There are many possible DGGS, each with their own advantages and disadvantages. Criteria for choosing an appropriate tessellation include: shape, adjacency, connectivity, orientation, self-similarity, refinement, and packing properties. Three shapes provide regular tiling of the plane: quadrilateral, triangle, and hexagon. Quadrilateral cells are an attractive choice since they are commonly used within raster imagery and textures, hardware devices, and image-processing algorithms. They are widely adopted in raster data structures. Triangular cells can be rendered very efficiently and are supported by many built-in graphic mesh functions. As a lattice, they provide an efficient network connectivity for interpolation of values such as elevation models. Hexagonal cells are favored for their statistically optimal sampling, close packing, and uniform adjacency. They are a preferred shape for modeling dynamic environmental systems. Quadrilaterals and triangles can be decomposed or refined into self-similar congruent shapes to form hierarchical structures. Triangular lattices and hexagonal tessellations form Delaunay/Voronoi duals and so transformations between them provide dual utility. Essentially,
The generation of a tessellation on a sphere is mathematically intensive. All methods must deal with the fact that a perfect regular partition for the surface of a sphere does not exist. Most methods start with regular polyhedron and then project the cells to the sphere. Preserving cell size or shape is an inevitable compromise in spherical geometry because projected shapes cannot be both equal area and conformal. Preservation of cell area is a preferred trait when a DGGS is intended to represent information consistently across the entire globe at the same resolution. The core value of the PYXIS DGGS SDK is high fidelity representation and integration of disparate geospatial data values sufficient for statistically valid spatial analysis. The ISEA3H is optimized for sampling and representation of information within its close packing cells and square root three refinement. The PYXIS DGGS SDK features the use of the ISEA3H DGGS. |