The Visual Computer

, Volume 11, Issue 7, pp 360–368 | Cite as

Approximate conversion of a rational boundary gregory patch to a nonuniform B-spline surface

  • Yoshimasa Tokuyama
  • Kouichi Konno
Original Articles


A rational boundary Gregory patch is characterized by the facts that anyn-sided loop can be smoothly interpolated and that it can be smoothly connected to an adjacent patch. Thus, it is well-suited to interpolate complicated wire frames in shape modeling. Although a rational boundary Gregory patch can be exactly converted to a rational Bézier patch to enable the exchange of data, problems of high degree and singularity tend to arise as a result of conversion. This paper presents an algorithm that can approximately convert a rational boundary Gregory patch to a bicubic nonuniform B-spline surface. The approximating surface hasC1 continuity between its inner patches.

Key words

Rational boundary Gregory patch Gregory patch Nonuniform B-spline surface Approximation Conversion C1 continuity Least squares 


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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Yoshimasa Tokuyama
    • 1
  • Kouichi Konno
    • 1
  1. 1.Software DivisionRICOH, Co., Ltd.TokyoJapan

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