An iterative algorithm for G(2) multiwise merging of Bezier curves

作者：Lu, Lizheng^*; Jiang, Chengkai

来源：Journal of Computational and Applied Mathematics, 2016, 296: 352-361.

DOI：10.1016/j.cam.2015.10.007

• Bezier curve
• Merging
• Geometric continuity
• L-2 distance
• Iterative method

This paper presents an iterative algorithm for G(2) multiwise merging of Bezier curves. By using the G(2) constraint, the 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 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 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.

• 出版日期2016-4
• 单位浙江工商大学