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Journal articles on the topic 'Space-filling curve'

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Published: 4 June 2021
Last updated: 1 February 2022

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1

Zhang, Yuefeng. "Space-filling curve ordered dither." Computers & Graphics 22, no. 4 (August 1998): 559–63. http://dx.doi.org/10.1016/s0097-8493(98)00043-0.

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2

T.V, Sushma, and Roopa M. "Hilbert space filling curve using scilab." International Journal of Engineering & Technology 7, no. 1.9 (March 1, 2018): 129. http://dx.doi.org/10.14419/ijet.v7i1.9.9748.

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Space filling curve is used widely for linear mapping of multi-dimensional space. This provides a new line of thinking for various applications in image processing, Image compression being the most widely used. The paper highlights the locality preserving property of Hilbert Space filling curve which is essential in numerous applications such asin image compression, numerical analysis of a large aray of data, parallel processing and so on. A simplistic approach forusingHilbert Space filling curve using Scilab code has been presented.
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3

Ye, Ruisong, and Li Liu. "A Matrix Iterative Approach to Systematically Generate Hilbert-type Space-filling Curves." INTERNATIONAL JOURNAL OF COMPUTERS & TECHNOLOGY 14, no. 12 (December 30, 2015): 6281–94. http://dx.doi.org/10.24297/ijct.v14i12.1741.

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Hilbert-type space-filling curve has attracted much interest thanks to its mathematical importance and extensive applications in signal processing. In this paper, we construct the complete six Hilbert-type space-filling curves form amatrix point of view. The address matrix for each considered Hilbert-type space-filling curve can be easily generated by a recursive manner. Besides the six Hilbert-type space-filling curves, we also construct their corresponding variation versions. The merit of the matrix approach is that the iterative algorithm is easy to implement and can be generalized to produce any other Hilbert-type space-filling curves and their variation versions.
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4

Janakirama, Siva, K. Thenmozhi, Sundararaman Rajagopala, Har Narayan Upadhyay, John Bosco Balaguru Rayappan, and Rengarajan Amirtharaj. "Space Filling Curve for Data Filling: An Embedded Security Approach." Research Journal of Information Technology 6, no. 3 (March 1, 2014): 188–97. http://dx.doi.org/10.3923/rjit.2014.188.197.

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5

Forman, Noah. "Brownian bricklayer: A random space-filling curve." Statistics & Probability Letters 143 (December 2018): 43–46. http://dx.doi.org/10.1016/j.spl.2018.07.010.

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6

Luitjens, J., M. Berzins, and T. Henderson. "Parallel space-filling curve generation through sorting." Concurrency and Computation: Practice and Experience 19, no. 10 (2007): 1387–402. http://dx.doi.org/10.1002/cpe.1179.

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7

Sagan, Hans. "A geometrization of Lebesgue’s space-filling curve." Mathematical Intelligencer 15, no. 4 (September 1993): 37–43. http://dx.doi.org/10.1007/bf03024322.

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8

Kapil, Sajan, Prathamesh Joshi, Hari Vithasth Yagani, Dhirendra Rana, Pravin Milind Kulkarni, Ranjeet Kumar, and K. P. Karunakaran. "Optimal space filling for additive manufacturing." Rapid Prototyping Journal 22, no. 4 (June 20, 2016): 660–75. http://dx.doi.org/10.1108/rpj-03-2015-0034.

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Purpose In additive manufacturing (AM) process, the physical properties of the products made by fractal toolpaths are better as compared to those made by conventional toolpaths. Also, it is desirable to minimize the number of tool retractions. The purpose of this study is to describe three different methods to generate fractal-based computer numerical control (CNC) toolpath for area filling of a closed curve with minimum or zero tool retractions. Design/methodology/approach This work describes three different methods to generate fractal-based CNC toolpath for area filling of a closed curve with minimum or zero tool retractions. In the first method, a large fractal square is placed over the outer boundary and then rest of the unwanted curve is trimmed out. To reduce the number of retractions, ends of the trimmed toolpath are connected in such a way that overlapping within the existing toolpath is avoided. In the second method, the trimming of the fractal is similar to the first method but the ends of trimmed toolpath are connected such that the overlapping is found at the boundaries only. The toolpath in the third method is a combination of fractal and zigzag curves. This toolpath is capable of filling a given connected area in a single pass without any tool retraction and toolpath overlap within a tolerance value equal to stepover of the toolpath. Findings The generated toolpath has several applications in AM and constant Z-height surface finishing. Experiments have been performed to verify the toolpath by depositing material by hybrid layered manufacturing process. Research limitations/implications Third toolpath method is suitable for the hybrid layered manufacturing process only because the toolpath overlapping tolerance may not be enough for other AM processes. Originality/value Development of a CNC toolpath for AM specifically hybrid layered manufacturing which can completely fill any arbitrary connected area in single pass while maintaining a constant stepover.
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9

