Representation and generation of space-filling curves: a higher-order functional approach
hossein narimani rad, Farid Karimipour · Journal of Spatial Science · 2019
Space-Filling Curves (SFCs) map a multi-dimensional cellular space into one dimension. Although several algorithms have been introduced that can generate different SFCs, they barely consider deploying SFCs for non-cellular spaces. This article presents a new higher-order functional approach that enables a new level of abstraction which separates the SFC representation (i.e. a set of functions that define the SFC) from the algorithms that use it (e.g. SFC generator, point ordering, etc.). We describe the proposed approach and, as example cases, show how different SFCs can be used as the ordering mechanism for generating the K-d trees and R-trees for a set of arbitrarily distributed points using the proposed higher-order representation of the SFCs.