--- res: bibo_abstract: - Although the concept of functional plane for naive plane is studied and reported in the literature in great detail, no similar study is yet found for naive sphere. This article exposes the first study in this line, opening up further prospects of analyzing the topological properties of sphere in the discrete space. We show that each quadraginta octant Q of a naive sphere forms a bijection with its projected pixel set on a unique coordinate plane, which thereby serves as the functional plane of Q, and hence gives rise to merely mono-jumps during back projection. The other two coordinate planes serve as para-functional and dia-functional planes for Q, as the former is ‘mono-jumping’ but not bijective, whereas the latter holds neither of the two. Owing to this, the quadraginta octants form symmetry groups and subgroups with equivalent jump conditions. We also show a potential application in generating a special class of discrete 3D circles based on back projection and jump bridging by Steiner voxels. A circle in this class possesses 4-symmetry, uniqueness, and bounded distance from the underlying real sphere and real plane.@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: 10.1007/978-3-319-32360-2_20 bibo_volume: 9647 dct_date: 2016^xs_gYear dct_isPartOf: - http://id.crossref.org/issn/0302-9743 - http://id.crossref.org/issn/1611-3349 - http://id.crossref.org/issn/978-3-319-32359-6 dct_language: eng dct_publisher: Springer Nature@ dct_title: On functionality of quadraginta octants of naive sphere with application to circle drawing@ ...