Ridesharing is an essential part of shared mobility for improving passengers' travel efficiency in cities. Existing studies usually determine shareable trips based on whether the arrival sequence of vehicles in more than one pick-up and drop-off points can meet predefined spatio-temporal constraints. Such a simple approach cannot quickly and comprehensively find all the potential shareable trips under scenarios involving large-scale car-sharing requests. Therefore, based on the modeling method of space-time prism and the spatial-temporal expression of passengers' sharing willing, we propose a potential spatio-temporal path area model of travel. Then, we apply the topological relation between the space-time prisms of trips for ridesharing identification, and quantify the strength of ridesharing of trips. Finally, two ridesharing matching strategies are proposed to simulate the result of ridesharing matching in real-world travel environment. Results confirm that the proposed ridesharing identification model can accurately delineate the potential space-time accessibility of vehicular travel, which makes it easier to discover all potential shareable trips and to realize the accurate and effective car-sharing identification. Our study will be helpful to vehicle resource scheduling and passenger ridesharing travel planning in urban shared mobility system.