Movement data collected through GPS or other technologies is increasingly common, but is difficult to visualize due to overplotting and occlusion of movements when displayed on 2D maps. An additional challenge is the extraction of useful higher-level information (such as meetings) derived from the raw movement data. We present a design study of MovementSlicer, a tool for visualizing the places visited, and behaviors of, individual actors, and also the meetings between multiple actors. We first present a taxonomy of visualizations of movement data, and then consider tasks to support when analyzing movement data and especially meetings of multiple actors. We argue that Gantt charts have many advantages for understanding the movements and meetings of small groups of moving entities, and present the design of a Gantt chart that can nest people within locations or locations within people along the vertical axis, and show time along the horizontal axis. The rows of our Gantt chart are sorted by activity level and can be filtered using a weighted adjacency matrix showing meetings between people. Empty time intervals in the Gantt chart can be automatically folded, with smoothly animated transitions, yielding a multi-focal view. Case studies demonstrate the utility of our prototype.