meshes are arguably the most common surface representation used
in geometry processing, their irregular and combinatorial structure often make
them unsuitable for learning-based applications. In this work, we present
VoroMesh, a novel and differentiable Voronoi-based representation of watertight
3D shape surfaces. From a set of 3D points (called generators) and their
associated occupancy, we define our boundary representation through the Voronoi
diagram of the generators as the subset of Voronoi faces whose two associated
(equidistant) generators are of opposite occupancy: the resulting polygon mesh
forms a watertight approximation of the target shape's boundary. To learn the
position of the generators, we propose a novel loss function, dubbed VoroLoss,
that minimizes the distance from ground truth surface samples to the closest
faces of the Voronoi diagram which does not require an explicit construction of
the entire Voronoi diagram. A direct optimization of the Voroloss to obtain
generators on the Thingi32 dataset demonstrates the geometric efficiency of our
representation compared to axiomatic meshing algorithms and recent
learning-based mesh representations. We further use VoroMesh in a
learning-based mesh prediction task from input SDF grids on the ABC dataset,
and show comparable performance to state-of-the-art methods while guaranteeing
closed output surfaces free of self-intersections.

使用 VoroMesh 作为一种基于 Voronoi 的表示方法，可以有效地生成学习用途的三维形状表面，并且在几何效率和闭合输出方面优于传统的基于网格的算法和最新的基于学习的网格表示方法。

VoroMesh：使用 Voronoi 图学习无漏网面

VoroMesh: Learning Watertight Surface Meshes with Voronoi Diagrams

Polygon meshes are an efficient representation of 3D geometry, and are of
central importance in computer graphics, robotics and games development.
Existing learning-based approaches have avoided the challenges of working with
3D meshes, instead using alternative object representations that are more
compatible with neural architectures and training approaches. We present an
approach which models the mesh directly, predicting mesh vertices and faces
sequentially using a Transformer-based architecture. Our model can condition on
a range of inputs, including object classes, voxels, and images, and because
the model is probabilistic it can produce samples that capture uncertainty in
ambiguous scenarios. We show that the model is capable of producing
high-quality, usable meshes, and establish log-likelihood benchmarks for the
mesh-modelling task. We also evaluate the conditional models on surface
reconstruction metrics against alternative methods, and demonstrate competitive
performance despite not training directly on this task.

该研究论文介绍了一种基于 Transformer 的方法来直接建模多边形网格，并通过输入不同的对象类别、体素和图像等信息，生成可用的高质量网格，同时在表面重建指标上表现出很好的性能。

PolyGen: 一个三维网格的自回归生成模型

PolyGen: An Autoregressive Generative Model of 3D Meshes

Jacobson et al. [JKSH13] hypothesized that the local coherency of the
generalized winding number function could be used to correctly determine
consistent facet orientations in polygon meshes. We report on an approach to
consistently orienting facets in polygon meshes by minimizing the Dirichlet
energy of generalized winding numbers. While the energy can be concisely
formulated and efficiently computed, we found that this approach is
fundamentally flawed and is unfortunately not applicable for most handmade
meshes shared on popular mesh repositories such as Google 3D Warehouse.

本文探讨利用广义绕组数函数的本地连通性来确定多边形网格中的一致面向，通过最小化广义绕组数的狄利克雷能量，但发现该方法基本上无效，无法应用于大多数手工制作的网格。