Point clouds and polygonal meshes are widely used when modeling real-world scenarios. Here, point clouds arise, for instance, from acquisition processes applied in various surroundings, such as reverse engineering, rapid prototyping, or cultural preservation. Based on these raw data, polygonal meshes are created to, for example, run various simulations. For such applications, the utilized meshes must be of high quality. This paper presents an algorithm to derive triangle meshes from unstructured point clouds. The occurring edges have a close to uniform length and their lengths are bounded from below. Theoretical results guarantee the output to be manifold, provided suitable input and parameter choices. Further, the paper presents several experiments establishing that the algorithms can compete with widely used competitors in terms of quality of the output and timing and the output is stable under moderate levels of noise. Additionally, we expand the algorithm to detect and respect features on point clouds as well as to remesh polyhedral surfaces, possibly with features. Supplementary material, an extended preprint, a link to a previously published version of the article, utilized models, and implementation details are made available online: https://ms-math-computer.science/projects/guaranteed-smallest-edge-length-manifold-meshing.html

翻译：点云和多边形网格在真实场景建模中被广泛应用。点云通常来源于多种环境下的采集过程，例如逆向工程、快速原型制作或文化遗产保护。基于这些原始数据，多边形网格被构建以运行各类仿真。在此类应用中，所使用的网格必须具备高质量。本文提出一种从非结构化点云生成三角形网格的算法。生成的边长度接近均匀分布，且其长度存在下界保证。理论分析证明，在适当的输入和参数选择下，输出结果可保证为流形结构。此外，本文通过多组实验验证了该算法在输出质量和计算时间方面可与广泛使用的同类方法竞争，且在适度噪声水平下输出保持稳定。进一步地，我们扩展了该算法以检测并保留点云特征，并对可能包含特征的多面体曲面进行重网格化。补充材料、扩展预印本、先前发表版本的链接、所用模型及实现细节已在线发布：https://ms-math-computer.science/projects/guaranteed-smallest-edge-length-manifold-meshing.html