Abstract
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.
Original language | English |
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Journal | Journal of Inverse and Ill-Posed Problems |
Volume | 22 |
Issue number | 4 |
Pages (from-to) | 537-550 |
ISSN | 0928-0219 |
DOIs | |
Publication status | Published - 2014 |
Keywords
- Spherical x-ray transform
- hypercube
- hypersphere
- central section
- convex polygon
- gnomonic projection