Curvature Based Mesh Improvement (original) (raw)

It is very important to improve the quality of surface meshes for numerical simulations, solid mesh generation, and computer graphics applications. Optimizing the form of the mesh elements it is necessary to preserve new nodes of the mesh as close as possible to a surface approximated by the initial mesh. This paper proposes a novel technique in which both of the requirements to mesh improvement are implemented. In the method presented here the new location of each node is found using values of principal curvatures in this node. Such procedure allows preserving new mesh very close to the initial surface while improving element quality. The method has been successfully tested on triangular meshes both for analytical surfaces (sphere, ellipsoid, paraboloid) and for arbitrary surfaces with great number of points. Comparison of the deviation of the mesh optimized by our method and by Laplacian smoothing from the original analytical surfaces shows advantage of the proposed method.