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Many engineering disciplines can profitably use large high-resolution geometric models whose computational requirements exceed current computer hardware capacities. This paper presents an adaptive visualization solution for interactively building such models. Whereas adaptive visualization techniques have conventionally been applied to existing complete models, our work permits adaptive visualization of models while under construction. To achieve this, we use a multiresolution surface representation for both geometric computation and visualization. The paper develops techniques that dynamically and adaptively decimate models, adjusting to changing camera positions. The decimation algorithm preserves intersection curves between surfaces, and applies to models whose surface triangulation is either globally coherent or incoherent. We have embedded the technology presented in this paper into a 3D geoscience geometric modeling application framework that supports many applications.