In previous reports, the concept of solid fitting has been presented as a new indirect approach to volume visualization. Solid fitting relies on a simple, but powerful geometric data model, termed interval volume, that allows one to represent a three-dimensional subvolume for which the associated scalar values lie within a specified closed interval. This paper combines the latest results obtained through the course of the solid fitting project. After reviewing the salient features of interval volume and the fundamentals of solid fitting in the first two sections, Section 3 discusses improvements to the original solid fitting algorithm so as to extract interval volumes in a topologically-consistent manner. Also, the octree-based acceleration mechanism incorporated into the algorithm is analyzed further with a complex, time-evolving, volumetric data set. Section 4 is devoted to the presentation of several representative operations related to interval volume, including focusing and measurement-coupled visualization. In addition, a candidate for the volumetric coherence measure is introduced for adaptive solid fitting and its application to multi-scalar visualization. Lastly, Section 5 summarized the paper with some remarks on a hybrid volume exploration environment, in which solid fitting plays various roles.