Time-series data-usually presented in the form of lines-plays an important role in many domains such as finance, meteorology, health, and urban informatics. Yet, little has been done to support interactive exploration of large-scale time-series data, which requires a clutter-free visual representation with low-latency interactions. In this paper, we contribute a novel line-segment-based KD-tree method to enable interactive analysis of many time series. Our method enables not only fast queries over time series in selected regions of interest but also a line splatting method for efficient computation of the density field and selection of representative lines. Further, we develop KD-Box, an interactive system that provides rich interactions, e.g., timebox, attribute filtering, and coordinated multiple views. We demonstrate the effectiveness of KD-Box in supporting efficient line query and density field computation through a quantitative comparison and show its usefulness for interactive visual analysis on several real-world datasets.