Visualization: Volumetric Finite Element Visualization

The finite element (FE) method is an important computational technique in science, engineering and medicine for solving partial differential and integral equations. Applications include simulations of physical processes (e.g. disease processes), derivation of new entities from measured data (e.g. computation of material strain from displacement data), and analysis and comparison of data defined over objects with similar topology (e.g. performance analysis of healthy and diseased hearts). All of these applications involve large amounts of multi-dimensional and multi-parametric data.

In this project we develop novel visualization methods for data obtained with and/or defined over FE models. The visualization of that data is essential for developing novel solution through simulations, gaining insight into physical processes, and recognizing common patterns and structures, e. g. indicating a developing heart problem. While surface-based visualizations of FE models are already well established, visualization techniques allowing the interactive analysis of the entire 3D structure of FE data are rare and usually achieved by resampling. This introduces errors and removes the relationship between material geometry and material properties. In particular, this makes it difficult to analyze multi-modal data and compare different data sets since the common reference system represented by the objects’ material space is removed. An apparent alternative is a direct ray-casting based techniques. However, when dealing with complex curvilinear elements the numerical complexity of the world-to-material space transformation prevents them from being applied in interactive scenarios, and thus limits their applicability. In this project, we plan to exploit spatio-temporal coherence of rays in material space to simplify the world-to-material coordinate mapping using a precomputed proxy representation, and thus reduce the numerical complexity involved during visualization. This allows us to achieve an interactive, high-quality visualization through ray-casting on modern graphics hardware.