We describe VARIANT (VAriable Resolution Interactive ANalysis of Terrain), an extensible system for processing and visualizing terrains represented through Triangulated Irregular Networks (TINs), featuring the accuracy of the representation, possibly variable over the terrain domain, as a further parameter in computation. VARIANT is based on a multiresolution terrain model, which we developed in our earlier research. Its architecture is made of a kernel, which provides primitive operations for building and querying the multiresolution model; and of application programs, which access a terrain model based on the primitives in the kernel. VARIANT directly supports basic queries (e.g., windowing, buffering, computation of elevation at a given point, or along a given line) as well as high-level operations (e.g., ̄y-over visualization, contour map extraction, viewshed analysis). However, the true power of VARIANT lies in the possibility of extending it with new applications that can exploit its multiresolution features in a transparent way.