---
res:
bibo_abstract:
- A discrete spherical geodesic path between two voxels s and t lying on a discrete
sphere is a/the 1-connected shortest path from s to t, comprising voxels of the
discrete sphere intersected by the real plane passing through s, t, and the center
of the sphere. We show that the set of sphere voxels intersected by the aforesaid
real plane always contains a 1-connected cycle passing through s and t, and each
voxel in this set lies within an isothetic distance of 32 from the concerned plane.
Hence, to compute the path, the algorithm starts from s, and iteratively computes
each voxel p of the path from the predecessor of p. A novel number-theoretic property
and the 48-symmetry of discrete sphere are used for searching the 1-connected
voxels comprising the path. The algorithm is output-sensitive, having its time
and space complexities both linear in the length of the path. It can be extended
for constructing 1-connected discrete 3D circles of arbitrary orientations, specified
by a few appropriate input parameters. Experimental results and related analysis
demonstrate its efficiency and versatility.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Ranita
foaf_name: Biswas, Ranita
foaf_surname: Biswas
foaf_workInfoHomepage: http://www.librecat.org/personId=3C2B033E-F248-11E8-B48F-1D18A9856A87
orcid: 0000-0002-5372-7890
- foaf_Person:
foaf_givenName: Partha
foaf_name: Bhowmick, Partha
foaf_surname: Bhowmick
bibo_doi: 10.1007/978-3-319-09955-2_33
bibo_volume: 8668
dct_date: 2014^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/0302-9743
- http://id.crossref.org/issn/1611-3349
- http://id.crossref.org/issn/9783642387081
- http://id.crossref.org/issn/9783642387098
dct_language: eng
dct_publisher: Springer@
dct_title: On Finding Spherical Geodesic Paths and Circles in ℤ3@
...