|Abstract:||Computational simulations frequently generate solutions defined over very large tetrahedral volume meshes containing many millions of elements. Furthermore, solutions over these meshes may often be expressed using non-linear basis functions. Certain solution techniques, such as discontinuous Galerkin finite element methods, may even produce non-conforming meshes. Such data is difficult to visualize interactively, as it is far too large to fit in memory and many common data reduction techniques, such as mesh simplification, cannot be applied to non-conforming meshes. Common linear interpolation method cannot faithfully and accurately evaluate the non-linear solutions.
To provide accurate visualization, in the first part of this dissertation, we introduce a method for pixel-exact evaluation of higher order solution data on the GPU. We demonstrate the importance of per-pixel rendering versus simple linear interpolation for producing high quality visualizations. We also show that our system can accommodate reasonably large datasets---spacetime meshes containing up to 20 million tetrahedra.
To provide interactive visualization, in the second part, we introduce a point-based visualization system for interactive rendering of large, potentially non-conforming, tetrahedral meshes. We propose methods for adaptively sampling points from non-linear solution data and for decimating points at run time to fit GPU memory limits. Because these are streaming processes, memory consumption is independent of the input size. We also present an order-independent point rendering method that can efficiently render volumes on the order of $20$ million tetrahedra at interactive rates.
To provide efficient visualization, in the third part, we introduce a feature based visualization system to meaningfully reveal the complex structures from large volumetric data which may have noisy non-linear discontinuous fields as well as regular linear fields. We propose methods to partition the volume according to feature distribution and process each feature partition as a whole. We present TetGrid for efficient sampling to minimize the overlaps and gaps, which cause errors for our order-independent weighted accumulation point rendering method. Beside points depth, pixel coverage and integral density are also taken into consideration. We show that our feature-based visualization provide the even better quality result with less points than other methods.