Interactive visualization of high-dimension iteration and data sets

Many well-formalized program transformations rely on techniques derived from the linear algebra theory. In such transformations, program entities are represented using polyhedra, which are then transformed using linear or affine functions. However, reasoning within this abstract framework is made extremely difficult by high dimensionality of spaces used to represent complex program transformations and various entities in the resulting programs: data, sets, iteration domains, access functions etc. This difficulty can be alleviated, at least partly, by providing tools for interactive visualization and manipulation of polyhedra and integrating such tools into a programming environment. In this paper we explore the issues involved in designing an interactive visualization tool for high-dimensionality polyhedra, and discuss the possible research directions arising from our current experience.