McClure, Mark. "Self-Similar Structure in Hilbert's Space-Filling Curve." Mathematics Magazine 76, no. 1 (February 1, 2003): 40. http://dx.doi.org/10.2307/3219131.

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10

Korchmáros, G., L. Storme, and T. Szőnyi. "Space-filling subsets of a normal rational curve." Journal of Statistical Planning and Inference 58, no. 1 (March 1997): 93–110. http://dx.doi.org/10.1016/s0378-3758(96)00063-8.

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11

Murali, P., and Veeramalai Sankaradass. "An efficient space filling curve based image encryption." Multimedia Tools and Applications 78, no. 2 (July 5, 2018): 2135–56. http://dx.doi.org/10.1007/s11042-018-6234-8.

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12

McClure, Mark. "Self-Similar Structure in Hilbert's Space-Filling Curve." Mathematics Magazine 76, no. 1 (February 2003): 40–47. http://dx.doi.org/10.1080/0025570x.2003.11953945.

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13

Leong, Thin Yin, and Chao Hsien Chu. "Wireless network design: a space-filling curve approach." International Journal of Mobile Network Design and Innovation 2, no. 3/4 (2007): 180. http://dx.doi.org/10.1504/ijmndi.2007.017322.

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14

Tofigh, Farzad, Majid Amiri, Negin Shariati, Justin Lipman, and Mehran Abolhasan. "Low-Frequency Metamaterial Absorber Using Space-Filling Curve." Journal of Electronic Materials 48, no. 10 (July 18, 2019): 6451–59. http://dx.doi.org/10.1007/s11664-019-07433-x.

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15

Prethee, R. "A Steganographic Technique using Reverse-S-Space Filling Curve." International Journal for Research in Applied Science and Engineering Technology V, no. IV (April 26, 2017): 461–66. http://dx.doi.org/10.22214/ijraset.2017.4082.

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16

Lance, Timothy, and Edward Thomas. "Arcs with Positive Measure and a Space-Filling Curve." American Mathematical Monthly 98, no. 2 (February 1991): 124. http://dx.doi.org/10.2307/2323941.

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17

Lance, Timothy, and Edward Thomas. "Arcs with Positive Measure and a Space-Filling Curve." American Mathematical Monthly 98, no. 2 (February 1991): 124–27. http://dx.doi.org/10.1080/00029890.1991.11995713.

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18

He, Zhijian, and Art B. Owen. "Extensible grids: uniform sampling on a space filling curve." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 78, no. 4 (October 26, 2015): 917–31. http://dx.doi.org/10.1111/rssb.12132.

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19

McVay, John, Ahmad Hoorfar, and Nader Engheta. "Thin absorbers using space-filling curve artificial magnetic conductors." Microwave and Optical Technology Letters 51, no. 3 (March 2009): 785–90. http://dx.doi.org/10.1002/mop.24186.

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20

Caramanica, Federico. "Microstrip multistopband filter based on prefractal space-filling curve." Microwave and Optical Technology Letters 56, no. 2 (December 23, 2013): 450–55. http://dx.doi.org/10.1002/mop.28116.

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21

Burstedde, Carsten, and Johannes Holke. "A Tetrahedral Space-Filling Curve for Nonconforming Adaptive Meshes." SIAM Journal on Scientific Computing 38, no. 5 (January 2016): C471—C503. http://dx.doi.org/10.1137/15m1040049.

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22

Gottstein, Cyprien, Philippe Raipin Parvedy, Michel Hurfin, Thomas Hassan, and Thierry Coupaye. "Partitioning Wide Area Graphs Using a Space Filling Curve." International Journal of Data Mining & Knowledge Management Process 11, no. 1 (January 31, 2021): 13–31. http://dx.doi.org/10.5121/ijdkp.2021.11102.

