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.

摘要

空间填充曲线 (SFC) 将多维细胞空间映射到一维。尽管已经引入了几种可以生成不同 SFC 的算法，但他们几乎没有考虑为非蜂窝空间部署 SFC。本文介绍了一种新的高阶函数方法，该方法实现了一个新的抽象级别，它将 SFC 表示（即定义 SFC 的一组函数）与使用它的算法（例如 SFC 生成器、点排序等）分开。 . 我们描述了所提出的方法，并作为示例，展示了如何使用不同的 SFC 作为排序机制，使用所提出的 SFC 的高阶表示为一组任意分布的点生成 Kd 树和 R 树。