200 SW 35th Street Corvallis, Oregon 97333 White, Denis, A.J. Kimerling, K. Shar, and L. Song. Comparing area and shape distortion on polyhedral-based recursive partitions of the sphere.
Regular grid sampling structures in the plane are a common spatial framework for many studies.
Constructing grids with desirable properties such as equality of area and shape is more difficult on a sphere. We studied the distortion characteristics of recursive partitions of the surface of the globe starting with the octahedron and icosahedron polyhedral models. We measured the area and perimeter of each cell at each level of recursion for each method on each model using each density ratio. We looked at these basic measurements and their statistics using graphs of variation with recursion level, sums of squares analyses of variation, histograms of the distributions, maps of the spatial variation, and correlograms. The Snyder projection performed best in area distortion and the Gnomonic projection performed best in compactness distortion.