Resumen de Combining refinement and improvement techniques for the generation and modification of 2d/2. 5d triangular meshes
María Ethel Guerrieri Basualdo
A mesh is a discretization of a geometric domain into simple elements, Meshes find use in different fields like Finite Element Methods, Computer Graphics, or Geographical Information Systems. Although different applications have different requirements, it is commonly established that a good mesh needs quality (nice shaped) and small enough elements to provide accurate results. Often these applications require the incremental adaptation of a mesh to the interactively insertion/deletion of domain elements.
Achieving a quality mesh requires choosing a quality measure for its elements and a refinement process guided by it which inserts additional vertices into the mesh. Many quality measures have been studied. The minimum angle and the maximum angle are the most developed. Among the existing refinement algorithms, those based on Delaunay triangulation have received a lot of attention in recent years. Moreover, an improvement process can be applied to the obtained refined mesh in order to optimize the position of its additional vertices.
In this thesis we propose methods that combine Delaunay refinement and improvement techniques to achieve a quality mesh on planar domains and terrains. This combination represents the main difference with existing refinement methods which apply improvement processes as a second step after the refinement process. Our methods insert and move points into/to an optimal position and delete vertices when it is possible. In two dimensions, we generate and modify meshes with good quality considering minimum angle and aspect-ratio criteria, and area based constraints. In terrains, we study the problem of approximating a terrain from a set of grid data points so that the elements of the mesh have good quality where possible. Moreover, we have developed an object-oriented framework for implementing mesh generation and mesh refinement processes based on the Unified Modelling Language (UML) and Design Patterns. The framework, exploiting the benefits of reuse, provides an environment which enables new components to be deployed and assembled easily.
