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Continued fractions and digital lines with irrational slopes
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics. (Digital geometry and mathematical morphology)
2008 (English)In: Proceedings of DGCI, the 14th International Conference on DISCRETE GEOMETRY for COMPUTER IMAGERY. DGCI 2008, Berlin Heidelberg: Springer-Verlag , 2008, 93-104 p.Conference paper, Published paper (Refereed)
Abstract [en]

This paper expands on previous work on relationships between digital linesand continued fractions (CF). The main result is a parsimonious description of the construction of the digital line based only on the elements of the CF representing its slope and containing only simple integer computations. The description reflects the hierarchy of digitization runs, which raises the possibility of dividing digital lines into equivalence classes depending on the CF expansions of their slopes. Our work is confined to irrational slopes since, to our knowledge, there exists no such description for these,  in contrast to rational slopes which have been extensively examined. The description is exact and does not use approximations by rationals. Examples of lines withirrational slopes and with very simple digitization patterns are presented. These include both slopes with periodic and non-periodic CF expansions, i.e.\ both quadratic surds and other irrationals.

Place, publisher, year, edition, pages
Berlin Heidelberg: Springer-Verlag , 2008. 93-104 p.
Series
Lecture Notes in Computer Science, ISSN 0302-9743 ; 4992
Keyword [en]
digital geometry; theory of digital lines; irrational slope; continued fraction; quadratic surd
National Category
Discrete Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-105920DOI: 10.1007/978-3-540-79126-3ISBN: 978-3-540-79125-6 (print)OAI: oai:DiVA.org:uu-105920DiVA: diva2:222867
Projects
Ph.D. project
Available from: 2009-06-09 Created: 2009-06-09 Last updated: 2009-06-26Bibliographically approved

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Uscka-Wehlou, Hanna

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