Cubic Grids

The original expanded cubic grid proprosed by Sadourny (19??) was based on the gnomonic projection (grid shown below). Although this grid has excellent properties such as near uniform resolution and perfect scaling with resolution it is not based on an orthogonal coordinate system. Instead we followed the proposal of Rancic et al. (19??) who use a conformal mapping to generate a cubic grid (shown below).

Gnomonic cubic grid

Conformal cubic grid

The conformal grid does not scale as well as the gnomonic grid but is still orders of magnitude better than the latitude-longitude grid.