A New Projection for Spherical Triangle: Equal Angle Ratio Projection(EARP)
YUAN Wen1, MA Ai-nai1, GUAN Xiao-jing2
(1. Inst.of Remote Sensing and Geography Information System, Peking University, Beijing 100871, China; 2. State Information Center, Beijing 100045, China)
Abstract£ºA projection named Equal Angle Ratio Projection (EARP) is proposed in this paper, which has two kinds of geometric models. EARP supports several Plato polyhedrons, including tetrahedron, octahedron and icosahedron, and arbitary Voronoi spherical tessellations. The coordinates in the projection of a arbitary triangle are determined by the ratios between spherical angles. Spherical points are evenly projected into a regular triangle mesh in 2-D plane. Two concrete equations are given for octahedron and spherical icosahedron (EARPIH), and it is found that Goodchild's and Otoo's projections are two special implements of EARP.We also compare EARPIH with other projections in area distorion and the area distorion of EARPIH is kept in a shallow range. In EARP, coordinate translation between geodetic coordinates and spherical triangle mesh is reduced to the relation of a point with a discrete 2D triangle mesh.
Key words£ºglobal grid; projection; coordinate transfer; icosahedron