Parametrization and smooth approximation of surface triangulations
Computer Aided Geometric Design
Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator
FCRC '96/WACG '96 Selected papers from the Workshop on Applied Computational Geormetry, Towards Geometric Engineering
Computer Aided Geometric Design
Simplification and Repair of Polygonal Models Using Volumetric Techniques
IEEE Transactions on Visualization and Computer Graphics
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
SMI '04 Proceedings of the Shape Modeling International 2004
An intuitive framework for real-time freeform modeling
ACM SIGGRAPH 2004 Papers
Robust repair of polygonal models
ACM SIGGRAPH 2004 Papers
A robust hole-filling algorithm for triangular mesh
The Visual Computer: International Journal of Computer Graphics
A lightweight approach to repairing digitized polygon meshes
The Visual Computer: International Journal of Computer Graphics
An Integrated Approach to Filling Holes in Meshes
AICI '10 Proceedings of the 2010 International Conference on Artificial Intelligence and Computational Intelligence - Volume 03
Single-tooth modeling for 3D dental model
Journal of Biomedical Imaging
Hole filling of triangular mesh segments using systematic grey prediction
Computer-Aided Design
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Hole filling of teeth and gums is an essential stage in orthodontics after segmentation. The patching mesh should keep the morphological features of generic teeth and gums while avoiding collision between two adjacent teeth. This paper presents an efficient hole-filling algorithm to reconstruct the missing part of teeth and gums. Our proposed method involves four necessary steps: boundary construction and projection, hole triangulation in 2D, back projection of vertices to 3D, and mesh fairing. By combining constrained Delaunay triangulation in 2D with back projection of vertices to 3D using mean value coordinates, we achieve high robustness of hole triangulation and a high-quality initial patching mesh. In addition, we propose an automatic method to control the deformation degree to avoid collision. Our experiments demonstrate that the proposed method can achieve satisfactory results, not only in morphology, but also in efficiency. The results are very similar to real teeth and gums and can meet the requirements of orthodontics in medicine.