Mathematical Modeling and Analysis
Mathematical Modeling and Analysis
Surface meshes play an important role in mesh generation and mesh based analysis applications. The success of mesh generation algorithms and the accuracy of numerical analyses often depend on the quality of the surface mesh. Therefore, optimization of surface mesh quality is a very important problem.
In this research, a novel procedure has been developed to optimize polygonal surface meshes by repositioning nodes in a series of local parametric spaces originating from a barycentric mapping of the triangular facets of the original mesh faces. The repositioning of nodes is directed by a two-stage numerical optimization procedure that is designed to improve the geometric shape of mesh faces while keeping the modified mesh as close as possible to the base mesh. Repositioning nodes in the parametric space of the surface guarantees that the nodes will remain on the surface when mapped back to real space.
The procedure has been tested using a number of surface meshes and has proved to be very effective in improving mesh quality while minimizing changes to the surface characteristics.
Figures below show the surface mesh of a pig before and after optimization using two different quality optimization procedures. The top center picture shows the initial mesh, the bottom left picture shows an optimized mesh where the quality of the mesh is improved while keeping the nodes close to their original positions and the bottom right picture shows an optimized mesh where the quality of the mesh is improved as much as possible.
