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Conic-like subdivision curves on surfaces

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Abstract

In this paper, we introduce a novel nonlinear curve subdivision scheme, suitable for designing curves on surfaces. The scheme is based on the concept of geodesic conic Bézier curves, which represents a natural extension of geodesic Bézier curves for the rational quadratic case. Given a set of points on a surface S, the scheme generates a sequence of geodesic polygons that converges to a continuous curve on S. If the surface S is C 2-continuous, then the subdivision curve is C 1-continuous and if S is a plane, then the limit curve is a conic Bézier spline curve. Each section of the subdivision curve depends on a free parameter that may be used to obtain a local control of the shape of the subdivision curve. Extending these results to triangulated surfaces, it is shown that the scheme has the convex hull property and that it is suitable for free-form design on triangulations.

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Acknowledgements

The first two authors has been supported by TWAS-UNESCO-CNPq and Visgraf-IMPA Brazil in the frame of the TWAS-UNESCO/CNPq-Brazil Associateship Ref. 3240173676 and Ref. 3240173677, respectively. We thank to the anonymous referees for their valuable criticisms and suggestions.

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Authors and Affiliations

  1. ICIMAF, Havana, Cuba

    Jorge Estrada Sarlabous, Victoria Hernández Mederos & Nayla López Gil

  2. UFAL, Maceió, Brazil

    Dimas Martínez Morera

  3. IMPA, Rio de Janeiro, Brazil

    Luiz Velho

Authors
  1. Jorge Estrada Sarlabous
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  2. Victoria Hernández Mederos
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  3. Dimas Martínez Morera
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  4. Luiz Velho
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  5. Nayla López Gil
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Corresponding author

Correspondence to Dimas Martínez Morera.

Additional information

This paper is an extended version of the work “Geodesic conic subdivision curves on surfaces” presented in the Conference SIBGRAPI’2011, held in Maceió, Brazil, in August 2011.

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Estrada Sarlabous, J., Hernández Mederos, V., Martínez Morera, D. et al. Conic-like subdivision curves on surfaces. Vis Comput 28, 971–982 (2012). https://doi.org/10.1007/s00371-012-0728-6

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  • DOI: https://doi.org/10.1007/s00371-012-0728-6

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