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Graph structure is a very powerful tool to model system and represent their actual shape. For instance, modelling an infrastructure or social network naturally leads to graph. Yet, graphs can be very different from one another as they do not share the same properties (size, connectivity, communities, etc.) and building a system able to manage graphs should take into account this diversity. A big challenge concerning graph management is to design a system providing a scalable persistent storage and allowing efficient browsing. Mainly to study social graphs, the most recent developments in graph partitioning research often consider scale-free graphs. As we are interested in modelling connected objects and their context, we focus on partitioning geometric graphs. Consequently our strategy differs, we consider geometry as our main partitioning tool. In fact, we rely on Inverse Space-filling Partitioning, a technique which relies on a space filling curve to partition a graph and was previously applied to graphs essentially generated from Meshes. Furthermore, we extend Inverse Space-Filling Partitioning toward a new target we define as Wide Area Graphs. We provide an extended comparison with two state-of-the-art graph partitioning streaming strategies, namely LDG and FENNEL. We also propose customized metrics to better understand and identify the use cases for which the ISP partitioning solution is best suited. Experimentations show that in favourable contexts, edge-cuts can be drastically reduced, going from more 34% using FENNEL to less than 1% using ISP.
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23

Shao, Yi Chuan, Xing Jia Yao, and Li Wei Tian. "Peano Space Filling Curve Applied in Managing P2P Service Resources." Applied Mechanics and Materials 220-223 (November 2012): 2508–11. http://dx.doi.org/10.4028/www.scientific.net/amm.220-223.2508.

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According to the deficiency of Chord algorithm supporting single keyword query only, a P2P framework-Peano Chord (PC) by combining the Peano and Chord is proposed for managing service resources, which combines Peano space filling curve and P2P Service Resources and supports DHT-based multi-keyword query and approximate query by means of Peano index to improve resources searching ability.
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24

El-Khouly, Essam, Hani Ghali, and Salah A. Khamis. "High Directivity Antenna Using a Modified Peano Space-Filling Curve." IEEE Antennas and Wireless Propagation Letters 6 (2007): 405–7. http://dx.doi.org/10.1109/lawp.2007.903492.

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25

Norman, Michael G., and Pablo Moscato. "The euclidean traveling salesman problem and a space-filling curve." Chaos, Solitons & Fractals 6 (January 1995): 389–97. http://dx.doi.org/10.1016/0960-0779(95)80046-j.

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26

Robertson, A. Guyan. "Multiplicativity of the uniform norm and independent functions." Bulletin of the Australian Mathematical Society 42, no. 1 (August 1990): 153–55. http://dx.doi.org/10.1017/s0004972700028264.

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It has long been known that there is a close connection between stochastic independence of continuous functions on an interval and space-filling curves [9]. In fact any two nonconstant continuous functions on [0, 1] which are independent relative to Lebesgue measure are the coordinate functions of a space filling curve. (The results of Steinhaus [9] have apparently been overlooked in more recent work in this area [3, 5, 6].)
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27

Deiotte, R., and R. La Valley. "COMPARISON OF SPATIOTEMPORAL MAPPING TECHNIQUES FOR ENORMOUS ETL AND EXPLOITATION PATTERNS." ISPRS Annals of Photogrammetry, Remote Sensing and Spatial Information Sciences IV-4/W2 (October 19, 2017): 7–13. http://dx.doi.org/10.5194/isprs-annals-iv-4-w2-7-2017.

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The need to extract, transform, and exploit enormous volumes of spatiotemporal data has exploded with the rise of social media, advanced military sensors, wearables, automotive tracking, etc. However, current methods of spatiotemporal encoding and exploitation simultaneously limit the use of that information and increase computing complexity. Current spatiotemporal encoding methods from Niemeyer and Usher rely on a Z-order space filling curve, a relative of Peano’s 1890 space filling curve, for spatial hashing and interleaving temporal hashes to generate a spatiotemporal encoding. However, there exist other space-filling curves, and that provide different manifold coverings that could promote better hashing techniques for spatial data and have the potential to map spatiotemporal data without interleaving. The concatenation of Niemeyer’s and Usher’s techniques provide a highly efficient space-time index. However, other methods have advantages and disadvantages regarding computational cost, efficiency, and utility. This paper explores the several methods using a range of sizes of data sets from 1K to 10M observations and provides a comparison of the methods.
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28

Sai Charan, Karnati Kumar, Seshadri Reddy Nagireddy, Sumana Bhattacharjee, and Aftab M. Hussain. "Design of Heating Coils Based on Space-Filling Fractal Curves for Highly Uniform Temperature Distribution." MRS Advances 5, no. 18-19 (2020): 1007–15. http://dx.doi.org/10.1557/adv.2020.17.

