Point clouds arise from acquisition processes applied in various scenarios, such as reverse engineering, rapid prototyping, or cultural preservation. To run various simulations via, e.g., finite element methods, on the derived data, a mesh has to be created from it. In this paper, a meshing algorithm for point clouds is presented, which is based on a sphere covering of the underlying surface. The algorithm provides a mesh close to uniformity in terms of edge lengths and angles of its triangles. Additionally, theoretical results guarantee the output to be manifold, given suitable input and parameter choices. We present both the underlying theory, which provides suitable parameter bounds, as well as experiments showing that our algorithm can compete with widely used competitors in terms of quality of the output and timings.

翻译：点云数据来源于逆向工程、快速成型、文化遗产保护等多种应用场景中的采集过程。为了对派生数据通过有限元等方法进行各类仿真计算，必须从点云创建网格。本文提出了一种基于底层表面球体覆盖的点云网格化算法，该算法能够生成三角形边长和角度接近均匀的网格。此外，理论结果保证了在合适的输入参数条件下，输出网格具有流形结构。我们不仅阐述了提供合适参数边界的理论基础，还通过实验表明，本算法在输出质量和计算时间方面可与广泛使用的竞争算法相媲美。