The making of a Global Grid - Remembering my escape from flatland

Quaternary Triangular Mesh (QTM) is a spherical subdivision scheme for encoding vector geodata across a planet as recursive triangular subdivisions of an octahedron. This model of location and its hierarchical coordinate system evolved from experiments with a hierarchical raster data structure for encoding terrain relief named DEPTH (Delta Encoded Polynomial Terrain Hierarchy). This 2D pyramid- type structure encoded attributes (surface elevations) explicitly and locations (grid cell indices) implicitly. The paper describes how DEPTH evolved into QTM through a global discrete data grid called Geodesic Elevation Model (GEM), which more resembled QTM than a raster model. It used DEPTH to encode surface elevations in a forest of geodesic triangular quadtrees instead of in a planar rectangular quadtree. All three models were designed to make limitations of data accuracy and scale explicit. DEPTH and GEM capture elevations as ranges of values that decrease as the structure densifies, and perform limited interpolation. QTM captures vector data by encoding spherical 2D locations to the extent that their positional accuracy, certainty, or precision warrant, but did not use DEPTH. This paper is a memoir that summarizes the thinking that went into these data models and explores how properties and deficiencies of one led to the other. It does not present any breakthroughs or new applications. Rather, it documents inventions that influenced subsequent developments of discrete global grids, and might still do so.