- Research Interests
- Scientific visualization
- Between scientific visualization and geometry Processing
- Trivariate splines
- Topology preserving vector field compression
- Surface parametrization
- Shape editing
- Shape analysis
My research interest focus on geometric modeling and scientific visualization including trivariate splines, vector field compression, surface parameterization, shape editing, shape analysis, remeshing. In the Visal Computing Group we try to bridge the gap between scientific visualization and geometry processing.
Our main interest is in understanding and visualizing flow phenomena.
Between scientific visualization and geometry Processing¶
We apply geometry processing in the context of scientific visualization: for instance, geometric predicates are used to select representative stream surfaces, flux minimization can be beneficial for stream surface generation, mesh quality is optimized during advancing-front stream surface integration.
Maik Schulze, Tobias Germer, Christian Rössl, and Holger Theisel.
Stream surface parametrization by flow-orthogonal front lines.
Computer Graphics Forum (Proc. SGP ), 31(5):1725-1734, 2012.
Maik Schulze, Christian Rössl, Tobias Germer, and Holger Theisel.
As-perpendicular-as-possible surfaces for flow visualization.
In Proceedings of IEEE PacificVis, Songdo, South Korea, 2012.
Splines are a well-established and important tool in Computer Aided Geometric Design (CAGD), best known for modeling surfaces. Their application to volumetric domains was only rarely exploited so far. We developed new trivariate spline models for gridded and general volume data. Typical applications are medical imaging and surface reconstruction from scattered points, respectively. An important research aspect is the analysis of the spline spaces w.r.t. approximation and smoothness properties.
Gregor Schlosser, Jürgen Hesser, Frank Zeilfelder, Christian Rössl,
Reinhard Männer, Günther Nürnberger, and Hans-Peter Seidel.
Fast visualization by shear-warp on quadratic super-spline models using wavelet data decompositions.
Topology preserving vector field compression¶
In scientific visualization, the topology of complex flow fields provides an intuitive and compact view of the data. At the same time, typical data sets are huge and require compression in practical applications. We developed new methods for vector field compression which preserve the topology of the input. As a main contribution, it was shown that these methods can rely on local operations only although topology is a global property.
Surface parameterization refers to establishing bijective maps to a parametric domain. This is a basic and essential tool in digital geometry processing with many applications. Existing approaches based on interior angles were improved, and new methods relying on linear setups were developed. The latter improve on map distortion including free evolution of the boundary in the parametric domain.
Various approaches and tools for shape editing exist in computer graphics. New detail preserving approaches were developed based on linear Laplace and Poisson systems. These methods enable direct shape manipulation, transplanting of surface parts and geometric details transfer to a target shape.
Curvature is an essential tool in shape analysis with a variety of applications, however, its mathematical definition is not directly appropriate to discrete settings. A new discrete curvature measure based on individual triangles with position and normal information was proposed and analyzed. Applications include feature detection/segmentation and non-photorealistic rendering.
Surfaces are often approximated by triangle meshes. Remeshing is concerned with optimizing triangulations w.r.t. certain quality criteria, while approximating the input shape. Approaches to feature-sensitive (isotropic) remeshing were proposed, i.e., sharp edges and corners are detected and preserved. Local parameterizations serve as a basic tool.