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In this paper, we propose a hybrid spatio-semantic model and a computing platform for trajectories of moving objects. Our hybrid model can represent trajectories in terms of both spatio and semantic mobility characteristics, supporting different levels of data abstraction. Through experimental analysis of real-life GPS feeds, we demonstrate how our model and platform achieve the purpose of progressive abstraction of the raw mobility data. We present spatio-semantic trajectory computing results in various live mobility feeds, and present insights on parameters that guide the sensitivity of such computing platform. This approach can be applied to other location feeds like cellular location data. Our future work focuses on inferring spatio-semantic trajectories from diverse location (and sensory) sources.