Due to the wide use of increasingly larger tetrahedral meshes in volumetric visualization, simplification of tetrahedral meshes has become more and more popular in last two decades. In this thesis, we first introduce a basic tetrahedral mesh simplification algorithm based on cell collapse. Then, we present a new feature preserving simplification algorithm for tetrahedral meshes. The algorithm decimates the original dataset by iteratively removing tetrahedra without significantly altering boundary or interior field features. In a pre-processing step, we apply a level set method to find a segmentation of the volume dataset, and then label vertices on the region boundaries that potentially contribute to visually perceptible features in the rendered volume. The simplification algorithm preserves these labeled vertices as much as possible. Both incremental and greedy strategies are used to decimate tetrahedra that contain at most one labeled vertex. Field gradients, tetrahedral aspect ratio changes and variances of interior region values are further used so as to maintain features of the original dataset in regional interiors. A possible extension of combining edge collapse also presented to achieve higher decimation rates. We have implemented these algorithms and tested them using a number of standard volumetric datasets. The results have shown that the feature preserving simplification algorithm is able to preserve more features at the same decimation rates in comparison to other simplification algorithms.
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