Variable resolution triangulations

A comprehensive study of multiresolution decompositions of planar domains into triangles is given. A model introduced that is more general than other multiresolution models proposed in the literature. The model is based on a collection of fragments of plane triangulations arranged into a partially ordered set. Diierent decompositions of a domain can be obtained by combining diierent fragments from the model. Theoretical results on the expressive power of such a model are given. An eecient algorithm is proposed that can extract a triangulation from the model, whose level of detail is variable over the domain according to a given threshold function. The algorithm works in linear time, and the extracted representation has minimum size among all possible triangulations that can be built from triangles in the model, and that satisfy the given level of detail. Major applications of these results are in real time rendering of complex surfaces, such as topographic surfaces ight simulation. A preliminary work on the subject of this paper appeared under title \Variable resolution terrain surfaces" in the