Burstedde, Carsten und Holke, Johannes und Isaac, Tobin (2018) On the Number of Face-Connected Components of Morton-Type Space-Filling Curves. Foundations of Computational Mathematics, Seiten 1-26. Springer. doi: 10.1007/s10208-018-9400-5. ISSN 1615-3375. (im Druck)
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Kurzfassung
The Morton- or z-curve is one example for a space-filling curve: Given a level of refinement L iit maps the interval [0, 2^(dL)) one-to-one to a set of d-dimensional cubes of edge length 2^-L that form a subdivision of the unit cube. Similar curves have been proposed for triangular and tetrahedral unit domains. In contrast to the Hilbert curve that is continuous, the Morton-type curves produce jumps between disconnected subdomains. We prove that any contiguous subinterval of the curve divides the domain into a bounded number of face-connected subdomains. For the hypercube case in arbitrary dimension, the subdomains are star-shaped and the bound is indeed two. For the simplicial case in dimension 2, the bound is 2(L - 1), and in dimension 3 it is 2L + 1, where L is the depth of refinement. We supplement the paper with theoretical and computational studies on the distribution of the number of jumps. For the hypercube curve, we can characterize the distribution by the fraction of segments of a given length that have no jump, and find that the fraction has a lower bound of 1/(2^d -1) and an asymptotic upper bound of 1/2. For the simplicial curve, over 90% of all segments have three components or less.
elib-URL des Eintrags: | https://elib.dlr.de/124370/ | ||||||||||||||||
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Dokumentart: | Zeitschriftenbeitrag | ||||||||||||||||
Titel: | On the Number of Face-Connected Components of Morton-Type Space-Filling Curves | ||||||||||||||||
Autoren: |
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Datum: | 5 Oktober 2018 | ||||||||||||||||
Erschienen in: | Foundations of Computational Mathematics | ||||||||||||||||
Referierte Publikation: | Ja | ||||||||||||||||
Open Access: | Ja | ||||||||||||||||
Gold Open Access: | Nein | ||||||||||||||||
In SCOPUS: | Ja | ||||||||||||||||
In ISI Web of Science: | Ja | ||||||||||||||||
DOI: | 10.1007/s10208-018-9400-5 | ||||||||||||||||
Seitenbereich: | Seiten 1-26 | ||||||||||||||||
Herausgeber: |
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Verlag: | Springer | ||||||||||||||||
ISSN: | 1615-3375 | ||||||||||||||||
Status: | im Druck | ||||||||||||||||
Stichwörter: | Space-filling curve Adaptive mesh refinement Morton code | ||||||||||||||||
HGF - Forschungsbereich: | Luftfahrt, Raumfahrt und Verkehr | ||||||||||||||||
HGF - Programm: | Raumfahrt | ||||||||||||||||
HGF - Programmthema: | Technik für Raumfahrtsysteme | ||||||||||||||||
DLR - Schwerpunkt: | Raumfahrt | ||||||||||||||||
DLR - Forschungsgebiet: | R SY - Technik für Raumfahrtsysteme | ||||||||||||||||
DLR - Teilgebiet (Projekt, Vorhaben): | R - Vorhaben SISTEC (alt) | ||||||||||||||||
Standort: | Köln-Porz | ||||||||||||||||
Institute & Einrichtungen: | Institut für Simulations- und Softwaretechnik > High Performance Computing | ||||||||||||||||
Hinterlegt von: | Holke, Johannes | ||||||||||||||||
Hinterlegt am: | 07 Dez 2018 14:27 | ||||||||||||||||
Letzte Änderung: | 01 Dez 2019 03:00 |
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- On the Number of Face-Connected Components of Morton-Type Space-Filling Curves. (deposited 07 Dez 2018 14:27) [Gegenwärtig angezeigt]
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