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AbstractHeating coils utilize the concept of resistive heating to convert electrical energy into thermal energy. Uniform heating of the target area is the key performance indicator for heating coil design. Highly uniform distribution of temperature can be achieved by using a dense metal distribution in the area under consideration, however, this increases the cost of production significantly. A low-cost and efficient heating coil should have excellent temperature uniformity while having minimum metal consumption. In this work, space-filling fractal curves, such as Peano curve, Hilbert curve and Moore curve of various orders, have been studied as geometries for heating coils. In order to compare them in an effective way, the area of the geometries has been held constant at 30 mm × 30 mm and a constant power of 2 W has been maintained across all the geometries. Further, the thickness of the metal coils and their widths have been kept constant for all geometries. Finite Element Analysis (FEA) results show Hilbert and Moore curves of order-4, and Peano curve of order-3 outperform the typical double-spiral heater in terms of temperature uniformity and metal coil length.
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29

Gong, Jiang Bo, Lei Luo, and Jun Hu. "Tool Path Generation Algorithm Based on the Double Spiral Filling Curve." Applied Mechanics and Materials 190-191 (July 2012): 790–93. http://dx.doi.org/10.4028/www.scientific.net/amm.190-191.790.

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The steering frequent problems in the five-axis NC machining tool path planning based on space-filling curve method was researched, then a double spiral space-filling curve was proposed. Owing to frequently reverse, it was adopted that an arc on transition instead of the right angle, so the impact in tool and the part in machining process was reduced. Combined with the free surface, the plane filling curve with the surface parameters corresponding to the mapping on the surface thereby generated the idea of machining tool paths. Finally, the method was used for a specific surface, and the effectiveness of the method was verified.
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30

Sagan, Hans. "An Elementary Proof that Schoenberg's Space-Filling Curve Is Nowhere Differentiable." Mathematics Magazine 65, no. 2 (April 1, 1992): 125. http://dx.doi.org/10.2307/2690494.

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31

Jho, Cheung-Wonn. "A Study on Improvement of Halftoning using Random Space Filling Curve." Journal of Digital Policy and Management 12, no. 1 (January 28, 2014): 415–21. http://dx.doi.org/10.14400/jdpm.2014.12.1.415.

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32

Lawder, J. K., and P. J. H. King. "Querying multi-dimensional data indexed using the Hilbert space-filling curve." ACM SIGMOD Record 30, no. 1 (March 2001): 19–24. http://dx.doi.org/10.1145/373626.373678.

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33

Sagan, Hans. "An Elementary Proof that Schoenberg's Space-Filling Curve Is Nowhere Differentiable." Mathematics Magazine 65, no. 2 (April 1992): 125–28. http://dx.doi.org/10.1080/0025570x.1992.11995996.

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34

Zang, Yu, Hua Huang, and Lei Zhang. "Efficient Structure-Aware Image Smoothingby Local Extrema on Space-Filling Curve." IEEE Transactions on Visualization and Computer Graphics 20, no. 9 (September 2014): 1253–65. http://dx.doi.org/10.1109/tvcg.2014.2298017.

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35

Moon, B., H. V. Jagadish, C. Faloutsos, and J. H. Saltz. "Analysis of the clustering properties of the Hilbert space-filling curve." IEEE Transactions on Knowledge and Data Engineering 13, no. 1 (2001): 124–41. http://dx.doi.org/10.1109/69.908985.

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36

Tsinganos, Panagiotis, Bruno Cornelis, Jan Cornelis, Bart Jansen, and Athanassios Skodras. "The Effect of Space-filling Curves on the Efficiency of Hand Gesture Recognition Based on sEMG Signals." International journal of electrical and computer engineering systems 12, no. 1 (April 21, 2021): 23–31. http://dx.doi.org/10.32985/ijeces.12.1.3.

