  Timepix3 pixel detectors have demonstrated great potential for tracking
applications. With $256\times 256$ pixels, 55 $\mathrm{\mu}$m pitch and
improved resolution in time (1.56 ns) and energy (2 keV at 60 keV), they have
become powerful instruments for characterization of unknown radiation fields. A
crucial pre-processing step for such analysis is the determination of particle
trajectories in 3D space from individual tracks. This study presents a
comprehensive comparison of regression methods that tackle this task under the
assumption of track linearity. The proposed methods were first evaluated on a
simulation and assessed by their accuracy and computational time. Selected
methods were then validated with a real-world dataset, which was measured in a
well-known radiation field. Finally, the presented methods were applied to
experimental data from the Large Hadron Collider. The best-performing methods
achieved a mean absolute error of 1.99{\deg} and 3.90{\deg} in incidence angle
$\theta$ and azimuth $\varphi$, respectively. The fastest presented method
required a mean computational time of 0.02 ps per track. For all experimental
applications, we present angular maps and stopping power spectra.
