The approximation tree is a hybrid, hierarchical data structure for real-time terrain visualization which represents both geometry data and texture data of a terrain in a hierarchical manner. This framework can integrate different multiresolution modeling techniques operating on different types of data sets such as TINs, regular grids, and non-regular grids. An approximation tree recursively aggregates terrain patches which reference geometry data and texture data. The rendering algorithm selects patches based on a geometric approximation error and a texture approximation error. Terrain shading and thematic texturing, which can be generated in a preprocessing step, improve the visual quality of level of detail models and eliminate the defects resulting from a Gouraud shaded geometric model since they do not depend on the current (probably reduced) geometry. The approximation tree can be implemented efficiently using object-oriented design principles. A case study for cartographic landscape visualization illustrates the use of approximation trees.
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