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Over the past few years, Deep learning (DL) has revolutionized the field of data analysis. Not only are the algorithmic paradigms changed, but also the performance in various classification and prediction tasks has been significantly improved with respect to the state-of-the-art, especially in the area of computer vision. The progress made in computer vision has produced a spillover in many other domains, such as biomedical engineering. Some recent works are directed towards surface electromyography (sEMG) based hand gesture recognition, often addressed as an image classification problem and solved using tools such as Convolutional Neural Networks (CNN). This paper extends our previous work on the application of the Hilbert space-filling curve for the generation of image representations from multi-electrode sEMG signals, by investigating how the Hilbert curve compares to the Peano- and Z-order space-filling curves. The proposed space-filling mapping methods are evaluated on a variety of network architectures and in some cases yield a classification improvement of at least 3%, when used to structure the inputs before feeding them into the original network architectures.
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37

Chen, Chi-Chang, and Zheng-Da Xie. "A STUDY OF FRACTAL GEOMETRY IN WIRELESS SENSOR NETWORKS." International Journal of Engineering Technologies and Management Research 8, no. 4 (April 24, 2021): 58–70. http://dx.doi.org/10.29121/ijetmr.v8.i4.2021.925.

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Fractal geometry is a subject that studies non-integer dimensional figures. Most of the fractal geometry figures have a nested or recursive structure. This paper attempts to apply the nested or recursive structure characteristics of fractal geometry to wireless sensor networks. We selected two filling curves, Node-Gosper and Moore, as our research subjects. Node-Gosper Curve is a curve based on node-replacement with a fractal dimension of two. Its first-order graph consists of seven basic line segments. When the hierarchy becomes larger, it can be filled with a hexagonal-like shape. To allow the mobile anchor node of wireless sensor networks to walk along this curve, the number of levels of the Node-Gosper Curve can be adjusted according to parameters such as the sensing area and transmission range. Many space-filling curves have the common shortcoming that they cannot loop on their own, that is, the starting point and the end point are not close, which will cause the mobile anchor node to use extra paths from the end point back to the starting point. The Moore curve has a self-loop, i.e., the starting point and the ending point are almost at the same position. This paper applies Moore curve to the path planning of the mobile anchor node. We can use this path to traverse the entire sensing area and stay in the central point of each square cluster to collect the information of the nodes where the events occurred. The self-loop characteristic of the Moore curve is expected to reach each sensor to collect data faster than other space filling curves, that is, the transmission latency of the sensor traversal will be reduced
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38

S.JeyaKarthikka, N., S. Bhaggiaraj, and V. Sumathy. "Secure and Efficient Data Retrieval Process based on Hilbert Space Filling Curve." International Journal of Computer Applications 91, no. 4 (April 18, 2014): 36–40. http://dx.doi.org/10.5120/15873-4885.

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39

Akhendra, P., and N. Bheema. "Fractal Parallel Stacked Inductor using Modified Hilbert Space Filling Curve for RFIC." Communications on Applied Electronics 7, no. 5 (August 25, 2017): 1–4. http://dx.doi.org/10.5120/cae2017652660.

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40

Olakkenghil, Senoj Joseph, and K. Baskaran. "An FPGA Task Placement Algorithm Using Reflected Binary Gray Space Filling Curve." International Journal of Reconfigurable Computing 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/495080.

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With the arrival of partial reconfiguration technology, modern FPGAs support tasks that can be loaded in (removed from) the FPGA individually without interrupting other tasks already running on the same FPGA. Many online task placement algorithms designed for such partially reconfigurable systems have been proposed to provide efficient and fast task placement. A new approach for online placement of modules on reconfigurable devices, by managing the free space using a run-length based representation. This representation allows the algorithm to insert or delete tasks quickly and also to calculate the fragmentation easily. In the proposed FPGA model, the CLBs are numbered according to reflected binary gray space filling curve model. The search algorithm will quickly identify a placement for the incoming task based on first fit mode or a fragmentation aware best fit mode. Simulation experiments indicate that the proposed techniques result in a low ratio of task rejection and high FPGA utilization compared to existing techniques.
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41

Koga, Takanori, and Noriaki Suetake. "Image coarsening by using space-filling curve for decomposition-based image enhancement." Journal of Visual Communication and Image Representation 24, no. 7 (October 2013): 806–18. http://dx.doi.org/10.1016/j.jvcir.2013.05.008.

