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Novel Wearable Antennas for Wireless Communication Systems
Published in Albert Sabban, Novel Wearable Antennas for Communication and Medical Systems, 2017
In mathematics, a space-filling curve is a curve whose range contains the entire two-dimensional unit square. Most space-filling curves are constructed iteratively as a limit of a sequence of piecewise linear continuous curves, each one closely approximating the space-filling limit. Where two sub-curves intersect (in the technical sense) in space-filling curves, there is self-contact without self-crossing. A space-filling curve can be (everywhere) self-crossing if its approximation curves are self-crossing. A space-filling curve's approximations can be self-avoiding, as presented in Figure 8.46. In three dimensions, self-avoiding approximation curves can even contain joined ends. Space-filling curves are special cases of fractal constructions. No differentiable space-filling curve can exist.
Improved security in the genetic algorithm-based image steganography scheme using Hilbert space-filling curve
Published in The Imaging Science Journal, 2019
Gyan Singh Yadav, Aparajita Ojha
A Hilbert space-filling curve or simply a Hilbert curve is a continuous fractal curve drawn by joining point locations in a particular space depending upon the value of an iteration number. These locations can be mapped onto the image pixel locations (see Figure 4). If the number of iteration is z then point locations will be generated in a row \ column. Hence, the total number of points will be or . Hilbert curve generation algorithm starts with initialization of complex numbers p, q and , and subsequent points will be generated as follows.
Editorial
Published in Journal of Spatial Science, 2021
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. Rad and Karimipour present a new higher-order functional approach that enables a new level of abstraction which separates the SFC representation from algorithms that use it. They describe the proposed approach and show how different SFCs can be used as the ordering mechanism for generating K-d trees and R-trees for a set of arbitrarily distributed points using proposed higher-order representation of the SFCs.