Feature-Preserving Mesh Repair via Restricted Power Diagram

摘要

Mesh repair is a critical process in 3D geometry processing aimed at correcting errors and imperfections in polygonal meshes to produce watertight, manifold, and feature-preserving meshes suitable for downstream tasks. While errors such as degeneracies, duplication, holes, and overlaps can be addressed through standard repair processes, cracks along trimmed curves require special attention and should ideally be repaired to align with sharp feature lines. In this paper, we present a unified framework for repairing diverse mesh imperfections by leveraging a manifold wrap surface as a mediating agent. The primary role of the wrap surface is to define spatial connections between points on the original surface, thereby decoupling the challenges of edge connectivity and point relocation during repair. Throughout the process, our algorithm operates on the dual objects: the original defective mesh and the manifold wrap surface. The implementation begins by extracting a set of samples from the wrap surface and projecting them onto the original surface. These projected samples are optimized by minimizing the quadratic error relative to the tangent planes of neighboring points on the original surface. Notably, samples far from feature lines remain unchanged, while samples near feature lines converge to those lines even when the input surface lacks correct mesh topology. We then assign an adaptive weight to each sample based on the squared moving distance. By introducing this weight setting, we observe that the restricted power diagram prioritizes connectivity along feature lines, thereby effectively preserving sharp features. Through extensive experiments, we demonstrate the superiority of our proposed algorithm over existing methodologies in terms of manifoldness, watertightness, topological correctness, triangle quality, and feature preservation.