  A concise and highly performant branchless formulation of a Joseph-type
interpolating ray-casting algorithm for the computation of X-ray projections is
presented. It efficiently utilizes the hardware resources of modern graphics
processing units at the scale of their theoretic maximum performance reaching
access rates of 600 GB/s within read-and-write memory, and is further shown to
do so without compromising on image quality. The computation of X-ray
projections from discrete voxel grids is an ubiquitous task in many problems
related to volume image processing, including tomographic reconstruction and
visualization. Although its central role has given rise to numerous
publications discussing the optimal modeling of ray-volume intersections, a
unique benchmark in this respect does not exist. Here, a 3D Shepp-Logan phantom
is used, which allows the computation of analytic reference projections that
can further serve as input to iterative reconstructions without committing the
inverse crime. The proposed algorithm (GJP) is compared to the competing and
widely adopted digital differential analyzer (DDA), which computes exact
line-box intersections. It is thereby found to outperform the DDA on recent
graphics processors in all respects: Despite accessing twice as much memory,
the GJP is still able to calculate projections twice as fast. It further
exhibits considerably less discretization artifacts, and neither oversampling
of the DDA nor a smooth interpolation kernel within the GJP are able to improve
on these results in any respect.
