Explicit G2-constrained Merging of a Pair of Bézier Curves by Control Point Optimization

This paper presents a simple and explicit method for G2-constrained merging of a pair of Bézier curves by minimizing the l2 distance defined in terms of control points. After expressing the l2 distance as a quadratic function of two parameters, the optimally merged curve can be explicitly obtained, which is achieved by control point optimization such that the l2 distance is minimized. The existence of the unique solution is shown by proving that the l2 distance is convex. The proposed method is explicit and efficient since it is non-iterative and expressed by known control points. Numerical examples demonstrate the effectiveness of the new method.