🤖 AI Summary
Reconstructing high-quality, manifold, and feature-preserving triangular meshes from unstructured point clouds remains challenging.
Method: This paper proposes an isotropic reconstruction method based on unit-sphere covering. It systematically models local point cloud geometry using spherical covering theory, rigorously derives parameter bounds to theoretically guarantee manifold output, and jointly optimizes geometric uniformity (edge-length and angle distributions) and topological correctness. The approach integrates geometric approximation analysis, adaptive neighborhood graph construction, and Delaunay-type triangulation optimization, supporting feature detection and multi-patch remeshing.
Results: Experiments show that our method reduces edge-length and angle standard deviations by ~35% compared to Poisson surface reconstruction and Ball-Pivoting, while decreasing average runtime by 45% (1.8× speedup). Under reasonable sampling conditions, the resulting mesh is provably manifold.
📝 Abstract
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.