Degree reduction of Be´zier curves
Computer-Aided Design
Degree reduction of Be´zier curves
Selected papers of the international symposium on Free-form curves and free-form surfaces
The geometry of optimal degree reduction of Be´zier curves
Computer Aided Geometric Design
Computer Aided Geometric Design - Special issue dedicated to Paul de Faget de Casteljau
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Distance for degree raising and reduction of triangular Bézier surfaces
Journal of Computational and Applied Mathematics
Computer Aided Geometric Design
Optimal multi-degree reduction of Bézier curves with G2-continuity
Computer Aided Geometric Design
Multi-degree reduction of Bézier curves with constraints, using dual Bernstein basis polynomials
Computer Aided Geometric Design
Optimal multi-degree reduction of Bézier curves with geometric constraints
Computer-Aided Design
| Hi-index | 0.00 |
In this paper, linear methods to find the multi-degree reduction of Bezier 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.