Chebyshev economization for parametric surfaces
Computer Aided Geometric Design
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
Journal of Computational and Applied Mathematics
Best one-sided approximation of polynomials under L1 norm
Journal of Computational and Applied Mathematics - Selected papers of the international symposium on applied mathematics, August 2000, Dalian, China
Application of Legendre--Bernstein basis transformations to degree elevation and degree reduction
Computer Aided Geometric Design
Optimal multi-degree reduction of Bézier curves with constraints of endpoints continuity
Computer Aided Geometric Design
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Computer Aided Geometric Design
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
Application of Chebyshev II-Bernstein basis transformations to degree reduction of Bézier curves
Journal of Computational and Applied Mathematics
Constrained multi-degree reduction of Bézier surfaces using Jacobi polynomials
Computer Aided Geometric Design
Multi-degree reduction of Bézier curves with constraints, using dual Bernstein basis polynomials
Computer Aided Geometric Design
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
Constrained multi-degree reduction of triangular Bézier surfaces using dual Bernstein polynomials
Journal of Computational and Applied Mathematics
Multi-degree reduction of Bézier curves using reparameterization
Computer-Aided Design
Multiple degree elevation and constrained multiple degree reduction for DP curves and surfaces
Computers & Mathematics with Applications
An explicit method for G3 merging of two Bézier curves
Journal of Computational and Applied Mathematics
| Hi-index | 7.29 |
In this paper, we revisit G^2-constrained degree reduction of Bezier curves which has been solved in our previous work by using iterative methods. We propose an explicit and effective method for G^1-constrained degree reduction and C^1G^2-constrained degree reduction. Our main idea is to express the distance function defined in the L"2-norm as a strictly convex quadratic function of two variables, which becomes a quadratic optimization problem. We can explicitly obtain the unique solution by solving two linear equations such that the distance function is minimized. The existence of the unique solution is also proved.