Techniques for three-dimensional scalar and vector field visualization with error evaluation
Authors: Jonathan D. Cohen
Venue:  (2009)

Computational advances over the past few decades have enabled scientists to create ever larger and more complex scientific data sets, which have become increasingly difficult to understand, analyze, compare and communicate. Scientific visualization has become an important tool for presenting the data in graphic form in order to convey insight and understanding of the data. A variety of technologies have been introduced that allow useful graphical presentation of scientific data, however there are limitations. To address this, in this thesis, we introduce four techniques for solving some challenges of scientific visualization. First, we propose a novel scheme to interactively visualize time-varying scalar fields defined on a curvilinear grid. Previous methods either resampled a scalar field on a curvilinear grid into a regular grid and used texture mapping, or cast rays from the image plane through volume, integrating all scalar values along the ray to determine the pixel color, or project grid cells onto image plane and add all cells' contributions together. All of these approaches have limitations: resampling field data into a regular grid is expensive in both computation and storage, especially for time-varying data sets with a large number of time steps; and the ray casting method cannot achieve interactive frame rate for even a single time step and work best for convex grids. In contrast, our method uses 3D texture mapping technique for high performance rendering and avoids resampling for each time step. We create a 3D warp texture that maps points in R3 into the grid coordinate system. At rendering time, the warping function is reconstructed at each fragment using tri-linear interpolation, and provides the 3D texture coordinates required to look up a scalar field value stored in a separate scalar texture. In essence, this approach reduces the complex problem of rendering a curvilinear grid to the simple problem of rendering a regular grid with one additional texture lookup. Comparing our scheme to other existing methods with regard to both computational expenses and rendering performance on multiple data sets, we demonstrate that our scheme is better suited than existing methods to the task of interactively visualizing large time-varying scalar data on curvilinear grid. Second, we use a new approach to adaptively place streamlines for steady vector fields in 2D and 3D. Most existing algorithms for streamline generation either provide a particular density of streamlines across the domain, or explicitly detect features, such as critical points, and follow customized rules to emphasize those features. However, the former generally provides streamline representation based on some criteria independent of the underlying flow function and the latter requires accurate prior knowledge of the field as well as Boolean decisions on the location of features, which may suffer from robustness problems for real-world data. In our approach, we define a metric for local similarity among streamlines and use this metric to grow streamlines from a dense set of candidate seed points. The metric considers not only Euclidean distance, but also a simple statistical measure of shape and directional similarity. We provide empirical results demonstrating that our streamline placement guided by this new similarity distance metric provides an improved representation of the field data that naturally accentuate regions of geometric interest without explicit feature detection. Third, we introduce a case study of visualizing time-varying magnetic field data in ideal MHD (magnetohydrodynamics). We utilize some special properties of magnetic field data and concurrent velocity data to produce an interesting representation using streamlines. The result is recognized as being useful and meaningful by professionals. Although the method is not suitable for generic cases yet, it's a very interesting referential attempt at visualizing time-varying vector field data. Lastly, we introduce an objective and quantitative evaluation strategy for scientific visualization. Where as most existing evaluations for visualization are based on user studies, we evaluate the visual representation based on how well the representation preserves the information from the original field data. The key idea is to reconstruct field data from the derived visual representation and compute a difference between the reconstruction and the original field. Our empirical evaluation results for both texture-based scalar field visualization and streamline-based vector field visualization demonstrate that in practice this objective and quantitative evaluation strategy is efficient and meaningful.