Approximate conversion of spline curves
Computer Aided Geometric Design - Special issue: Topics in CAGD
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
Bezier and B-Spline Techniques
Bezier and B-Spline Techniques
Computer Aided Geometric Design
Optimal multi-degree reduction of Bézier curves with G2-continuity
Computer Aided Geometric Design
Fast approach for computing roots of polynomials using cubic clipping
Computer Aided Geometric Design
Multi-degree reduction of Bézier curves with constraints, using dual Bernstein basis polynomials
Computer Aided Geometric Design
Matrix representation for multi-degree reduction of Bézier curves
Computer Aided Geometric Design
Multi-degree reduction of Bézier curves using reparameterization
Computer-Aided Design
Linear methods for G1, G2, and G 3-Multi-degree reduction of Bézier curves
Computer-Aided Design
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In this paper we present a novel algorithm for the multi-degree reduction of Bezier curves with geometric constraints. Based on the given constraints, we construct an objective function which is abstracted from the approximation error in L"2-norm. Two types of geometric constraints are tackled. With the constraints of G^2-continuity at one endpoint and G^1-continuity (or C^r-continuity) at the other endpoint, we derive the optimal degree-reduced curves in explicit form. With the constraints of G^2-continuity at two endpoints, the problem of degree reduction is equivalent to minimizing a bivariate polynomial function of degree 4. Compared with the traditional methods, we derive the optimal degree-reduced curves more effectively. Finally, evaluation results demonstrate the effectiveness of our method.