Linear methods for G1G1, G2G2, and G3G3—Multi-degree reduction of Bézier curves

In this paper, linear methods to find the multi-degree reduction of Bézier curves with G1G1-, G2G2-, and G3G3-continuity at the end points of the curves are derived. This is a significant improvement over existing geometric continuity degree reduction methods. The general equations for G2G2- and G3G3-multi-degree reduction schemes are non-linear; we were able to simplify these non-linear equations to linear ones by requiring C1C1-continuity. Our linear solution is given in an explicit, non-iterative form, and thus has lower computational costs than existing methods which were either non-linear or iterative. Further, there are no other existing G3G3-methods for multi-degree reduction. We give some examples and figures to demonstrate the efficiency, simplicity, and stability of our methods.

► We derive linear methods for multi-degree reduction of Bézier curves. ► Our linear solutions are given in an explicit, non-iterative form. ► Our methods have G1G1-, G2G2-, or G3G3-continuity at end points. ► For the G2G2 and G3G3 methods, we also require C1C1-continuity at end points.