Geometry-based Adaptive Mesh Generation for Continuous and Discrete Parametric Surfaces

摘要

Proximity features between parametric surface boundaries are captured based on the Constrained Delaunay Triangulation (CDT) of sampled surface boundaries. Coupled with curvature computation, a geometry-based mesh size field is automatically constructed along surface boundaries, serving the meshing procedure of boundary curves. Reusing the CDT as a background mesh, the size field along boundaries is extended to specify the mesh sizes in surface interiors, serving an advancing front meshing procedure employed in its parametric space. Furthermore, the proposed approach is applied for both composite continuous surfaces and Stereolithography (STL) surfaces. In the latter application, a sequence of procedures is suggested to aid in parameterizing the STL surface, i.e., feature identification, sub-domain formation and parameterization, and estimations of a surface intrinsic Riemannian metric and surface curvature. Finally, well graded and shaped mesh examples for both types of surface models are presented, which demonstrate that the approach satisfies the requirements of finite element analysis.