Interactive focus maps using least-squares optimization

摘要

We present a new algorithm that enlarges a focus region in a given network map without removing non-focus (i.e., context) network parts from the map or changing the map's size. In cartography, this problem is usually tackled with fish-eye projections, which, however, introduce severe distortion. Our new algorithm minimizes distortion and, with respect to this objective, produces results of similar quality compared to an existing algorithm. In contrast to the existing algorithm, the new algorithm achieves real-time performance that allows its application in interactive systems. We target applications where a user sets a focus by brushing parts of the network or the focus region is defined as the neighborhood of a moving user. A crucial feature of the algorithm is its capability of avoiding unwanted edge crossings. Basically, we first solve a least-squares optimization problem without constraints for avoiding edge crossings. The solution we find is then used to identify a small set of constraints needed for a crossing-free solution and, beyond this, allows us to start an animation enlarging the focus region before the final, crossing-free solution is found. Moreover, memorizing the non-crossing constraints from an initial run of the algorithm allows us to achieve a better runtime on any further run -assuming that the focus region does not move too much between two consecutive runs. As we show with experiments on real-world data, this enables response times well below 1 second.