A spherical x-ray transform and hypercube sections

We investigate the problem of sampling a unit great circle on the unit sphere S-3 as a support of orientation distribution functions on which acts the discrete spherical x-ray transform. The circle's partition subsets are gnomonically mapped onto lines that constitute a convex polygon inside the bounding cubes of hypercube.

Thus the problem of the great circle tracing is reduced to the problem of the four-dimensional cube sectioning by the plane containing the circle and the intersection figure (the polygon) vertices finding. In this paper, a fast, non-combinatorial approach for the polygon tracing within the general multi-dimensional frame is proposed.