Degree reduction of Be´zier curves
Computer-Aided Design
Chebyshev economization for parametric surfaces
Computer Aided Geometric 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
Least squares approximation of Bézier coefficients provides best degree reduction in the L2-norm
Journal of Approximation Theory
GPU-based trimming and tessellation of NURBS and T-Spline surfaces
ACM SIGGRAPH 2005 Papers
Optimal multi-degree reduction of Bézier curves with G2-continuity
Computer Aided Geometric Design
Optimal multi-degree reduction of triangular Bézier surfaces with corners continuity in the norm L2
Journal of Computational and Applied Mathematics
Approximating tensor product Bézier surfaces with tangent plane continuity
Journal of Computational and Applied Mathematics
Multi-degree reduction of triangular Bézier surfaces with boundary constraints
Computer-Aided Design
Optimal multi-degree reduction of Bézier curves with geometric constraints
Computer-Aided Design
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This paper first shows how the Bézier coefficients of a given degree n polynomial are perturbed so that it can be reduced to a degree m ( n) polynomial with the constraint that continuity of a prescribed order is preserved at the two endpoints. The perturbation vector, which consists of the perturbation coefficients, is determined by minimizing a weighted Euclidean norm. The optimal degree n - 1 approximation polynomial is explicitly given in Bézier form. Next the paper proves that the problem of finding a best L2-approximation over the interval [0, 1] for constrained degree reduction is equivalent to that of finding a minimum perturbation vector in a certain weighted Euclidean norm. The relevant weights are derived. This result is applied to computing the optimal constrained degree reduction of parametric Bézier curves in the L2-norm.