Geodesic
$L_\infty $-locality of three-dimensional Peano curves
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Topology and physics, Tome 302 (2018), pp. 234-267.

Voir la notice de l'article provenant de la source Math-Net.Ru

A theory and corresponding algorithms are developed for fast and accurate evaluation of the $L_\infty $-locality (i.e., the maximum cube-to-line ratio in the maximum metric) for polyfractal three-dimensional Peano curves.
Keywords: maximum metric, three-dimensional Peano curves, dyadic curves, cubically decomposable curves, cube-to-linear ratio.
Mots-clés : polyfractal curves 
@article{TM_2018_302_a10,
     author = {A. A. Korneev and E. V. Shchepin},
     title = {$L_\infty $-locality of three-dimensional {Peano} curves},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {234--267},
     publisher = {mathdoc},
     volume = {302},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2018_302_a10/}
}
TY  - JOUR
AU  - A. A. Korneev
AU  - E. V. Shchepin
TI  - $L_\infty $-locality of three-dimensional Peano curves
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2018
SP  - 234
EP  - 267
VL  - 302
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2018_302_a10/
LA  - ru
ID  - TM_2018_302_a10
ER  - 
%0 Journal Article
%A A. A. Korneev
%A E. V. Shchepin
%T $L_\infty $-locality of three-dimensional Peano curves
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2018
%P 234-267
%V 302
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2018_302_a10/
%G ru
%F TM_2018_302_a10
A. A. Korneev; E. V. Shchepin. $L_\infty $-locality of three-dimensional Peano curves. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Topology and physics, Tome 302 (2018), pp. 234-267. http://geodesic.mathdoc.fr/item/TM_2018_302_a10/

[1] Bader M., Space-filling curves: An introduction with applications in scientific computing, Springer, Berlin, 2013 | MR

[2] Gotsman C., Lindenbaum M., “On the metric properties of discrete space-filling curves”, IEEE Trans. Image Process., 5:5 (1996), 794–797 | DOI

[3] Haverkort H., An inventory of three-dimensional Hilbert space-filling curves, 2011, arXiv: 1109.2323v2 [cs.CG]

[4] Haverkort H., How many three-dimensional Hilbert curves are there?, 2017, arXiv: 1610.00155v2 [cs.CG] | MR

[5] Haverkort H., van Walderveen F., “Locality and bounding-box quality of two-dimensional space-filling curves”, Comput. Geom., 43:2 (2010), 131–147, arXiv: 0806.4787v2 [cs.CG] | DOI | MR

[6] Niedermeier R., Reinhardt K., Sanders P., “Towards optimal locality in mesh-indexings”, Discrete Appl. Math., 117:1–3 (2002), 211–237 | DOI | MR

[7] D. K. Shalyga, “On the accurate calculation of the cube-to-linear ratio of Peano curves”, Keldysh Institute preprints, 2014, 088, 13 pp.

[8] E. V. Shchepin, “On fractal Peano curves”, Proc. Steklov Inst. Math., 247 (2004), 272–280 | MR

[9] Shchepin E. V., “On Hölder maps of cubes”, Math. Notes, 87:5–6 (2010), 757–767 | DOI

[10] E. V. Shchepin, “The Leibniz differential and the Perron–Stieltjes integral”, J. Math. Sci., 233:1 (2018), 157–171 | DOI | MR

[11] E. V. Shchepin, “Attainment of maximum cube-to-linear ratio for three-dimensional Peano curves”, Math. Notes, 98:6 (2015), 971–976 | DOI | DOI | MR

[12] E. V. Shchepin, K. E. Bauman, “Minimal Peano curve”, Proc. Steklov Inst. Math., 263 (2008), 236–256 | DOI | MR

[13] S. S. Tokarev, Cubic Peano curve, Graduate Qualifying Work, Fac. Inf. Technol., Moscow State Psychol. Pedagog. Univ., M., 2010