A Fractal Method for Area Calculation of the Spherical Triangular Grid

Spherical triangle grid is a versatile discrete global grid, which is an effective scheme for spatial information representation in the digital earth domain. The general methods for calculating the area of a spherical triangular grid are not accurate. So a fractal method for area calculation is proposed. Firstly, in the same level, areas of spherical triangular grid recoded to 0 or 1 are computed respectively. Then multi-fractal area calculation functions are fitted, which is used as an area calculation model. Finally, the accuracy of the model is calculated by relative root mean square error. Experimental result shows that, with the increase of the number of multifractals, the accuracy of area calculation of grid cells increases and is controllable.