Indexing on spherical surfaces using semi-quadcodes

Abstract

The conventional method of referencing a point on a spherical surface of known radius is by specifying the angular position of φ and A with respect to an origin at the centre. This is akin to the ≪x,y≫ coordinates system in R ² cartesian plane. To specify a region in the cartesian plane, two points corresponding to the diagonal points ≪x ₁,y ₁≫ and ≪x ₂,y ₂≫ are sufficient to characterize the region. Given any bounded region, of 2^h×2^h an alternate form of referencing a square subregion is by the linear quadtree address [10] or quadcode [13]. Corresponding encoding scheme for spherical surfaces is lacking. Recently a method similar to the quadtree recursive decomposition method has been proposed independently by Dutton and Fekete. Namely, the quaternary triangular mesh (QTM) [4] and the spherical quadtree (SQT) [8]. The addressing method of the triangular regions suggested are very similar. We present a new labeling method for the triangular patches on the sphere that allows for a better and more efficient operation and indexing on spherical surfaces.