Finite element mesh generation has numerous applications such as modelling, animation, simulation and many other computer graphics applications. Unfortunately these meshes are usually generated in a raw form containing low-quality elements - especially when the mesh generation process is error-prone such as automated mesh generation. It is difficult to use such raw meshes in downstream applications directly. Therefore a remeshing process is demanded at this stage to improve the mesh quality. Existing methods often fail to efficiently remove low-quality  elements especially in regions with sharp features or application with  special quality requirements. 

 

In this thesis, we first present a novel method for elimination of obtuse triangles and small angle triangles from a 2D mesh. A pre-processing of Centroidal Voronoi Tessellation (CVT) is applied first. Consecutively the process of point’s insertions, point’s removal and mesh smoothing and optimization are applied in a loop till the generation of a high quality 2D mesh with elimination of all obtuse angles.  In experimental study, a complete comparison with the state-of-the-art methods is carried out for the analysis of the results.  The results show that our method performs well over the state-of-the-art methods in terms of maximal and minimal angle improvement and other mesh quality refinements. Our method removes all obtuse angles and generates a well-shaped mesh. 

 

We also present a user-guided surface remeshing method which is based on a prior robust mesh segmentation.  Mesh segmentation is initiated with an existing tool called live-wire which allows real-time user interaction. The mesh is further refined with local mesh operations.  Unlike live-wire, our method segments the input mesh with a minor (negligible) change in the input mesh. After segmentation, a segment wise surface remeshing is applied. We proposed a segment-based surface remeshing approach which uses local region operators to generate a considerably high-quality mesh with sharp feature preservation.   Experimental results reveal that our methods for mesh segmentation as well as surface remeshing perform well that that of the previous methods.     

Finally, we proposed a mesh refinement method for molecular surface meshes. The molecular sruface remeshing has additional challenges such as complex mesh and very tiny or zero degree angles. The proposed method uses local operators for the refinement of molecular surface meshes. A cut and fill strategy is used to remove small angle triangles with their local neighbourhoods; creating holes in the input mesh. The holes are carefully filled again and the newly filled regions are smoothed  locally for minimal angle improvement and other quality refinement. In experimental study, we compared our method with four different state-of-the-art methods and found that our method showed a significant improvement over  state-of-the-art methods in minimal angle, aspect ratio, and other meshing quality measurements. In addition, our method for molecular surface remeshing showed satisfactory results in terms of the ratio of regular vertices and  the preservation of area and volume