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- W1828949968 abstract "A discrete spherical geodesic path (DSGP) between two voxels s and t lying on a discrete sphere is a/the shortest path from s to t , comprising voxels of the discrete sphere intersected by the discrete geodesic plane passing through s , t , and the center of the sphere. We consider two classes of discretization, namely naive and standard , for both the sphere and the geodesic plane, which gives rise to four distinct topological classes of DSGP. We show that the naive–naive class does not guarantee the existence of a DSGP, whereas the other three classes do. We derive the upper bounds of the distance of a DSGP belonging to each class, from the real sphere and the real plane, for different neighborhood conditions. We propose an efficient integer-based algorithm to compute the DSGP for any class-and-neighborhood combination. Novel number-theoretic characterization of discrete sphere has been used for searching the voxels comprising a DSGP. The algorithm is output-sensitive , having its time and space complexities both linear in the length of the DSGP. It can also be extended for constructing discrete 3D circles of arbitrary orientations, specified by a few appropriate input parameters. Experimental results and related analysis demonstrate its efficiency and versatility." @default.
- W1828949968 created "2016-06-24" @default.
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- W1828949968 date "2015-11-01" @default.
- W1828949968 modified "2023-09-29" @default.
- W1828949968 title "On different topological classes of spherical geodesic paths and circles in Z3" @default.
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- W1828949968 doi "https://doi.org/10.1016/j.tcs.2015.09.003" @default.
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