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42

Jeya Bharathi, S., K. Thiagarajan, and K. Navaneetham. "Parikh factor matrices for finite words of rectangular Hilbert space filling curve." International Journal of Engineering & Technology 7, no. 2.31 (May 29, 2018): 50. http://dx.doi.org/10.14419/ijet.v7i2.31.13396.

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Ordered Factor Patterns in a word over an ordered alphabet aredefined. Also, Parikh StrictlyAscending FactorMatrix and Parikh StrictlyDescending Factor Matrix of a given word are introduced. The relation of these matrices with Ordered Factor Patterns is discussed. Moreover, the ParikhStrictly Ascending FactorMatrices and the Parikh Strictly Descending FactorMatricesfor finitewords of Rectangular Hilbert Space Filling Curve are determined.
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43

Sagan, Hans. "An analytic proof of the nowhere differentiability of Hilbert's space-filling curve." Journal of the Franklin Institute 330, no. 4 (July 1993): 763–66. http://dx.doi.org/10.1016/0016-0032(93)90052-v.

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44

Glover, Jennifer, and Dan O'Boy. "Acoustic space filling curve metamaterials for grazing flow in Jet engine inlets." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 263, no. 6 (August 1, 2021): 394–406. http://dx.doi.org/10.3397/in-2021-1458.

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Acoustic metamaterials research has grown exponentially in the past 10 years driven by the advances in manufacturing and an increased understanding of damaging environment noise. 2020 was the first noise reduction target as set by Advisory Council for Aircraft Research and Innovation in Europe with a relative 50% decrease. This was missed by current Jet engine noise control technology; however, metamaterials offer an encouraging alternative. Space Filling Curves (SFC) have the potential to provide a lightweight, thin, high performance acoustic liner. SFC have a history in mathematical geometry dating back to the 1890's but are a comparatively new addition to acoustics. They are designed with a sub-wavelength curled cross-section creating a maze-like pattern which slows acoustic wave propagation through the liner enabling characteristics such as negative refraction and low frequency attenuation. This paper contains a comparison of some of the most promising SFC metamaterial acoustic liner designs, in terms of the fundamental theory of the design category and a discussion of the reflection, absorption and transmission characteristics in terms of a grazing flow conditions. Computer simulation and impedance tube based experimental testing compares the designs. The paper concludes with future application for aeroacoustics with particular focus on the engine inlet.
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45

Shen, Hongyao, Bing Liu, Senxin Liu, and Jianzhong Fu. "Five-Axis Freeform Surface Color Printing Technology Based on Offset Curve Path Planning Method." Applied Sciences 10, no. 5 (March 3, 2020): 1716. http://dx.doi.org/10.3390/app10051716.

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Great progress has been made in 2D color printing with inkjet technology, and mature related products have come out, but there still exists great developmental space in 3D color printing. Therefore, a new path planning method based on the offset curve for 3D inkjet technology is proposed in this paper. Offset curves are generated on a freeform surface with geodesic equidistance, and then points for color printing are generated along the offset curves. In this paper, the principle of color printing technology with a 5-axis platform and the offset curve path planning (OCPP) method are presented. In addition, comparisons between the OCPP and adaptive filling algorithm based on the section method (AFSM) have been implemented. The OCPP significantly increased the rate of the theoretical filling area from 0.89 to 0.99 on a freeform surface.
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46

Ujang, Uznir, Francois Anton, Suhaibah Azri, Alias Abdul Rahman, and Darka Mioc. "3D Hilbert Space Filling Curves in 3D City Modeling for Faster Spatial Queries." International Journal of 3-D Information Modeling 3, no. 2 (April 2014): 1–18. http://dx.doi.org/10.4018/ij3dim.2014040101.

