Geodesic Modelling of Planetary Relief

SUMMARY A METHOD for assembling and managing global terrain data is presented, the Geodesic Elevation Model. Derived from concepts in geometry, geography , geodesy, applied mathematics and computer science, GEM is designed to digitally archive and access measurements of points given in latitude, longitude and elevation from any source, by embedding them in a regular, polyhedral data structure. To do this, the model recursively tessellates a regular solid, initially an octahedron, into equilateral triangular facets. Spot measurements are encoded by successive approximation, mapping a given geodetic location to proximal centroids of nested triangles. As encoding proceeds, a new vertex appears at the center of each existing facet; an elevation code for it is entered in a linear tree, an estimated coordinate which locally wrinkles the polyhedron. The more times this takes place, the better is the approximation: each such step of encoding triples the number of facets, and diminishes horizontal and vertical error by the square root of three. As the structure is a regular geodesic grid, its horizontal coordinates are implicit by their ordering. Elevations alone are stored, using 1-bit flags quantizing height changes, triangulating the enclosed terrain with less than one bit of data per facet. Reconstruction of the data yields estimates of longitude, latitude and elevation anywhere on the planet, along with the error of estimate. Consequently, the slope, size and aspect of facets can be derived at any level of precision required, up to the limit of detail encoded for their neighborhoods. Beyond this, if desired, fictitious detail can be fractally synthesized, landforms resembling features above them in the hierarchy, smoothing the surface simultaneously. Local regions (small initial facets) can be encoded and stored independently, then subsequently merged at will to assemble larger terrain models. As measurements accumulate in a GEM database, superfluous and erroneous data are rejected with increasing frequency, due to the self-calibrating nature of the ensemble. Were sources of data and motivation sufficient, the relief of the entire Earth could be uniformly encoded in GEM format at a horizontal resolution of less than one kilometer, with a vertical precision of several meters, on a single disk volume.