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Item QEM-Filtering: A New Technique for Feature-Sensitive Terrain Mesh Simplification(The Eurographics Association, 2010) Löffler, Falko; Schumann, Heidrun; Reinhard Koch and Andreas Kolb and Christof Rezk-SalamaTerrain simplification generates multi-resolution models, from which - traditionally - irregular or semi-regular triangulations are extracted to render a terrain at a suitable level of detail. Recent terrain simplification techniques, in contrast, rely on GPU-friendly regular grids and generate multiple resolutions by applying the filtering and sub-sampling paradigm. However, due to the smoothing and uniform sampling, these techniques sparsely approximate the terrain surface. Consequently, in order to guarantee a certain error threshold, considerably more triangles need to be rendered. In this paper, we present a novel feature-sensitive simplification technique. Our approach follows the aforementioned paradigm. The key idea is to maintain the regularity while recomputing the vertex positions by taking a specific error metric into account, namely the quadric error metric (QEM). Compared to previous approaches, we apply the paradigm to the grid of vertex-associated quadrics. From these we extract vertices of the new resolution by relying on quadric error minimization. We, thus, maintain the regular grid structure while preserving terrain features. Compared to methods, which are solely based on vertex-filtering and sub-sampling, our approach reduces the approximation error. As a consequence, we require fewer triangles, which improves the rendering performance.Item Continuous Deformations of Implicit Surfaces(The Eurographics Association, 2010) Esturo, Janick Martinez; Rössl, Christian; Theisel, Holger; Reinhard Koch and Andreas Kolb and Christof Rezk-SalamaWe introduce an approach for the continuous deformation of implicit surfaces which considers properties of all isosurfaces of a volume data set simultaneously. This is achieved by integrating divergence-free vector fields which is carried out by an efficient backward Lagrangian integration scheme. Our deformation guarantees volume preservation inside each isosurface as well as the preservation of continuity and topology of every isosurface. For visualization and interaction, we offer a real-time mode that allows interactive working on the resolution of the underlying volumetric grid as well as a grid resolution independent mode offering exact extraction of arbitrary isosurfaces. We apply the approach to the deformation of measured volume data sets as well as to the design of complex implicit shapes with a simple pre-defined topology.