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Tensor Product q −Bernstein Bézier Patches

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Numerical Analysis and Its Applications (NAA 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5434))

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Abstract

In this work we define a new de Casteljau type algorithm, which is in barycentric form, for the q −Bernstein Bézier curves. We express the intermediate points of the algorithm explicitly in two ways. Furthermore we define tensor product patches, based on this algorithm, depending on two parameters. Degree elevation procedure for the tensor product patch is studied. Finally, the matrix representation of tensor product patch is given and we find the transformation matrix between classical tensor product Bézier patch and tensor product q −Bernstein Bézier patch.

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, Dokuz Eylül University, Fen Edebiyat Fakültesi, Tınaztepe Kampüsü, Buca, 35160, İzmir, Turkey

    Çetin Dişibüyük & Halil Oruç

Authors
  1. Çetin Dişibüyük
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  2. Halil Oruç
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Editor information

Editors and Affiliations

  1. Institute for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. Bl. 25-A, 1113, Sofia, Bulgaria

    Svetozar Margenov

  2. FNSE, Department of Numerical Methods and Statistics, University of Rousse, 8 Studentska str., 7017, Rousse, Bulgaria

    Lubin G. Vulkov

  3. Department of Informatics and Mathematical Modelling, Technical University of Denmark, 2800, Kongens, Lyngby, Denmark

    Jerzy Waśniewski

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© 2009 Springer-Verlag Berlin Heidelberg

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Dişibüyük, Ç., Oruç, H. (2009). Tensor Product q −Bernstein Bézier Patches. In: Margenov, S., Vulkov, L.G., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2008. Lecture Notes in Computer Science, vol 5434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00464-3_28

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  • DOI: https://doi.org/10.1007/978-3-642-00464-3_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00463-6

  • Online ISBN: 978-3-642-00464-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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