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

Revista internacional de métodos numéricos para cálculo y diseño en ingeniería; Vol.: 19 Núm.: 1
Source: OAI

ABSTRACT En este artículo se presenta y discute una clase de algoritmos de refinamiento adaptativo para generar mallas de triángulos 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 versión 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 triangulación se reformulan estos algoritmos y adquieren una descripción más 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.


Available from: Angel Plaza, May 28, 2015
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    ABSTRACT: A mesh is a discretization of a certain geometry of varying dimensions. Meshes may be composed of different elements, e.g., triangles, quadrilaterals, tetrahedra, etc. A meshing tool is a software application that allows creating, refining, derefining, improving, smoothing, visualizing and postprocessing meshes and/or particular mesh regions, and also assigning physical values to mesh elements (temperature, concentration, etc.) depending on their intended use. Meshing tools are complex and sophisticated software, and building a new tool from scratch as well as evolving an existing tool demands an enormous effort. There is a need and an opportunity for new approaches in meshing tool software development in order to reduce development time and costs without compromising quality. Experience developing meshing tools has provided the motivation for building new ones by reusing a large amount of the work done during those developments. Meshing tools share several characteristics and their variations can be managed in a systematic way. This makes meshing tool development an appropriate opportunity for applying Software Product Lines (SPL). Existing processes for engineering SPL are needlessly general and usually require a series of steps and documentation not necessary in the meshing tool domain. Therefore, this thesis proposes a SPL process model specifically for the meshing tool domain. A SPL development process is centered in software reuse, and mainly involves two phases: domain engineering (DE) and application engineering (AE). The process presented in this work is centered in two stages of the DE phase: the domain analysis (DA) and the domain design (DD) stages. In the DA stage, the domain model and the scope of the SPL are defined. In the DD stage, the product line architecture (PLA) is produced; this architecture is valid and shared for all particular products in the SPL. A feature model is commonly used to model the domain. In this work, the DA stage also uses a lexicon, scenarios, actions and goals that provide the rationale for building the feature model. This thesis presents a rigorous process for collecting SPL features, through the identification of the aforementioned artifacts. Furthermore, the domain model is formalized by providing consistency and completeness conditions. The scope definition process is presented through an activity diagram. Furthermore, the approach presented in this thesis explicitly presents the different products of the SPL, establishing relationships between products and the SPL features, which permits managing the product development. The proposed DD stage focuses on the creation of the PLA, an essential artifact for building specific SPL products. To this purpose, this work provides a deductive process and a transformational one. In the deductive process, an explicit PLA is developed using the artifacts produced in the DA stage. Furthermore, both architectural structural and architectural behavioral views are established for meshing tool SPL. Both views are general and allow representing any product in the SPL scope. In the transformational process, an implicit PLA is developed using transformation rules, which have been created using the artifacts produced in the DA stage. In this process, only single product architectures are produced, and the PLA is defined as the sum of all single architectures. Both DA and DD stages are described in detail, and the SPL model application is illustrated through a suitably documented example with a relatively high degree of complexity in the meshing tool domain. In this example, a formalized domain model is introduced, and architectures are defined using both the deductive and transformational processes.
    03/2013, Degree: PhD, Supervisor: María Cecilia Bastarrica, Nancy Hitschfeld-Kahler
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    ABSTRACT: Summary In this work we introduce a geometrical diagram to study the geometric quality of triangles generated by iterative application of the four Triangles Longest Edge (4TLE) partition. The diagram provides a convenient graphic tool to visualize the evolution and migration of element shapes leading to a better understanding of the improvement process and the efiect of recursive subdivision schemes. A complex variable mapping analysis supports the diagram and similarity class speciflcations. In addition, it is introduced a mesh subdivision method (hybrid 4TLE-SS) that combines the four Triangles Longest Edge (4TLE) subdivision pattern and the self-similar 4TSS. It is showed that the number of triangles of superior quality is greater than in the 4TLE method. The presented work is of interest in mesh generation and reflnement for triangle meshes.