A Force-Directed Power Diagram Approach for Interactive Voronoi Treemaps

Abstract

Voronoi treemaps represent weighted hierarchical data as nested Voronoi diagram partitions with cells' area proportional to the weights. Current techniques to compute them propose static visualizations which can be used for reporting, or dynamic one to capture data update. However, no ideal solution exists yet to interactively rearrange the treemap layout, for instance for a data journalist to tell a story, or for a scientist to create data categorization. We propose a new way to get an interactive Voronoi treemap, where a child cell can be moved by drag-and-drop within a parent cell attempting to preserve both stability (position) and weight (area) during the move. We use a force-directed approach applied to the dual circles of the Power cells to guide the computation of the Power diagram under the hood. Our preliminary quantitative experiments show the force-directed approach provides areas with 10% weighted average error, which is an order of magnitude higher than standard static approaches, but qualitative observations show that it gives a more predictable and smoother interaction, and a direct control over the stability of the remaining cells. Assuming the user would focus less on getting high accuracy of the areas than keeping a good and stable overview of the treemap while dragging a cell, the force-directed approach appears to be a valuable option to explore further. We also discovered a trade-off between stability and accuracy and the force-directed approach lets the user control it directly.