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View all- Ren ZChen GLu W(2019)Malware visualization methods based on deep convolution neural networksMultimedia Tools and Applications10.1007/s11042-019-08310-979:15-16(10975-10993)Online publication date: 16-Dec-2019
Generation of Spatial Orders and Space-Filling Curves
Pages 1791 - 1800
Abstract
Space-filling curves have been found useful for many applications in diverse fields. A space-filling curve is a path in a 2<sup>r</sup>×2<sup>r</sup> raster domain, which visits each location exactly once. In mathematical terms, space-filling curves linearize a 2D integer space, bijectively mapping the space to the integer line. An algorithm is presented, which generates a large number of space-filling curves/spatial orders. Functions are derived such that the code of each location can be calculated from its coordinates and, conversely, a location code can be decoded to yield the coordinates. The algorithm first generates generate 4×4 spatial orders; they subsequently may be scaled up to any desired domain of size 2<sup>r</sup> × 2<sup>r</sup>. The underlying theory of the algorithm, the processes for scaling up, encoding, and decoding are described in detail. The curves are generated as a set of incongruent curves, followed, if required, by the sets of associated congruent curves. A number of space-filling curves are illustrated.
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Published: 01 June 2015
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Cited By
View all- Ren ZChen GLu W(2019)Malware visualization methods based on deep convolution neural networksMultimedia Tools and Applications10.1007/s11042-019-08310-979:15-16(10975-10993)Online publication date: 16-Dec-2019