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Item Subdivision Surfaces for Scattered-data Approximation(The Eurographics Association, 2001) Bertram, Martin; Hagen, Hans; David S. Ebert and Jean M. Favre and Ronald PeikertWe propose a modified Loop subdivision surface scheme for the approximation of scattered data in the plane. Starting with a triangulated set of scattered data with associated function values, our scheme applies linear, stationary subdivision rules resulting in a hierarchy of triangulations that converge rapidly to a smooth limit surface. The novelty of our scheme is that it applies subdivision only to the ordinates of control points, whereas the triangulated mesh in the plane is fixed. Our subdivision scheme defines locally supported, bivariate basis functions and provides multiple levels of approximation with triangles. We use our subdivision scheme for terrain modeling.Item Extraction of Crack-free Isosurfaces from Adaptive Mesh Refinement Data(The Eurographics Association, 2001) Weber, Gunther H.; Kreylos, Oliver; Ligocki, Terry J.; Shalf, John M.; Hagen, Hans; Hamann, Bernd; Joy, Kenneth I.; David S. Ebert and Jean M. Favre and Ronald PeikertAdaptive mesh refinement (AMR) is a numerical simulation technique used in computational fluid dynamics (CFD). It permits the efficient simulation of phenomena characterized by substantially varying scales in complexity of local behavior of certain variables. By using a set of nested grids at different resolutions, AMR combines the simplicity of structured rectilinear grids with the possibility to adapt to local changes in complexity and spatial resolution. Hierarchical representations of scientific data pose challenges when isosurfaces are extracted. Cracks can arise at the boundaries between regions represented at different resolutions. We present a method for the extraction of isosurfaces from AMR data that avoids cracks at the boundaries between levels of different resolution.Item Vector and Tensor Field Topology Simplification on Irregular Grids(The Eurographics Association, 2001) Tricoche, Xavier; Scheuermann, Gerik; Hagen, Hans; Clauss, Stefan; David S. Ebert and Jean M. Favre and Ronald PeikertTopology-based visualization of planar turbulent flows results in visual clutter due to the presence of numerous features of very small scale. In this paper, we attack this problem with a topology simplification method for vector and tensor fields defined on irregular grids. This is the generalization of previous work dealing with structured grids. The method works for all interpolation schemes.Item Topology-Based Visualization of Time-Dependent 2D Vector Fields(The Eurographics Association, 2001) Tricoche, Xavier; Scheuermann, Gerik; Hagen, Hans; David S. Ebert and Jean M. Favre and Ronald PeikertTopology-based methods have been successfully applied to the visualization of instantaneous planar vector fields. In this paper, we present the topology-based visualization of time-dependent 2D flows. Our method tracks critical points over time precisely. The detection and classification of bifurcations delivers the topological structure of time dependent vector fields. This offers a general framework for the qualitative analysis and visualization of parameterdependent 2D vector fields.Item Clifford Algebra, Clifford Analysis and Applications in Physics and Visualization(Eurographics Association, 2001) Scheuermann, Gerik; Hagen, Hans-