Approximate merging of a pair of Bezier curves

Shi-Min Hu Tsinghua University Ruofeng Tong Zhejiang University Tao JU Tsinghua University Jia-Guang Sun Tsinghua University

Geometric Modeling and Processing mathscidoc:1608.16082

Computer Aided Design, 33, (2), 125-136, 2001
This paper deals with the merging problem, i.e. to approximate two adjacent Bézier curves by a single Bézier curve. A novel approach for approximate merging is introduced in the paper by using the constrained optimization method. The basic idea of this method is to find conditions for the precise merging of Bézier curves first, and then compute the constrained optimization solution by moving the control points. “Discrete” coefficient norm in L2 sense and “squared difference integral” norm are used in our method. Continuity at the endpoints of curves are considered in the merging process, and approximate merging with points constraints are also discussed. Further, it is shown that the degree elevation of original Bézier curves will reduce the merging error.
Approximate merging, Bezier curves
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  title={Approximate merging of a pair of Bezier curves},
  author={Shi-Min Hu, Ruofeng Tong, Tao JU, and Jia-Guang Sun},
  booktitle={Computer Aided Design},
Shi-Min Hu, Ruofeng Tong, Tao JU, and Jia-Guang Sun. Approximate merging of a pair of Bezier curves. 2001. Vol. 33. In Computer Aided Design. pp.125-136.
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