Abstract:
Finite element (FE) model is an important modelling technique in science, biomedicine and engineering. It is used for simulating physical processes, data fitting, computation of shape parameters, simulating deformations, and as reference frames for model and data comparison. Finite Elements discretise domains into (often curvilinear) elements and material properties can be defined over these elements using nodal parameters and interpolation functions. Many applications of FEs result in large multi-dimensional data sets. Direct Volume Rendering (DVR) is a popular data visualisation technique and is especially effective for the visualisation of complex multi-dimensional data sets. By assigning different colour and opacity values to different data values, the entire data set can be visualised in one image. Direct Volume Rendering is an attractive solution for visualising FE data sets, since FE simulations and other applications of finite elements usually involve complex volumetric geometries and multiple and/or high-dimensional dependent variables. However, FE models visualisation with DVR is a challenging topic since the visualisation process is computationally expensive. In particular, most FE models define variables over the elements material coordinates, while the DVR process is performed in a scene's world coordinates. Obtaining material coordinates during the visualisation requires computing the inverse of the FE interpolation function which is a slow and numerically complex computation. In previous research real-time DVR of FE data sets was achieved by either converting the data from material to world coordinates, e.g. by re-sampling, or by focusing on low-order Finite Elements. The first approach introduces numerical inaccuracies and reduces the information content of the data set, e.g. by making it more difficult to investigate the relationship between field values and FE geometry. The second approach is not applicable for high-order FE models, which are common in biomedicine and engineering. In order to achieve fast and high-quality DVR visualisations for high-order finite element models, we develop new algorithms for visualizing FE data sets directly (without re-sampling) in this thesis. We integrate them into the Voreen DVR engine and evaluate them. The first solution implements ray tracing in FE material coordinates on the GPU, and involves efficient hardware implementations of FE interpolation functions and a multi-dimensional Newton's method. The second solution was developed in collaboration with the Voreen team in Norrkopping, Sweden, and introduces a novel intermediate representation to decouple the expensive coordinate inverse transformation from the visualization process without losing the relationship between the data and material coordinates. For comparison purposes the first solution was additionally implemented on the CPU. Our evaluation shows that the first solution (GPU accelerated direct visualisation approach) renders high-quality visualisation for high-order finite element models in seconds, which is about 3,000 times faster than the CPU direct visualisation approach. Running FE interpolations on GPUs is about 50 times faster than running them on CPUs. Furthermore, the second solution (proxy-ray interpolation approach) runs on interactive frame rates for visualising high-order finite element model at high resolutions. It is more than 8 times faster than the GPU accelerated direct visualisation approach for high resolution visualisations.