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Curve subdivision with arc-length control

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Abstract

In this paper we present a new nonstationary, interpolatory, curve subdivision scheme. We show that the scheme converges and the subdivision curve is continuous. Moreover, starting with the chord length parametrization of the initial polygon, we obtain a subdivision curve parametrized by a multiple of the arc-length. The proposed method focuses on convexity preservation, limiting the oscillations of the subdivision curve and avoiding artifacts. A bound for the Hausdorff distance between the limit curve and the initial polygon is also obtained.

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References

  1. Chalmoviasky P, Juttler B (2007) A nonlinear circle-preserving subdivision scheme. Adv Comput Math 27: 375–400

    Article  MathSciNet  Google Scholar 

  2. Deslauriers G, Dubuc S (1989) Symmetric iterative interpolation processes. Constr Approx 5(1): 49–68

    Article  MATH  MathSciNet  Google Scholar 

  3. Dubuc S (1986) Interpolation through an iterative scheme. J Math Anal Appl 114: 185–204

    Article  MATH  MathSciNet  Google Scholar 

  4. Dyn N (1992) Subdivision schemes in computer-aided geometric design. In: Light W(eds) Advances in numerical analysis, vol 2. Clarendon Press, Oxford, pp 36–104

    Google Scholar 

  5. Dyn N, Floater M, Hormann K (2009) Four point curve subdivision based on iterated chordal and centripetal parameterizations. Comput Aided Geom Des 26: 279–286

    Article  MathSciNet  Google Scholar 

  6. Dyn N, Levin D, Gregory JA (1987) A four-point interpolatory subdivision scheme for curve design. Comput Aided Geom Des 4: 257–268

    Article  MATH  MathSciNet  Google Scholar 

  7. Kobbelt L, Schröder P (1998) A multiresolution framework for variational subdivision. ACM Trans Graph 17(4): 209–237

    Article  Google Scholar 

  8. Marinov M, Dyn N, Levin D (2005) Geometrically controlled 4-point interpolatory schemes. In: Advances in multiresolution for geometric modelling, pp 302–315

  9. Yang X (2006) Normal based subdivision scheme for curve design. Comput Aided Geom Des 23: 243–260

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Instituto de Cibernética, Matemática y Física, ICIMAF, Havana, Cuba

    Victoria Hernández-Mederos, Jorge C. Estrada-Sarlabous & Silvio R. Morales

  2. Durham University, Durham, UK

    Ioannis Ivrissimtzis

Authors
  1. Victoria Hernández-Mederos
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  2. Jorge C. Estrada-Sarlabous
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  3. Silvio R. Morales
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  4. Ioannis Ivrissimtzis
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Corresponding author

Correspondence to Victoria Hernández-Mederos.

Additional information

Communicated by C. H. Cap.

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Hernández-Mederos, V., Estrada-Sarlabous, J.C., Morales, S.R. et al. Curve subdivision with arc-length control. Computing 86, 151–169 (2009). https://doi.org/10.1007/s00607-009-0068-1

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  • DOI: https://doi.org/10.1007/s00607-009-0068-1

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