Multiresolution terrain models provide a compact description of a topographic surface at multiple levels of accuracy, and they are useful in several applications to access terrain representations where the resolution in each area is defined based on application needs. In this paper we focus on a model, called the Multiresolution Triangular Model (MTM), which generalizes many other multiresolution models proposed in the literature, and is based on a collection of fragments of plane triangulations organized into a directed acyclic graph. We consider a set of basic spatial operations, which include the extraction of a terrain representation at a user-defined level of resolution, as well as answering interference (e.g., point location, segment and region intersection) and navigation queries, at a certain resolution. We present two data structures to encode the MTM, and related algorithms to perform the above operations. Experimental results from implementation within a prototype system are reported.