Implementing natural neighbour interpolation implies the construction of a geometric Voronoi diagram, however this is not strictly the case. Since the Delaunay triangulation is the dual graph of the Voronoi diagram, all the information needed to perform natural neighbour interpolation is already implicit within the triangulation itself. Algorithms to determine natural neighbours from the Delaunay triangulation can be found in several papers within the literature[4][5]. Unfortunately the relative complexity of natural neighbour interpolation means that it is slower than barycentric interpolation by a considerable margin.
The challenge was clear: achieve a quantum leap in speed while preserving extreme flexibility, minimal storage, regional map support, and dynamic update capabilities. Standard Highway Hierarchies were a starting point, but we needed something more – a uniquely OsmAnd solution.
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