To handle broken 3D models can be a very time consuming problem. Several methods aiming for automatic mesh repair have been presented in the recent years. This thesis gives an extensive evaluation of automatic mesh repair algorithms, presents a mesh repair pipeline and describes an implemented automatic mesh repair algorithm. The presented pipeline for automatic mesh repair includes three main steps: octree generation, surface reconstruction and ray casting. Ray casting is for removal of hidden objects. The pipeline also includes a pre processing step for removal of intersecting triangles and a post processing step for error detection. The implemented algorithm presented in this thesis is a volumetric method for mesh repair. It generates an octree in which data from the input model is saved. Before creation of the output, the octree data will be patched to remove inconsistencies. The surface reconstruction is done with a method called Manifold Dual Contouring. First new vertices are created from the information saved in the octree. Then there is a possibility to cluster vertices together for decimation of the output. Thanks to a special Manifold criterion, the output is guaranteedto be manifold. Furthermore the output will have sharp and clear edges and corners thanks to the use of Singular Value Decomposition during determination of the positions of the new vertices.

Aus besonders großen Volumendaten extrahierte Isoflächen besitzen eine kaum beherrschbare Anzahl an Polygonen, weshalb die Extraktion von adaptiven, also bezüglich einer geometrischen Fehlermetrik reduzierten, Isoflächen wünschenswert ist. Ein häufiges Problem gängiger adaptiver Verfahren ist, dass sie Datenstrukturen verwenden, die gerade für große Daten besonders viel Hauptspeicher benötigen und daher nicht direkt anwendbar sind. Nachdem auf die Grundlagen zur Isoflächenextration eingegangen wurde, wird im Rahmen dieser Diplomarbeit ein auf Dual Contouring basierendes Verfahren entworfen, das die adaptive Isoflächenextraktion aus sehr großen Volumendaten auch bei begrenztem Hauptspeicher mit einem zeitlich vertretbaren Aufwand erlaubt. Der verwendete Octree wird dazu nur implizit aufgebaut und temporär nicht benötigte Daten werden unter Nutzung von Out-of-core-Techniken in den Sekundärspeicher ausgelagert. Die verschiedenen Implementierungsansätze werden unter Berücksichtigung maximaler Effizienz verglichen. Die Tauglichkeit des Verfahrens wird an verschiedenen sehr großen Testdatensätzen nachgewiesen. / Isosurfaces that are extracted from massive volume data sets consist of a hardly processable amount of polygons. Hence adaptive isosurfaces should be extracted with respect to a geometric error metric. Popular adaptive methods frequently require an amount of memory that turns them unfeasible for large data sets. After dwelling on the fundamentals of isosurfaces, a dual contouring based method will be developed that allows for the extraction of adaptive isosurfaces from massive volume data sets. The required octree is built implicitly, and temporarily unneeded data is swapped out on a secondary storage using out of core techniques. Various implementation approaches will be discussed and compared concerning maximum efficiency. The suitability of the method will be demonstrated with various massive volume data sets.

[pt] A extração e visualização de isosuperfícies de campos escalares são importantes para inspeções e análises de modelos em diversas áreas. Uma isosuperfície é representada por uma malha de triângulos que aproxima um conjunto de nível do volume de dados. O foco deste trabalho é a extração e visualização de isosuperfícies de modelos de reservatório de petróleo, representados por malhas de hexaedros levemente côncavos. Para uma melhor representação das isosuperfícies, optou-se pela substituição de triângulos planares por superfícies curvas. Para assegurar a extração de superfícies contínuas e suaves, este trabalho propõe o uso de envelopes para determinação das normais. A técnica proposta é implementada em GPU com uso de subdivisão adaptativa das superfícies. / [en] The extraction and visualization of isosurfaces of scalar fields are important for inspections and analysis of models in several areas. An isosurface is represented by a mesh of triangles that approximates a level set of a data volume. The main focus of this work is the extraction and visualization of isosurfaces of black oil reservoir models, represented by hexahedral meshes with slightly concave cells. For a better representation of the isosurfaces, we have opted to replace planar triangles for curved patches. To ensure the extraction of continuous and smooth surfaces, this work proposes the use of envelopes to determine normals. The proposed technique is implemented in GPU with the usage of adaptive subdivision of patches.

Aus besonders großen Volumendaten extrahierte Isoflächen besitzen eine kaum beherrschbare Anzahl an Polygonen, weshalb die Extraktion von adaptiven, also bezüglich einer geometrischen Fehlermetrik reduzierten, Isoflächen wünschenswert ist. Ein häufiges Problem gängiger adaptiver Verfahren ist, dass sie Datenstrukturen verwenden, die gerade für große Daten besonders viel Hauptspeicher benötigen und daher nicht direkt anwendbar sind. Nachdem auf die Grundlagen zur Isoflächenextration eingegangen wurde, wird im Rahmen dieser Diplomarbeit ein auf Dual Contouring basierendes Verfahren entworfen, das die adaptive Isoflächenextraktion aus sehr großen Volumendaten auch bei begrenztem Hauptspeicher mit einem zeitlich vertretbaren Aufwand erlaubt. Der verwendete Octree wird dazu nur implizit aufgebaut und temporär nicht benötigte Daten werden unter Nutzung von Out-of-core-Techniken in den Sekundärspeicher ausgelagert. Die verschiedenen Implementierungsansätze werden unter Berücksichtigung maximaler Effizienz verglichen. Die Tauglichkeit des Verfahrens wird an verschiedenen sehr großen Testdatensätzen nachgewiesen. / Isosurfaces that are extracted from massive volume data sets consist of a hardly processable amount of polygons. Hence adaptive isosurfaces should be extracted with respect to a geometric error metric. Popular adaptive methods frequently require an amount of memory that turns them unfeasible for large data sets. After dwelling on the fundamentals of isosurfaces, a dual contouring based method will be developed that allows for the extraction of adaptive isosurfaces from massive volume data sets. The required octree is built implicitly, and temporarily unneeded data is swapped out on a secondary storage using out of core techniques. Various implementation approaches will be discussed and compared concerning maximum efficiency. The suitability of the method will be demonstrated with various massive volume data sets.

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We present an implicit approach for constructing smooth isolated or interconnected 3-D inscribed volumes which can be employed for volumetric modeling of various kinds of spongy or porous structures, such as volcanic rocks, pumice stones, Cancellus bones *, liquid or dry foam, radiolarians, cheese, and other similar materials. The inscribed volumes can be represented in their normal or positive forms to model natural pebbles or pearls, or in their inverted or negative forms to be used in porous structures, but regardless of their types, their smoothness and sizes are controlled by the user without losing the consistency of the shapes. We introduce two techniques for blending and creating interconnections between these inscribed volumes to achieve a great flexibility to adapt our approach to different types of porous structures, whether they are regular or irregular. We begin with a set of convex polytopes such as 3-D Voronoi diagram cells and compute inscribed volumes bounded by the cells. The cells can be irregular in shape, scale, and topology, and this irregularity transfers to the inscribed volumes, producing natural-looking spongy structures. Describing the inscribed volumes with implicit functions gives us a freedom to exploit volumetric surface combinations and deformations operations effortlessly / Graduate