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Internet of things systems are increasingly common nowadays. They feature spatially-distributed, mobile entities with an arising collective behavior. Such entities bear radionavigation sensors that produce positioning information, then used by the (software-enabled) device to produce positioning information over time, referred to as trajectories. However, software applications built on top of this require composite models of space to be in place; such models can provide adaptive behaviors by observing, evaluating, and reacting to a constantly changing spatial environment. This is typically achieved by monitoring for changes, analyzing requirements violations and then planning and executing adequate countermeasures. We are concerned with the fact that model representations of space are highly pertinent to requirements reasoning of internet of things systems, and such spatial models can be very useful for engineering adaptation. To this end, we provide and implement a technique to infer analyzable models from general trajectories of spatially-distributed systems, which may be used for engineering analysis or planning facilities for the overall self-adaptive systems. Moreover, we illustrate how such spatial models are used for evaluation of requirements predicating about the structure of space, the spatial distribution of devices, temporal as well as quantitative aspects through formal spatio-temporal verification.