Visualization methods make use of interactive graphical representations embedded on a display area in order to enable data exploration and analysis. These typically rely on geometric primitives for representing data or building more sophisticated representations to assist the visual analysis process. One of the most challenging tasks in this context is to determinate an optimal layout of these primitives which turns out to be effective and informative. Existing algorithms for building layouts from geometric primitives are typically designed to cope with requirements such as orthogonal alignment, overlap removal, optimal area usage, hierarchical organization, dynamic update among others. However, most techniques are able to tackle just a few of those requirements simultaneously, impairing their use and flexibility. In this dissertation, we propose a set of approaches for building layouts from geometric primitives that concurrently addresses a wider range of requirements. Relying on multidimensional projection and optimization formulations, our methods arrange geometric objects in the visual space so as to generate well-structured layouts that preserve the semantic relation among objects while still making an efficient use of display area. A comprehensive set of quantitative comparisons against existing methods for layout generation and applications on text, image, and video data set visualization prove the effectiveness of our approaches.

No abstract