Showing papers by "Ángel Plaza published in 2003"

Mesh Refinement Based on the 8-Tetrahedra Longest- Edge Partition.

Abstract: The 8-tetrahedra longest-edge (8T-LE) partition of any tetrahedron is defined in terms of three consecutive edge bisections, the first one performed by the longest-edge. The associated local refinement algorithm can be described in terms of the polyhedron skeleton concept using either a set of precomputed partition patterns or by a simple edgemidpoint tetrahedron bisection procedure. An effective 3D derefinement algorithm can be also simply stated. In this paper we discuss the 8-tetrahedra partition, the refinement algorithm and its properties, including a non-degeneracy fractal property. Empirical experiments show that the 3D partition has analogous behavior to the 2D case in the sense that after the first refinement level, a clear monotonic improvement behavior holds. For some tetrahedra a limited decreasing of the tetrahedron quality can be observed in the first partition due to the introduction of a new face which reflects a local feature size related with the tetrahedron thickness.

Propagation Path Properties in Iterative Longest-Edge Refinement.

Abstract: In this work we investigate the refinement propagation process in longest-edge based local refinement algorithms for unstructured meshes of triangles. The conformity neighborhood of a triangle, the set of additional triangles that is needed to be refined to ensure mesh conformity is introduced to define the propagation path. We prove that asymptotically the propagation path extends on average to a few neighbor adjacent triangles. We also include numerical evidence which is in complete agreement with the theoretical study reported.

Refinement and Hierarchical Coarsening Schemes for Triangulated Surfaces.

Abstract: We present a refinement and a coarsening (also simplification or decimation) algorithm for the adaptive representation of bivariate functions. The algorithms have proved to be efficient tools in numerical methods such as finite element method or image processing, [Pla00, Sua01b]. In this paper we particularize the algorithms and apply to the generation of levels of detail of terrain models. The refinement algorithm is very simple and of linear complexity in the number of vertices, and proceeds uniformly or locally in triangular meshes. The coarsening algorithm shows a complexity of O(logn) and obtains an adaptive hierarchical representation of the input terrain. We provide the most important features of the algorithms as well as the application to generate levels of detail of regions in the Gran Canaria island, an island where the topography is of great irregularity. Several experimental data are presented, including times of the meshes generated, rendering times, error evolution, suitability of the meshes and size of the generated meshes. The algorithms have been tested for VRML visualization showing a real time generation of levels of detail, and this fact is showed in the numerical experiments.

Computational aspects of the refinement of 3D complex meshes

Abstract: The refinement of tetrahedral meshes is a significant task in many numerical and discretizations methods. The computational aspects for implementing refinement of meshes with complex geometry need to be carefully considered in order to have real-time and optimal results. In this paper we enumerate the relevant computational aspects of tetrahedral refinement algorithms. For local and adaptive refinement we give numerical results of the computational propagation cost of a general class of longest edge based refinement and show the implications of the complex geometry in the global process.

Estructuras de datos geométricas para algoritmos de refinamiento basados en el esqueleto

Abstract: En este articulo se presenta y discute una clase de algoritmos de refinamiento adaptativo para generar mallas de triangulos y tetraedros no estructuradas en dos y tres dimensiones. Concretamente, se estudian los algoritmos de refinamiento basados en el esqueleto (Skeleton Based Refinement (SBR) algorithms) propuestos por Plaza y Carey (23) y se presenta una version que hace uso del grafo del esqueleto de las mallas triangulares. Mediante el uso de estas estructuras de datos derivadas del concepto de esqueleto de la triangulacion se reformulan estos algoritmos y adquieren una descripcion mas natural y consistente. El caso bidimensional es discutido con detalle y para el caso 3D se propone una nueva estructura de datos tipo grafo basada en las caras triangulares de los tetraedros. Se muestran experimentos en 2D y se exploran algunas propiedades asociadas al grafo.