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

Abstract

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.