Ubiquitous taxi trajectory data has made it possible to apply it to different types of travel analysis. Of interest is the need to allow someone to monitor travel momentum and associated congestion in any location in space in real time. However, despite an abundant literature in taxi data visualization and its applicability to travel analysis, no easy method exists. To measure taxi travel momentum at a location, current methods require filtering taxi trajectories that stop at a location at a particular time range, which is computationally expensive. We propose an alternative, computationally cheaper way based on pre-processing vector fields from the trajectories. Algorithms are formalized for generating vector kernel density to estimate a travel-model-free vector field-based representation of travel momentum in an urban space. The algorithms are shared online as an open source GIS 3D extension called VectorKD. Using 17 million daily taxi GPS points within Beijing over a four-day period, we demonstrate how to generate in real time a series of projections from a continuously updated vector field of taxi travel momentum to query a point of interest anywhere in a city, such as the CBD or the airport. This method allows a policy-maker to automatically identify temporal net influxes of travel demand to a location. The proposed methodology is shown to be over twenty times faster than a conventional selection query of trajectories. We also demonstrate, using taxi data entering the Beijing Capital International Airport and the CBD, how we can quantify in nearly real time the occurrence and magnitude of inbound or outbound queueing and congestion periods due to taxis cruising or waiting for passengers, all without having to fit any mathematical queueing model to the data.