Industrial computed tomography (CT) has seen widespread adoption within certain areas of non-destructive testing (NDT), with many commercial systems capable of acquisition and reconstruction of cone-beam CT data. The majority of these systems utilise reconstruction algorithms based on the traditional filtered back-projection (FBP) methods, which are imperfect with respect to limited-angle cone-beam data. These techniques are also inherently restricted in the source trajectories that can be utilised due to the use of Fourier slice theorem. This restricts FBP-based techniques to a circular or helical trajectory. Iterative reconstruction algorithms provide a solution to these limitations as the volume reconstruction does not depend on the location or orientation of the source and detector, allowing the possibility of scanning trajectories that satisfy well-known CT data-sufficiency conditions. This paper proposes a method of reconstruction based on computationally efficient computer graphics algorithms with data collected from points in 3D space not restricted to a single circular trajectory, which is useful within NDT for automated robotic inspection. The algorithms developed allow for rapid processing of the algebraic reconstruction technique (ART) for use with X-ray transmission data for CT reconstruction. Experimental results are presented for reconstructions for circular trajectory and points on a sphere to demonstrate the suitability for NDT applications.