Smoothness preserving layout for dynamic labels by hybrid optimization.

Stable label movement and smooth label trajectory are critical for effective information understanding. Sudden label changes cannot be avoided by whatever forced directed methods due to the unreliability of resultant force or global optimization methods due to the complex trade-off on the different aspects. To solve this problem, we proposed a hybrid optimization method by taking advantages of the merits of both approaches. We first detect the spatial-temporal intersection regions from whole trajectories of the features, and initialize the layout by optimization in decreasing order by the number of the involved features. The label movements between the spatial-temporal intersection regions are determined by force directed methods. To cope with some features with high speed relative to neighbors, we introduced a force from future, called temporal force, so that the labels of related features can elude ahead of time and retain smooth movements. We also proposed a strategy by optimizing the label layout to predict the trajectories of features so that such global optimization method can be applied to streaming data. Electronic Supplementary Material Supplementary material is available in the online version of this article at 10.1007/s41095-021-0231-y.