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A moving body is a geometry that may translate and rotate over time. Computing the time-varying distance between moving bodies and surrounding static and moving objects is crucial to many application domains including safety at sea, logistics robots, and autonomous vehicles. Not only is it a relevant analytical operation in itself, but also it forms the basis of other operations, such as finding the nearest approach distance between two moving objects. Most moving objects databases represent moving objects using a point representation, and the computed temporal distance is thus inaccurate when working with large moving objects. This article presents an efficient algorithm to compute the temporal distance between a moving body and other static or moving geometries. We extend the idea of the V-Clip and Lin-Canney closest features algorithms of computational geometry to track the temporal evolution of the closest pair of features between two objects during their movement. We also present a working implementation of this algorithm in an open-source moving objects database and show, using a real-world example on AIS data, that this distance operator for moving bodies is only about 1.5 times as slow as the one for moving points while providing significant improvements in correctness and accuracy of the results.