Adaptive gap closing for complex triangular mesh repair using geometric and topological characteristics

Abstract

Gaps are prevalent defects in triangular meshes, often arising from various sources such as surface scanning and CAD model generation. Despite their significance, the automatic repair of complex gaps has received limited attention compared to other mesh imperfections. This study presents a novel surface-based gap-closing method for triangular mesh repair, leveraging both local geometric and topological characteristics to robustly match and merge gap boundaries. The proposed approach first employs a global–local vertex merging procedure with adaptive tolerances to eliminate duplicate vertices and simplify complex gaps. Subsequently, gaps are identified and classified into connected and disconnected types based on their topological and geometric features. For each detected gap, a non-iterative closing procedure is applied, simultaneously matching and merging all boundary vertices. An adaptive scheme is introduced to determine the geometric tolerance for vertex matching, ensuring the effective preservation of the original geometric shape. Extensive numerical experiments on a large dataset of discrete models demonstrate the effectiveness and robustness of the proposed method in closing both connected and disconnected gaps.