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NURBS curve blending using extension


Curve and surface blending is an important operation in CAD systems, in which a non-uniform rational B-spline (NURBS) has been used as the de facto standard. In local corner blending, two curves intersecting at that corner are first made disjoint, and then the third blending curve is added-in to smoothly join the two curves with G1-or G2-continuity. In this paper we present a study to solve the joint problem based on curve extension. The following nice properties of this extension algorithm are exploited in depth: (1) The parameterization of the original shapes does not change; (2) No additional fragments are created. Various examples are presented to demonstrate that our solution is simple and efficient.

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Corresponding author

Correspondence to Yong-jin Liu.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 60603085 and 60736019), the Hi-Tech Research and Development (863) Program of China (No. 2007AA01Z336), and Tsinghua Basic Research Foundation, China

Expanded based on “Note on industrial applications of Hu’s surface extension algorithm” by Yu Zang, Yong-Jin Liu, et al., which appeared in GMP2008, LNCS, 4975:304–314

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Liu, Yj., Qiu, Rq. & Liang, Xh. NURBS curve blending using extension. J. Zhejiang Univ. Sci. A 10, 570–576 (2009).

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Key words

  • Curve blending
  • Curve fairing
  • Curve extension
  • Non-uniform rational B-spline (NURBS)

CLC number

  • TN391.72