Another Definition for Digital Tangents

  • Thierry Monteil
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6607)


The aim of this short note is to describe the set of finite words that appear in the cutting sequences of a smooth curve to arbitrary small scale. This language strictly contains the factors of Sturmian words, and can be decided by a linear time algorithm.


Cutting sequence symbolic coding tangent estimation multigrid convergence digital straight segment Sturmian word 


  1. 1.
    Creutzburg, E., Hübler, A., Wedler, V.: On-line erkennung digitaler geradensegmente in linearer zeit. In: Proceedings of GEO-BILD 1982, Wiss. Beitrage der FSU Jena, pp. 48–65 (1982)Google Scholar
  2. 2.
    Hermann, S., Klette, R.: A comparative study on 2d curvature estimators. In: International Conference on Computing: Theory and Applications, pp. 584–589 (2007)Google Scholar
  3. 3.
    Klette, R., Rosenfeld, A.: Digital straightness—a review. Discrete Appl. Math. 139(1-3), 197–230 (2004), MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Kulpa, Z.: On the properties of discrete circles, rings, and disks. Computer Graphics and Image Processing 10(4), 348–365 (1979), CrossRefGoogle Scholar
  5. 5.
    Lothaire, M.: Algebraic combinatorics on words, Encyclopedia of Mathematics and its Applications. In: Berstel, J., Séébold, P. (eds.) Sturmian Words, vol. 90. Cambridge University Press, Cambridge (2002)Google Scholar
  6. 6.
    Mignosi, F.: On the number of factors of Sturmian words. Theoret. Comput. Sci. (Algorithms Automat. Complexity Games) 82(1), 71–84 (1991), MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Fogg, N.P.: Substitutions in dynamics, arithmetics and combinatorics. Lecture Notes in Mathematics, vol. 1794, p. 402. Springer, Berlin (2002),, chapter 6, Sturmian Sequences (by Pierre Arnoux)CrossRefzbMATHGoogle Scholar
  8. 8.
    Rojas, C., Troubetzkoy, S.: Coding Discretizations of Continuous Functions (2009), preprint, available at
  9. 9.
    Smillie, J., Ulcigrai, C.: Symbolic coding for linear trajectories in the regular octagon (2009), preprint, available at
  10. 10.
    de Vieilleville, F., Lachaud, J.-O., Feschet, F.: Convex digital polygons, maximal digital straight segments and convergence of discrete geometric estimators. J. Math. Imaging Vision 27(2), 139–156 (2007), MathSciNetCrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Thierry Monteil
    • 1
  1. 1.CNRS – Université Montpellier 2France

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