JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2026, Vol. 61 ›› Issue (6): 127-134.doi: 10.6040/j.issn.1671-9352.0.2025.156

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Control point generation and optimal interpolation for quadratic uniform B-splines with parameters

XIE Jin1,2, CHEN Xiaoquan1, WANG Shaoliang1, JIA Yushu1   

  1. 1. School of Mathematics and Statistics, Hefei University, Hefei 230601, Anhui, China;
    2. Journal Editorial Office, Hefei University, Hefei 230601, Anhui, China
  • Published:2026-06-04

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Abstract: In the modeling of B-spline curves that interpolate specific data points, it is often necessary to inversely solve for their control points. Once the control points are determined, a curve shapes that satisfy engineering requirements can be generated. An inverse method for determining the control points of interpolating quadratic B-spline curves is proposed based on the minimization of internal energy. The method selects a control vertex with minimal internal energy and then determines all control vertices step by step using a recursive relationship. After the control points are established, the optimal interpolating curve is determined by minimizing internal energy and achieving optimal approximation, tailored to engineering needs. Finally, the effectiveness of the proposed method is demonstrated through numerical examples.

Key words: quadratic uniform B-Spline, interpolation curve, minimization of internal energy, optimal interpolation

CLC Number: 

  • O241
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