Formulation and application of radial visualization properties
Karen Daniels, Adam Russell · 2013
Radial Visualizations such as RadViz have a long history and continue to see ever increasing use in many diverse fields. There is a lack of rigorous formal theory behind these visualizations which we conjecture is worthwhile to develop not only for the sake of discovery and deeper knowledge but also for the many corollary practical applications which may be obtained. This dissertation covers contributions to the development of a broad class of Radial Visualizations known as Normalized Radial Visualizations (NRVs) and then proceeds to explore three broadly related areas of application: (1) Visualization Analytics, (2) Point Sensitivity, and (3) Dimensional Anchor Placement. The Visualization Analytics section introduces a quality metric, Q, specific to NRVs and based on a well known mathematical structure: the Voronoi diagram. We show several example applications and establish Q as the standard in which we measure our results in the other sections. As the foundation of Q we formulate a new variant of the Voronoi diagram which we call the Barycentric Voronoi Diagram (BVD). Furthermore, we detail two sub-variants of BVDs: the Co-circular Barycentric Voronoi Diagram (CBVD) and Uniform Co-circular Barycentric Voronoi Diagram (UCBVD). In addition to our Visualization Analytics application we also explore the theoretical properties of BVDs. The Point Sensitivity section covers an analysis of the mobility of data image points within the image space. Of particular interest is the ability to manipulate dimensional anchors so as to better disclose the level of expression certain dimensions may have in the data. We conclude by using our Point Sensitivity results to inform a heuristic method for dimensional anchor placement.