An iterative algorithm for G2G2 multiwise merging of Bézier curves

This paper presents an iterative algorithm for G2G2 multiwise merging of Bézier curves. By using the G2G2 constraint, the L2L2 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 G2G2 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 G3G3 constraints, other energy functionals and curve representations are also outlined. Several comparative examples are provided to demonstrate the effectiveness of the proposed method.