In order to better understand the movement of an object with respect to a region, we propose a formal model of the evolving spatial relationships that transition between local topologies with respect to a trajectory and a region as well as develop a querying mechanism to analyze movement patterns. We summarize 12 types of local topologies built on trajectory‐region intersections, and derive their transition graph; then we capture and model evolving local topologies with two types of trajectory‐region strings, a movement string and a stop‐move string. The stop‐move string encodes the stop information further during a trajectory than the movement string. Such a string‐format expression of trajectory‐region movement, although conceptually simple, carries unprecedented information for effectively interpreting how trajectories move with respect to regions. We also design the corresponding Finite State Automations for a movement string as well as a stop‐move string, which are used not only to recognize the language of trajectory‐region strings, but also to deal effectively with trajectory‐region pattern queries. When annotated with the time information of stops and intersections, a trajectory‐region movement snapshot and its evolution during a time interval can be inferred, and even the relationships among trajectories with respect to the same region can be explored.