Robust Hole-Detection in Triangular Meshes Irrespective of the Presence of Singular Vertices

TL;DR

This paper introduces a robust, automated method for detecting holes in edge-manifold triangular meshes that works even with singular vertices, aiding CAD and robotic applications by accurately identifying boundary gaps.

Contribution

The proposed approach uniquely detects mesh boundaries and holes regardless of singular vertices, improving robustness over existing methods that require mesh modification or assume their absence.

Findings

Effective on synthetic and real-world data including sonar meshes.

Works in underwater robotic surface reconstruction scenarios.

Provides guaranteed boundary existence and uniqueness for each half-edge.

Abstract

In this work, we present a boundary and hole detection approach that traverses all the boundaries of an edge-manifold triangular mesh, irrespectively of the presence of singular vertices, and subsequently determines and labels all holes of the mesh. The proposed automated hole-detection method is valuable to the computer-aided design (CAD) community as all half-edges within the mesh are utilized and for each half-edge the algorithm guarantees both the existence and the uniqueness of the boundary associated to it. As existing hole-detection approaches assume that singular vertices are absent or may require mesh modification, these methods are ill-equipped to detect boundaries/holes in real-world meshes that contain singular vertices. We demonstrate the method in an underwater autonomous robotic application, exploiting surface reconstruction methods based on point cloud data. In such a scenario the determined holes can be interpreted as information gaps, enabling timely corrective action during the data acquisition. However, the scope of our method is not confined to these two sectors alone; it is versatile enough to be applied on any edge-manifold triangle mesh. An evaluation of the method is performed on both synthetic and real-world data (including a triangle mesh from a point cloud obtained by a multibeam sonar). The source code of our reference implementation is available: https://github.com/Mauhing/hole-detection-on-triangle-mesh.