In this paper, linear methods to find the multi-degree reduction of Bézier curves with G 1-, G 2-, and G 3-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 G 2- and G 3-multi-degree reduction schemes are non-linear; we were able to simplify these non-linear equations to linear ones by requiring C 1-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 G 3-methods for multi-degree reduction. We give some examples and figures to demonstrate the efficiency, simplicity, and stability of our methods.
- Bézier curves
- Geometric continuity
- Multiple degree reduction
ASJC Scopus subject areas
- Computer Science Applications
- Computer Graphics and Computer-Aided Design
- Industrial and Manufacturing Engineering