This paper introduces an adaptation of polar coordinates called root polar plotting that we have developed for our network pixel map, a computer security visualization capable of representing tens of thousands of hosts at a time. Root polar coordinates overcome two important problems of normal polar coordinates: plot density distortion and severe occlusion near the origin. We discuss several approaches we took while investigating this problem and provide empirical data from experiments we conducted comparing root polar coordinates against both normal polar and Cartesian coordinates. In any application where a polar plot would be useful but distortion of the data must be avoided, or where it is important to avoid some markers from being occluded by others, root polar coordinates may be useful. Our approach provides: (1) a novel adaptation of polar coordinates that overcomes plotting distortion; (2) a means of plotting network data in near real-time without complex layout optimization; (3) an algorithm that reduces occlusion of plotted points while maintaining consistent placement; and (4) an empirical comparison of Cartesian vs. polar plots.