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Filling N-sided Holes

  • Conference paper
Modeling in Computer Graphics

Part of the book series: IFIP Series on Computer Graphics ((IFIP SER.COMP.))

Abstract

Smooth surface patches, such as Gregory patch, Brown’s square and Nielson- Foley patch, which interpolate a given function and its derivatives on the boundary of a rectangle or a triangle, with incompatible twist terms, have been constructed with rational parametric representation by using boolean sum techniques, convex combination methods and procedural methods to fill N-sided holes. Chiyokura and Kimura proposed a representation of Gregory patch in Bernstein-Bezier form, where interior control points are expressed as convex combinations of incompatible control points via rational blending functions. No such representation is known for solutions to the above problem over pentagonal domains. We construct smooth rational surface patches which interpolate a given function and its cross-boundary C k derivatives on the boundary of any convex polygonal domain with incompatible twist data. These patches are represented in S-patch form, where control points are expressed as convex combinations of incompatible control points via rational blending functions. This constructive rational technique provides novel solutions for blending incompatible C k data over polygonal domains. In particular, new solutions are constructed for rectangular and triangular patches as well.

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Author information

Authors and Affiliations

  1. Department of Computer and Information Sciences, University of California, Santa Cruz, CA, 95064, USA

    Suresh Lodha

Authors
  1. Suresh Lodha
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Editor information

Editors and Affiliations

  1. Istituto per la Matematica Applicata, C.N.R., Via De Marini, 6 Torre di Francia, 16149, Genova, Italy

    Bianca Falcidieno

  2. Dept. of Information Science Faculty of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku Tokyo, 113, Japan

    Tosiyasu L. Kunii

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© 1993 Springer-Verlag Berlin Heidelberg

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Lodha, S. (1993). Filling N-sided Holes. In: Falcidieno, B., Kunii, T.L. (eds) Modeling in Computer Graphics. IFIP Series on Computer Graphics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-78114-8_20

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  • DOI: https://doi.org/10.1007/978-3-642-78114-8_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-78116-2

  • Online ISBN: 978-3-642-78114-8

  • eBook Packages: Springer Book Archive

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