Equal arc ratio projection and a new spherical triangle quadtree model

A projection family, named Equal Arc Ratio Projection (EARP), is proposed in this paper, which has two kinds of geometric cases. Coordinates in the projections are determined by the ratios between four special arcs. The projection for spherical octahedron is derived, which is available for Dutton's Quaternary Triangular Mesh (QTM), and both projections of Goodchild's and Otoo's for QTM are found to be two special implementations of EARP. The icosahedral projection and thus the corresponding spherical triangle quadtree partition model are also developed. The partition model is compared with several other global grid models