3D Tooth Semi-Closed Hole-Filling Algorithm Based on the Moving Least-Squares Method

Large-area semi-closed holes on the lateral surfaces of tooth models can cause difficulties in subsequent orthodontic tasks, such as collision detection and finite element analysis, and may affect the accuracy and stability of further processing. To address this issue, this paper proposes a three-dimensional tooth semi-closed hole repair method based on the moving least squares technique. First, key points were manually selected to transform semi-closed holes into closed ones, and new vertices were uniformly distributed within the hole region to construct an initial triangular mesh. Subsequently, a mesh homogenization algorithm was applied to improve the quality of the generated triangular patches. Then, a moving least-squares surface-fitting approach was employed. By incorporating the point cloud density and Gaussian curvature, an adaptive vertex influence region was designed to iteratively adjust the vertex positions and better fit the target surface. Finally, the generated mesh was smoothed using the Laplacian-Beltrami operator to obtain a repaired surface consistent with the original geometry. The experimental results demonstrate that the proposed method achieves superior efficiency and repair quality compared to existing approaches.