Bidirectional mapping between rhombic triacontahedron and icosahedral hexagonal discrete global grid systems

Abstract

ABSTRACT The icosahedron is currently the mainstream polygon in research and application of discrete global grid systems (DGGS). However, compared to the rhombic triacontahedron (RT), the icosahedron has disadvantages, such as lower sphere-fitting accuracy, greater projection distortion, and difficulty in incorporating the matrix structure for geospatial data storage. More importantly, the special positional relationship between the rhombic triacontahedron and the Earth enables it to effectively support event simulations related to geographical locations. To this end, bidirectional mapping of the hexagonal grid between the RT and icosahedron was proposed, which can efficiently integrate the existing datasets and algorithms of icosahedral DGGS into RT DGGS, thereby achieving seamless conversion between heterogeneous grid systems. We established geometric and topological correlations between the RT and icosahedron, abstracted the spatial algebraic structures of hexagonal grids on the two different polygons, and constructed mapping relationships between them. Finally, conversion between heterogeneous grid indices was achieved using dual quaternions. Experiments revealed that the proposed method was 3.9150 and 2.8151 times more efficient at grid conversion from RT to icosahedron and from icosahedron to RT, respectively, than was a method using latitude/longitude coordinates as a medium.