一种新的球面三角投影:等角比投影(EARP)

设计一种面向球面三角形的新的投影--等角比投影(Equal Angle Ratio Projection,EARP),该投影包括平行以及同轴两种模式,支持正六面体、正八面体、正二十面体等柏拉图立体(Plato Polvhedron)[1～3]以及任意Voronoi球面三角剖分.可以选择任意形状的投影平面三角,投影坐标由球面弧角度与特征球面弧角度之比决定,弧线族上的均分点与2维投影面上均匀分布的三角网格顶点相对应.本文给出了该模型正八面体以及正二十面体(EARPIH)的具体方程式的求解,证明了基于QTM的GoodChild[4]和Otoo[5 ]的离散投影方程是该投影的两种特例,并探讨了面积比性质,发现EARPIH投影的面积比变动范围相对狭小.支持该投影的球面剖分模型的地理坐标与球面三角格网之间的坐标转换可转换为均分三角网格的计算问题.

A New Projection for Spherical Triangle:Equal Angle Ratio Projection (EARP)

A 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.