In this thesis we present a wavelet-based geometry compression pipeline in the context of hierarchical surface and volume representations. Due to the increasing complexity of geometric models used in a vast number of different application fields, new methods have to be devised that enable one to store, transmit and manipulate large amounts of data. Based on a multi-resolution wavelet representation, we have developed a complete compression pipeline suitable for geometric data on uniform grids in two and three dimensions. Local and global oracles in wavelet space are employed to control the approximation error in lossy compression settings. Two novel geometry simplification schemes,
which are able to build hierarchical mesh representations, are an essential part of the pipeline.
The first method, a bottom-up vertex removal scheme, analyzes the detail information of the data at different levels after reconstruction from wavelet space. The resulting hierarchical quadtree data structure is triangulated subsequently using a look-up-table that
stores the necessary connectivity information. The second method implements a topdown vertex insertion strategy that is capable of progressively reconstructing the model. Vertex connectivity is derived using Delaunay triangulation. This approach provides high flexibility for the construction of adaptive surface and volume approximations. Furthermore, it is possible to extract high quality iso-contours and to compress texture attributes along with the geometric surface model.
In contrast to the two wavelet-based approximation schemes, we have devised the progressive
tetrahedralization method, an extension of the popular progressive meshes into volumetric settings. These strategies can be used to transform unstructured input meshes into special representations which enable a model to be reconstructed progressively. In the volumetric
setting, using tetrahedral mesh approximations, we have to account for potential mesh inconsistencies arising frequently during the course of the transformation. All methods developed in this dissertation have been implemented utilizing a software component-based approach. Several hundred components at different abstraction levels can be combined to build powerful prototype applications with high flexibility. We compare the three approximation schemes with each other using several two- and three-dimensional geometric models and provide an extensive error and performance analysis. These results emphasize the individual strengths of each of the introduced methods and concepts.