The PYXIS DGGS SDK uses the Snyder Equal Area Aperture 3 Hexagon (ISEA3H) DGGS to partition the Earth into a tessellation of nested hexagonal cells.  This is accomplished by projecting a square root three mesh from an icosahedron to an authentic sphere using a reverse Lambert Equal Area Projection (Snyder 1992). The process of partitioning a sphere in this manner includes the creation of 12 pentagonal cells at the vertices of the icosahedron, 5/6 the area of the hexagonal cells. The Snyder method, while preserving area, minimizes distortion in the cells through a loss of equal angles (non-conformal); distortion of the grid is concentrated along a great circle arc from vertex to the center each icosahedron face.   To form an Earth-centric reference, the vertices are arranged to align with minimized effects of the resulting 12 pentagonal artifacts (Sahr, 2003).

The PYXIS DGGS SDK includes operations to generate and exploit geometry of the ISEA3H on the authalic sphere.  The SDK provides efficient code for lossless bidirectional conversion between latitudinal and longitudinal coordinates (Any Datum) and PYXIS cell indices (Icosahedron) through forward and reverse Snyder Projection (ISEA).

1. John P. Snyder,  "An Equal-Area Map Projection For Polyhedral Globes", Cartographica, Vol. 29, No. 1, 1992

2. Sahr, K., White, D., and Kimerling, A.J., 2003. Geodesic discrete global grid systems. Cartography and Geographic Information Science 30(2):121-134.

Idan Shatz,
Jul 24, 2016, 8:00 AM