Adaptive triangular element generation and optimization-based smoothing: Part 2. On the surface

A general and systematic approach to adaptive triangular element generation and optimization-based smoothing on the surface is presented in this paper. The approach starts from a rough triangular mesh that needs to be remeshed in order to meet the desired mesh density. Various local transformation processes including edge and face splitting, edge collapsing and edge swapping are employed for enhancement of mesh quality as well as for generation of new triangular elements from the rough triangular elements. An edge swapping scheme is proposed, which satisfy both of the Delaunay criterion and topological consistency. To reduce the geometrical error that is inevitable in remeshing, curvature of the surface is not only considered in determining the mesh density distribution but the characteristic edges and the triangular elements are also interpolated by the third-order chord-length spline curves and the bi-cubic Bezier patches, respectively. The nodal points of the generated mesh are smoothed by the physically-based smoothing scheme and then optimally placed by the optimization-based smoothing scheme. Through various application examples, the characteristics and effects of the presented approaches are quantitatively investigated.