Smooth Interactive Visualization

Information visualization is a powerful tool for understanding large datasets. However, many commonly-used techniques in information visualization are not C^1 smooth, i.e. when represented as a function, they are either discontinuous or have a discontinuous first derivative. For example, histograms are a non-smooth visualization of density. Not only are histograms non-smooth visually, but they are also non-smooth over their parameter space, as they change abruptly in response to smooth change of bin width or bin offset. For large data visualization, histograms are commonly used in place of smooth alternatives, such as kernel density plots, because histograms can be constructed from data cubes, allowing histograms to be constructed quickly for large datasets.

Another example of a non-smooth technique in information visualization is the commonly-used transition approach to animation. Although transitions are designed to create smooth animations, the transition technique produces animations that have velocity discontinuities if the target is changed before the transition has finished. The smooth and efficient zooming and panning technique also shares this problem---the animations produced are smooth while in-flight, but they have velocity discontinuities at the beginning and end and of the animation as well as velocity discontinuities when interrupted.

This dissertation applies ideas from signal processing to construct smooth alternatives to these non-smooth techniques. To visualize density for large datasets, we propose BLOCs, a smooth alternative to data cubes that allows kernel density plots to be constructed quickly for large datasets after an initial preprocessing step. To create animations that are smooth even when interrupted, we present LTI animation, a technique that uses LTI filters to create animations that are smooth, even when interrupted. To create zooming and panning animations that are smooth, even when interrupted, we generalize signal processing systems to Riemannian manifolds, resulting in smooth, efficient, and interruptible animations.