Feature-aware manifold meshing and remeshing of point clouds and polyhedral surfaces with guaranteed smallest edge length

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 . • The contributions of the original article included: introduction of a geometric approach suitable to mesh point clouds; which creates high-quality triangles with edge lengths close to uniformity and of a guaranteed minimum length; as well as manifold output, provided a suitable input geometry; in a single sweep over said input. • In this extended version of the article, we build upon the previous contributions and extend the algorithm to handle: detection of sharp feature ridges in point clouds; remeshing of polyhedral surfaces obtaining high-quality meshes with edge lengths close to uniformity; and detection of sharp feature ridges on polyhedral meshes.