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Millimeter-wave (mmWave) systems in the 30-300 GHz bands are among the fundamental enabling technologies of 5G and beyond 5G, providing large bandwidths, not only for high data rate communication but also for precise positioning services, in support of high accuracy demanding applications such as for robotics, extended reality, or remote surgery. With the possibility to introduce relatively large arrays on user devices with a small footprint, the ability to determine the user orientation becomes unlocked. The estimation of the full user pose (joint 3D position and 3D orientation) is referred to as 6D localization. Conventionally, the problem of 6D localization using antenna arrays has been considered difficult and was solved through a combination of heuristics and optimization. In this paper, we reveal a close connection between the angle-of-arrivals (AoAs) and angle-of-departures (AoDs) and the well-studied perspective projection model from computer vision. This connection allows us to solve the 6D localization problem, by adapting state-of-the-art methods from computer vision. More specifically, two problems, namely 6D pose estimation from AoAs from multiple single-antenna base stations and 6D simultaneous localization and mapping (SLAM) based on single- base station (BS) mmWave communication, are first modeled with the perspective projection model, and then solved. Numerical simulations show that the proposed estimators operate close to the theoretical performance bounds. Moreover, the proposed SLAM method is effective even in the absence of the line-of-sight (LoS) path, or knowledge of the LoS/non-line-of-sight (NLoS) condition.