A Hierarchical Adaptive Mesh Generation Strategy for Parametric Surfaces Based on Tree Structures

This work presents a hierarchical adaptive mesh generation strategy for parametric surfaces based on tree structures. The error measured between the analytical and discrete curvatures guides the adaptive process. While the analytical curvature is an mathematical representation that models the domain, the discrete curvature is an approximation of that curvature and depends directly on the used mesh configuration. The presented strategy possess the following properties: it is able to refine and coarsen regions of the mesh; it ensures compatibility between neighbouring regions; it considers the contribution of the local error measures to ensure good global mesh quality and it works with any type of parametric surface geometry, since the process is performed in the parametric space.