Peano Curve

Peano curves are space-filling curves first introduced by Italian mathematician Giuseppe Peano (1890). A variation and more complicated form is called Hilbert curves because Hilbert (1891) visualized the space filling idea described in Peano curves and later referred to it as “topological monsters” (Bartholdi and Platzman 1988).

Peano and Hilbert curves have been used to find all-nearest-neighbors (Chen and Chang 2011) and spatial ordering of geographic data (Guo and Gahegan 2006). Conceptually, Peano curves use algorithms to assign spatial orders to points in 2D space and map the points onto one-dimensional (1D) space.

Following the spatial order, a point in 2D space can be mapped onto the 1D line underneath, and the connected line in 2D space (on the right) is the Peano curve. Following the spatial orders along the 1D line, spatial clustering can be achieved by classification with many methods.

The value of the binary-digit scale (n) will be calculated as the grid scale value, 2^n. This value will then be used to generate a 2^n x 2^n grid.