The traffic infrastructure greatly impacts the quality of life in urban environments. To optimize this infrastructure, engineers and decision makers need to explore traffic data. In doing so, they face two important challenges: the sparseness of speed sensors that cover only a limited number of road segments, and the complexity of traffic patterns they need to analyze. In this paper we take a first step at addressing these challenges. We use New York City (NYC) taxi trips as sensors to capture traffic information. While taxis provide substantial coverage of the city, the data captured about taxi trips contain neither the location of taxis at frequent intervals nor their routes. We propose an efficient traffic model to derive speed and direction information from these data, and show that it provides reliable estimates. Using these estimates, we define a time-varying vector-valued function on a directed graph representing the road network, and adapt techniques used for vector fields to visualize the traffic dynamics. We demonstrate the utility of our technique in several case studies that reveal interesting mobility patterns in NYC’s traffic. These patterns were validated by experts from NYC’s Department of Transportation and the NYC Taxi & Limousine Commission, who also provided interesting insights into these results.