Quantization

Populating DGGS cells with data values is a fundamental operation in a DGGS. Strategies for sampling data preserve the fidelity of the original data. These principles are fundamental to digital signal processing (See Shannon-Nyquist Theorem).

Some DGGS structures are optimized for statistically valid sampling. Hexagonal grids achieve higher spatial resolution with the same number of samples as rectangular grids and the isotropy of local neighborhoods provides uniform transformations.  Use of the ISEA3H to align raw data also has the advantage of providing very fine increments between resolutions.  Generally, the closest packing, and the finer cell areas change between resolutions, the more efficient the sampling rate.

Some DGGS structures provide a lattice that converges monotonically with each refinement.  This is an important characteristic when indices are used to represent points in vector space.  As an example, square quadtree structures do not represent more precision with each additional refinement; centroidal points used to define vector geometries (lines and polygons) can move further away from a real value with a refinement.  However, when centroids of child cells align with a parent’s vertices, as they do on some hexagonal DGGS tessellations, the resulting hierarchical indices will converge monotonically as it refines (as seen in the video demonstration below).  This gives those tessellations the characteristics of a Cartesian coordinate lattice where each decimal place indicates a level of precision.



Subpages (2): Raster Data Vector Data
Comments