Extended Reality is a revolutionary method of delivering multimedia content to users. A large contributor to its popularity is the sense of immersion and interactivity enabled by having real-world motion reflected in the virtual experience accurately and immediately. This user motion, mainly caused by head rotations, induces several technical challenges. For instance, which content is generated and transmitted depends heavily on where the user is looking. Seamless systems, taking user motion into account proactively, will therefore require accurate predictions of upcoming rotations. Training and evaluating such predictors requires vast amounts of orientational input data, which is expensive to gather, as it requires human test subjects. A more feasible approach is to gather a modest dataset through test subjects, and then extend it to a more sizeable set using synthetic data generation methods. In this work, we present a head rotation time series generator based on TimeGAN, an extension of the well-known Generative Adversarial Network, designed specifically for generating time series. This approach is able to extend a dataset of head rotations with new samples closely matching the distribution of the measured time series.

The need for statistical models of orientations arises in many applications in engineering and computer science. Orientational data appear as sets of angles, unit vectors, rotation matrices or quaternions. In the field of directional statistics, a lot of advances have been made in modelling such types of data. However, only a few of these tools are used in engineering and computer science applications. Hence, this paper aims to serve as a cheat sheet for those probability distributions of orientations. Models for 1-DOF, 2-DOF and 3-DOF orientations are discussed. For each of them, expressions for the density function, fitting to data, and sampling are presented. The paper is written with a compromise between engineering and statistics in terms of notation and terminology. A Python library with functions for some of these models is provided. Using this library, two examples of applications to real data are presented.