Helical and circular trajectories are expected to be adopted dominantly for data acquisition in X-ray cone-beam (CB) computed tomography (CT) imaging. However, non-conventional trajectories, such as tilted helical, saddle, circle-circle, and circle-line trajectories, may also find important applications. Therefore, accurate image reconstruction from data acquired with these non-conventional trajectories remains of practical significance. However, the non-conventional trajectories have been studied on a case-per-case basis and little effort has been made to investigate all of these trajectories on a single algorithm. Recently, there has been significant development on image reconstruction for general CB trajectories. In particular, chord-based algorithms have been developed for image reconstruction in CBCT. In this work, we investigate the chord-based algorithms, which can accommodate data containing both longitudinal and transverse truncations to a certain extent, for image reconstruction from data acquired with four different trajectories: the tilted helical, saddle, circle-circle, and circle-line trajectories. The first two represent smooth trajectories, whereas the last two are non-smooth trajectories containing kinks. The significance of the work lies not only in demonstrating the ability of the algorithm for image reconstruction from CB data but also in visualizing the reconstructible regions-of-interest (ROIs) for those general trajectories so that one can setup the scanning parameters with an appropriate guide. (c) 2007 Published by Elsevier B.V.