[pt] Subdivisão de superfícies triangulares é um problema importante nas atividades de modelagem e animação. Ao deformar uma superfície a qualidade da triangulação pode ser bastante prejudicada na medida em que triângulos, antes equiláteros, se tornam alongados. Uma solução para este problema consiste em refinar a região deformada. As técnicas de refinamento requerem uma estrutura de dados topológica que seja eficiente em termos de memória e tempo de consulta, além de serem facilmente armazenadas em memória secundária. Esta dissertação propõe um framework baseado na estrutura Corner Table com suporte para subdivisão de malhas triangulares. O framework proposto foi implementado numa biblioteca C mais mais de forma a dar suporte a um conjunto de testes que comprovam a eficiência pretendida. / [en] Subdivision of triangular surfaces is an important problem in modeling and animation activities. Deforming a surface can be greatly affected the quality of the triangulation when as equilateral triangles become elongated. One solution to this problem is to refine the deformed region. Refinement techniques require the support of topological data structure. These structures must be efficient in terms of memory and time. An additional requirement is that these structures must also be easily stored in secondary memory. This dissertation proposes a framework based on the Corner Table data structure with support for subdivision of triangular meshes. The proposed framework was implemented in a C plus plus library. With this library this work presents a set of test results that demonstrate the desired efficiency.

In recent decades, scientific data has become available in increasing sizes and precision. Therefore techniques to analyze and summarize the ever increasing datasets are of vital importance. A common form of scientific data, resulting from simulations as well as observational sciences, is in the form of scalar-valued function on domains of interest. The Morse-Smale complex is a topological data-structure used to analyze and summarize the gradient behavior of such scalar functions. This thesis deals with efficient parallel algorithms to compute the Morse-Smale complex as well as its application to datasets arising from cosmological sciences as well as structural biology. The first part of the thesis discusses the contributions towards efficient computation of the Morse-Smale complex of scalar functions de ned on two and three dimensional datasets. In two dimensions, parallel computation is made possible via a paralleizable discrete gradient computation algorithm. This algorithm is extended to work e ciently in three dimensions also. We also describe e cient algorithms that synergistically leverage modern GPUs and multi-core CPUs to traverse the gradient field needed for determining the structure and geometry of the Morse-Smale complex. We conclude this part with theoretical contributions pertaining to Morse-Smale complex simplification. The second part of the thesis explores two applications of the Morse-Smale complex. The first is an application of the 3-dimensional hierarchical Morse-Smale complex to interactively explore the filamentary structure of the cosmic web. The second is an application of the Morse-Smale complex for analysis of shapes of molecular surfaces. Here, we employ the Morse-Smale complex to determine alignments between the surfaces of molecules having similar surface architecture.