Piece by Piece: a Method of Cartographic Line Generalization Using Regular Hexagonal Tessellation

Several methods of automated line simplification exist, but most involve parameters selected arbitrarily or heuristically, with little or no reference to the scale change between original data and generalized output. Also, while routines such as the Douglas-Peucker algorithm achieve simplified line correlates by retention of characteristic points from the input line, little analysis has been devoted to whether those points remain characteristic at the generalization target scale. A new algorithm is presented based on regular hexagonal tessellation. Mosaics of equilateral hexagons are used to sample lines, where the hexagon width relates directly to target scale. Inside each hexagon tessera, input line vertices are collapsed to a single vertex, and the resulting set of points constitute simplified correlate lines appropriate for the generalized map scale. Hexagonal width is derived in relation to target scale in two ways: by applying the Radical Law, and by selecting measures pursuant to Tobler's ideas on spatial resolution. Results yield a useful scale-specific method of line generalization.