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Two Extensions of the Quadratic Nonuniform B -Spline Curve with Local Shape Parameter Series

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  • Xiang Kong
  • Jun Chen

Abstract

Two extensions of the quadratic nonuniform B -spline curve with local shape parameter series, called the W 3 D 3 C 1 P 2 spline curve and the W 3 D 4 C 2 P 1 spline curve, are introduced in the paper. The new extensions not only inherit most excellent properties of the quadratic nonuniform B -spline curve but also can move locally toward or against the fixed control polygon by varying the shape parameter series. They are C 1 and C 2 continuous separately. Furthermore, the W 3 D 3 C 1 P 2 spline curve includes the quadratic nonuniform B -spline curve as a special case. Two applications, the interpolation of the position and the corresponding tangent direction and the interpolation of a line segment, are discussed without solving a system of linear functions. Several numerical examples indicated that the new extensions are valid and can easily be applied.

Suggested Citation

  • Xiang Kong & Jun Chen, 2021. "Two Extensions of the Quadratic Nonuniform B -Spline Curve with Local Shape Parameter Series," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-12, September.
    • Handle: RePEc:hin:jnlmpe:9980320
    DOI: 10.1155/2021/9980320
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