Representation and generation of space-filling curves: a higher-order functional approach. Issue 3 (2nd September 2021)

• Record Type: Journal Article
• Authors: Narimani Rad, Hossein; Karimipour, Farid
• Is Part Of: Journal of spatial science. Volume 66:Issue 3(2021)
• Page Start: 459
• Page End: 479
• Publication Date: 2021-09-02
• Subjects: Space-filling curves -- higher-order functions -- spatial ordering -- K-d tree -- R-tree; Geographic information systems -- Periodicals; Cartography -- Periodicals; Surveying -- Periodicals; Geodesy -- Periodicals; Photogrammetry -- Periodicals; Cartography; Geodesy; Geographic information systems; Photogrammetry; Surveying; Periodicals; 526.05
• DOI: 10.1080/14498596.2019.1668870
• Languages: English
• ISSNs: 1449-8596

Abstract

ABSTRACT: 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.