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Properties of G1 Continuity Conditions Between Two B-Spline Surfaces

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Advances in Computer Graphics (CGI 2006)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 4035))

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Abstract

This paper addresses some properties of G 1 continuity conditions between two B-spline surfaces with arbitrary degrees and generally structured knots. Key issues addressed in the paper include necessary G 1 continuity conditions between two B-spline surfaces, general connecting functions, continuities of the general connecting functions, and intrinsic conditions of the general connecting functions along the common boundary. In general, one may use piecewise polynomial functions, i.e. B-spline functions, as connecting functions for G 1 connection of two B-spline surfaces. Based on the work reported in this paper, some recent results in literature using linear connecting functions are special cases of the general connecting functions reported in this paper. In case that the connecting functions are global linear functions along the common boundary commonly used in literature, the common boundary degenerates as a Bézier curve for proper G 1 connection. Several examples for connecting two uniform biquadratic B-spline surfaces with G 1 continuity are also presented to demonstrate the results.

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Authors and Affiliations

  1. Hangzhou Dianzi University, Hangzhou, Zhejiang, 310018, P.R. China

    Nailiang Zhao

  2. City University of Hong Kong, Kowloon, Hong Kong SAR, China

    Weiyin Ma

Authors
  1. Nailiang Zhao
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  2. Weiyin Ma
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Editor information

Editors and Affiliations

  1. The University of Tokyo,, P.O. Box

    Tomoyuki Nishita

  2. State Key Lab. of CAD&CG, Zhejiang Univerisity,, 310027, Hangzhou, China

    Qunsheng Peng

  3. Max Planck Institute for Computer Science, Saarbrücken, Germany

    Hans-Peter Seidel

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© 2006 Springer-Verlag Berlin Heidelberg

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Zhao, N., Ma, W. (2006). Properties of G1 Continuity Conditions Between Two B-Spline Surfaces. In: Nishita, T., Peng, Q., Seidel, HP. (eds) Advances in Computer Graphics. CGI 2006. Lecture Notes in Computer Science, vol 4035. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11784203_73

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  • DOI: https://doi.org/10.1007/11784203_73

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-35638-7

  • Online ISBN: 978-3-540-35639-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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