A reconstrução de superfícies a partir de nuvens de pontos faz parte de um novo paradigma de modelagem em que modelos computacionais para objetos reais são reconstruídos a partir de dados amostrados sobre a superfície dos mesmos. O principal problema que surge nesse contexto é o fato de que não são conhecidas relações de conectividade entre os pontos que compõe a amostra. Os objetivos do presente trabalho são estudar métodos implícitos para a reconstrução de superfícies e propor algumas melhorias pouco exploradas por métodos já existentes. O uso de funções implícitas no contexto da reconstrução conduz a métodos mais robustos em relação a ruídos, no entanto, uma das principais desvantagens de tais métodos está na dificuldade de capturar detalhes finos e sharp features. Nesse sentido, o presente trabalho propõe o uso de abordagens adaptativas, tanto na poligonalização de superfícies quanto na aproximação de superfícies. Além disso, questões relativas à robustez das soluções locais e à qualidade da malha também são abordadas. Por fim, o método desenvolvido é acoplado aumsoftware traçador de raios afimde se obterumamaneira de modelar cenas tridimensionais utilizando nuvens de pontos, além dos objetos gráficos tradicionais. Os resultados apresentados mostram que muitas das soluções propostas oferecem um incremento à qualidade dos métodos de reconstrução anteriormente propostos / Surface reconstruction from point clouds is part of a new modeling paradigm in which computational models for real objects are reconstructed from data sampled from their surface. The main problem that arises in this context is the fact that there are no known connectivity relationships amongst the points that compose the sample. The objectives of the present work are to study implicit methods for surface reconstruction and to propose some improvements scarcely explored by previous work. The use of implicit functions in the context of surface reconstruction leads to less noise sensitive methods; however, one major drawback of such methods is the difficulty in capturing fine details and sharp features. Towards this, the present work proposes the use of adaptive approaches, not only in the polygonization but also in the surface approximation. Besides, robustness issues in local solutions and mesh quality are also tackled. Finally, the developed method is embedded in a ray tracer software in order to set a basis for modeling tridimensional scenes using point sets, in addition to traditional graphic objects. The presented results show that a great deal of the proposed solutions offer a quality increase to the reconstruction method previously proposed

This thesis focuses on the analysis of the latest techniques for surface and solid binary voxelization of 3D models. It briefly describes current trends in this problematics and identifies a suitable method with an aim to parallelize the given solution on GPUs. It concretely explains the implementation process of the selected algorithm described in the paper Fast Parallel Surface and Solid Voxelization on GPUs , which produces a sparse voxel octree. The results are very close to those of the original authors. A new solution for extracting a smooth isosurface from this structure based on Marching Cubes is presented as well, providing up to 98 % reduction of the traversed cubes in higher resolutions. The resulting implementation is a framework usable for further voxel scene processing.

Level-set methods have become a valuable and well-established field of visualization over the last decades. Different implementations addressing different design goals and different data types exist. In particular, level sets can be used to extract isosurfaces from scalar volume data that fulfill certain smoothness criteria. Recently, such an approach has been generalized to operate on unstructured point-based volume data, where data points are not arranged on a regular grid nor are they connected in form of a mesh. Utilizing this new development, one can avoid an interpolation to a regular grid which inevitably introduces interpolation errors. However, the global processing of the level-set function can be slow when dealing with unstructured point-based volume data sets containing several million data points. We propose an improved level-set approach that performs the process of the level-set function locally. As for isosurface extraction we are only interested in the zero level set, values are only updated in regions close to the zero level set. In each iteration of the level-set process, the zero level set is extracted using direct isosurface extraction from unstructured point-based volume data and a narrow band around the zero level set is constructed. The band consists of two parts: an inner and an outer band. The inner band contains all data points within a small area around the zero level set. These points are updated when executing the level set step. The outer band encloses the inner band providing all those neighbors of the points of the inner band that are necessary to approximate gradients and mean curvature. Neighborhood information is obtained using an efficient kd-tree scheme, gradients and mean curvature are estimated using a four-dimensional least-squares fitting approach. Comparing ourselves to the global approach, we demonstrate that this local level-set approach for unstructured point-based volume data achieves a significant speed-up of one order of magnitude for data sets in the range of several million data points with equivalent quality and robustness.

[pt] Ao extrair isosuperfícies de dados volumétricos massivos, em geral a superfície de saída é densa, podendo demandar muita memória para seu processamento. Além disso, dependendo do método de extração utilizado, podese também obter um resultado contendo diversos problemas geométricos e topológicos. Neste estudo, experimentamos combinações de diferentes métodos de extração de isosuperfícies juntamente com estratégias out-of-core que permitem uso inteligente do recurso computacional para sintetizar aproximações poligonais dessas superfícies, preservando a topologia original segmentada. O método implementado foi testado em um volume sísmico real para extração da superfície de domo de sal. / [en] When extracting isosurfaces from massive volumetric datasets, in general, the output surface is dense, and may require a lot of memory for processing. In addition to this, depending on the extraction method used, the result can also include several geometric and topological problems. In this study, we experimented combinations of different isosurface extraction methods along out-of-core strategies to generate polygonal approximations to these surfaces, preserving the original topology segmented in the volumetric dataset. The implemented method was tested in a real seismic volume dataset for the salt dome extraction.