Scientific visualization is a growing area of computational science and has been for about the past three decades. As software and hardware have advanced, the range of applications has grown. Two of the extreme areas of application are the visualization of domains that cannot be seen otherwise. At one end is the visualization of the microscopic events in biology and chemistry. At the other end is the universe from the solar system on up to the galactic level and beyond. Addressing these domains requires an approach that is scalable and extensible.

The authors use a modular approach to address this topic, an approach that involves three conceptual/software levels: the application (virtual astronomy), transformations (including rescaling techniques), and power-scaled coordinates (PSC) at the innermost level. They begin with an introduction including references to popular visualizations of scale, and a survey of related work and software. Then, they introduce the scaling issues and the modular approach. The PSC representation is then introduced, in which a fourth coordinate (beyond (x,y,z)) is used as a generalized exponential scaling term, and the algebra of PSC transformations is presented. The third part of the paper involves the “depth rescaling method,” which is developed mathematically in this section. Related topics of eye-space coordinates and advanced topics (PSC acceleration and virtual astronomy) are discussed before a section on the implementation and design of the software and results. The paper concludes with a discussion of future work.

This paper is highly readable and interesting. It also provides a template for the interactions between mathematics, computer science, and applications.