We present a novel approach for generating isotropic surface triangle meshes directly from unoriented 3D point clouds, with the mesh density adapting to the estimated local feature size (LFS). Popular reconstruction pipelines first reconstruct a dense mesh from the input point cloud and then apply remeshing to obtain an isotropic mesh. The sequential pipeline makes it hard to find a lower-density mesh while preserving more details. Instead, our approach reconstructs both an implicit function and an LFS-aware mesh sizing function directly from the input point cloud, which is then used to produce the final LFS-aware mesh without remeshing. We combine local curvature radius and shape diameter to estimate the LFS directly from the input point clouds. Additionally, we propose a new mesh solver to solve an implicit function whose zero level set delineates the surface without requiring normal orientation. The added value of our approach is generating isotropic meshes directly from 3D point clouds with an LFS-aware density, thus achieving a trade-off between geometric detail and mesh complexity. Our experiments also demonstrate the robustness of our method to noise, outliers, and missing data and can preserve sharp features for CAD point clouds.

翻译：我们提出了一种直接从无定向三维点云生成各向同性表面三角形网格的新方法，其网格密度能够自适应于估计的局部特征尺寸。流行的重建流程通常首先从输入点云重建一个密集网格，然后应用重新网格化以获得各向同性网格。这种顺序流程难以在保持更多细节的同时找到较低密度的网格。相反，我们的方法直接从输入点云同时重建一个隐式函数和一个LFS感知的网格尺寸函数，随后无需重新网格化即可用于生成最终的LFS感知网格。我们结合局部曲率半径和形状直径直接从输入点云估计LFS。此外，我们提出了一种新的网格求解器来求解隐式函数，其零水平集可在无需法向定向的情况下描绘表面。本方法的核心价值在于能够直接从三维点云生成具有LFS感知密度的各向同性网格，从而在几何细节与网格复杂度之间实现平衡。我们的实验还证明了该方法对噪声、离群点和数据缺失的鲁棒性，并能够保持CAD点云的尖锐特征。