# A Fast Hole-Filling Method for Triangular Mesh in Additive Repair
###### Abstract  
In the triangular meshes obtained in additive repair, it is a challenge to find one single hole-filling method to close all holes and make the filling patches assort with surrounding meshes well with low time complexity, which is mainly caused by the shape complexity and size difference of the various holes, especially in the fields of intelligent manufacturing, 3D measurement, and reverse engineering. Therefore, it is reasonable to adopt different algorithms to fill different types of holes. In this research, a fast hole-filling method for triangular mesh is proposed based on the hole size. First, a group of basic concepts is defined to make them uniform throughout the whole text, followed by the descriptions of hole detection and boundary cleaning. Second, three different algorithms are developed to fill the small-sized, middle-sized, and large-sized holes classified by hole size respectively, which can fill all the detected holes in a fast and proper manner. Finally, two experiments are carried out to verify the efficiency, robustness, and ability to recover the shape of our method. Compared to two state-of-the-art hole-filling methods in the first experiment, the quantitative evaluation results demonstrate that our proposed method is much faster than them with the ability to guarantee the regularity of most filling triangles. The second experiment proves that our method can produce satisfactory filling results by making the filling patches be compatible with surrounding meshes well. hole filling; additive manufacturing; repair; minimum area triangulation; advancing front Article  
A Fast Hole-Filling Method for Triangular Mesh in Additive Repair  
12202  
which may result in several holes after the point cloud triangulation. Besides, some triangular mesh processing algorithms may also cause a small number of holes in their outputs, such as defect repair. The existence of holes in mesh decreases the performance of the downstream mesh processing algorithms, e.g., mesh alignment, Boolean operation, which may introduce some illness problems or result in processing failure. On the other hand, incomplete triangular meshes may lead to poor visualization effects. Although many hole-filling techniques have been proposed in the last two decades [3; 4], most of them are originally designed to handle one or fewer types of holes. For example, to repair the mesh holes generated by the Poisson surface reconstruction algorithm towards 3D printing, [PERSON] et al. proposed an iterative postprocessing algorithm for partial differential equation (PDE) patch generation based on biharmonic-like four-order PDEs [5]. However, this method seems to be complicated and time-consuming. Due to the variety of hole size, it is still a challenge to adopt one single algorithm to fill all holes quickly while ensuring the filling patches to assort with the surrounding meshes well, especially in additive manufacturing repair. In the case of small-sized holes, the missing shapes are usually small and will not affect the completeness of the whole mesh. Instead of using one complex algorithm to close the small-sized holes, a fast and simple hole-filling method is desirable. As for middle-sized holes, they usually account for a large proportion of the total number of holes occurring in one mesh. To make the resulting mesh as close to the original mesh as possible, the missing regions must not only be filled but also ensure the shapes of the filling patches are compatible with surrounding meshes well. Hence, efficiency and the ability to shape recovery for the missing regions are two important factors that need to be considered. Regarding large-sized holes, the size of the hole boundary vertices is greater than that of middle-sized holes. The hole-filling processing may be heavily time-consuming if a traditional technique is applied, such as the minimum area triangulation [6], so how to close large-sized holes fastly has become a hot research topic in additive repair.