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The advantages of three dimensional (3D) city models can be seen in various applications including photogrammetry, urban and regional planning, computer games, etc. They expand the visualization and analysis capabilities of Geographic Information Systems on cities, and they can be developed using web standards. However, these 3D city models consume much more storage compared to two dimensional (2 D) spatial data. They involve extra geometrical and topological information together with semantic data. Without a proper spatial data clustering method and its corresponding spatial data access method, retrieving portions of and especially searching these 3D city models, will not be done optimally. Even though current developments are based on an open data model allotted by the Open Geospatial Consortium (OGC) called CityGML, its XML-based structure makes it challenging to cluster the 3D urban objects. In this research, the authors propose an opponent data constellation technique of space-filling curves (3D Hilbert curves) for 3D city model data representation. Unlike previous methods, that try to project 3D or n-dimensional data down to 2D or 3D using Principal Component Analysis (PCA) or Hilbert mappings, in this research, they extend the Hilbert space-filling curve to one higher dimension for 3D city model data implementations. The query performance was tested for single object, nearest neighbor and range search queries using a CityGML dataset of 1,000 building blocks and the results are presented in this paper. The advantages of implementing space-filling curves in 3D city modeling will improve data retrieval time by means of optimized 3D adjacency, nearest neighbor information and 3D indexing. The Hilbert mapping, which maps a sub-interval of the ([0,1]) interval to the corresponding portion of the d-dimensional Hilbert's curve, preserves the Lebesgue measure and is Lipschitz continuous. Depending on the applications, several alternatives are possible in order to cluster spatial data together in the third dimension compared to its clustering in 2 D.
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47

Jin, Xin, Hai Wang, and Caixin Feng. "Space Charge Effect and Resistance Switching in Doped Monocrystalline Silicones." Applied Sciences 9, no. 3 (January 28, 2019): 434. http://dx.doi.org/10.3390/app9030434.

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In this work, we report the nonlinear carriers’ transport in n-doped monocrystalline silicone with millimeter-scale length. Ohm, effective trap filling, and Mott–Gurney regimes are distinguished from the current–voltage (I–V) curve. Two critical voltages are identified for the lower and upper limitations of an effective trap-filling regime. Meanwhile, the electrode spacing, temperature, and magnetic field dependence of the two critical voltages are demonstrated experimentally. In particular, we propose that the effective trap-filling process is irreversible under electric field. It is observed that the hysteresis of I–V curve initiates from the effective trap-filling regime and extends to the Mott–Gurney regime, forming the resistance-switching loop. In addition, the temperature dependence and the magnetic field dependence of the resistance-switching loop are reported. The above observations may shed light on dopants engineering on carrier dynamics in a space charge regime and further advance resistance-switching devices technology.
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Hou, Fang, Cheng Hui Huang, and Ji Yuan Lu. "A Multi-Dimensional Data Storage Using Quad-Tree and Z-Ordering." Applied Mechanics and Materials 347-350 (August 2013): 2436–41. http://dx.doi.org/10.4028/www.scientific.net/amm.347-350.2436.

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Multi-dimensional applications use tree structure to store data and space filling curves to traverse data. Most frequently used Quad-tree and Z-ordering curve are analyzed. By importing these to a HDF5 file format, a multi-dimensional data storage subsystem is constructed. Performance test results show in a sequential reading application environment, this method is feasible and efficient.
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Hussain, Ali A., and Rehab F. Hassan. "Enhancing Quad Tree for Spatial Index Using Space Filling Curves." Engineering and Technology Journal 38, no. 1B (April 25, 2020): 15–25. http://dx.doi.org/10.30684/etj.v38i1b.264.

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Spatial indexes, such as those based on the Quad Tree, are important in spatial databases for the effective implementation of queries with spatial constraints, especially when queries involve spatial links. The quaternary trees are a very interesting subject, given the fact that they give the ability to solve problems in a way that focuses only on the important areas with the highest density of information. Nevertheless, it is not without the disadvantages because the search process in the quad tree suffers from the problem of repetition when reaching the terminal node and return to the behavior of another way in the search and lead to the absorption of large amounts of time and storage. In this paper, the quad tree was improved by combining it with one of the space filling curve types, resulting in reduced storage space requirements and improved implementation time
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Peter Devadoss, C., Balasubramanian Sankaragomathi, and Thirugnanasambantham Monica. "Region of Interest Based MRI Brain Image Compression Using Peano Space Filling Curve." Current Signal Transduction Therapy 11, no. 2 (November 10, 2016): 114–20. http://dx.doi.org/10.2174/1574362411666160616124516.

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