An iterative algorithm for multiwise merging of Bézier curves

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• 作者：Lizheng Lu ; ^{lulz99@163.com" class="auth_mail" title="E-mail the corresponding author} ; Chengkai Jiang
• 关键词：Bé ; zier curve ; Merging ; Geometric continuity ; L2L2 distance ; Iterative method
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：296
• 期：Complete
• 页码：352-361
• 全文大小：760 K

文摘

This paper presents an iterative algorithm for 03c52b2f81e74243080" title="Click to view the MathML source">G²$G^2$ multiwise merging of Bézier curves. By using the 03c52b2f81e74243080" title="Click to view the MathML source">G²$G^2$ constraint, the L₂$L_2$ distance is represented after simplification as a quartic polynomial in two parameters relating to the magnitudes of end tangents of the merged curve. These two parameters are restricted in a feasible region, in order for the merged curve to preserve the specified directions of end tangents. Then 03c52b2f81e74243080" title="Click to view the MathML source">G²$G^2$ multiwise merging is formulated as a constrained minimization problem, and the classic projected Newton method is applied to find the minimizer. Some extensions of multiwise merging using c64f60fd9" title="Click to view the MathML source">G³$G^3$ constraints, other energy functionals and curve representations are also outlined. Several comparative examples are provided to demonstrate the effectiveness of the proposed method.