Universiẗat, Diss., 2002--Stuttgart.

Universiẗat, Diss., 2005--Tübingen.

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.

Universiẗat, Diss., 2004--Mannheim.

Force fields of 3d objects are used for different purposes in computer graphics as skeletonization and collision detection. In this paper we present a novel method to approximate the force field of a discrete 3d object in linear time. Similar to the distance transformation we define a rule that describe how the forces associated with boundary points are propagated into the interior of the object. The result of this propagation depends on the order in which the points of the object are processed. Therefore we analyze how to obtain an order-invariant approximation formula. For a chosen iteration order (i, j, k) the set of boundary points that influence the force of a particular point p of the object can be described by a spatial region Rijk. The geometries of these regions are characterized both for the Cartesian and the body-centered cubic grid (bcc grid). We show that in the case of the bcc grid these regions can be combined in such a way that E3 is uniformly covered which basically means that each boundary point is contained in the same number of regions. Based on the covering an approximation formula for the force field is proposed that has linear complexity and gives good results for standard objects. We also show that such a uniform covering can not be built from the regions of influence of the Cartesian grid. With our method it becomes possible to use features of the force field for a fast and topology preserving skeletonization. We use a thinning strategy on the bcc grid to compute the skeleton and ensure that critical points of the force field are not removed. This leads to improved skeletons with respect to the properties of centeredness and rotational invariance.

Force fields of 3d objects are used for different purposes in computer graphics as skeletonization and collision detection. In this paper we present a novel method to approximate the force field of a discrete 3d object in linear time. Similar to the distance transformation we define a rule that describe how the forces associated with boundary points are propagated into the interior of the object. The result of this propagation depends on the order in which the points of the object are processed. Therefore we analyze how to obtain an order-invariant approximation formula. For a chosen iteration order (i, j, k) the set of boundary points that influence the force of a particular point p of the object can be described by a spatial region Rijk. The geometries of these regions are characterized both for the Cartesian and the body-centered cubic grid (bcc grid). We show that in the case of the bcc grid these regions can be combined in such a way that E3 is uniformly covered which basically means that each boundary point is contained in the same number of regions. Based on the covering an approximation formula for the force field is proposed that has linear complexity and gives good results for standard objects. We also show that such a uniform covering can not be built from the regions of influence of the Cartesian grid. With our method it becomes possible to use features of the force field for a fast and topology preserving skeletonization. We use a thinning strategy on the bcc grid to compute the skeleton and ensure that critical points of the force field are not removed. This leads to improved skeletons with respect to the properties of centeredness and rotational invariance.