Triangular Berstein-Be´zier patches
Computer Aided Geometric Design
Discrete Be´zier curves and surfaces
Mathematical methods in computer aided geometric design II
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
Distance for degree raising and reduction of triangular Bézier surfaces
Journal of Computational and Applied Mathematics
Connections between two-variable Bernstein and Jacobi polynomials on the triangle
Journal of Computational and Applied Mathematics
Optimal multi-degree reduction of triangular Bézier surfaces with corners continuity in the norm L2
Journal of Computational and Applied Mathematics
Constrained degree reduction of polynomials in Bernstein-Bézier form over simplex domain
Journal of Computational and Applied Mathematics
Constrained multi-degree reduction of Bézier surfaces using Jacobi polynomials
Computer Aided Geometric Design
A note on constrained degree reduction of polynomials in Bernstein-Bézier form over simplex domain
Journal of Computational and Applied Mathematics
Multi-degree reduction of Bézier curves with constraints, using dual Bernstein basis polynomials
Computer Aided Geometric Design
Multi-degree reduction of triangular Bézier surfaces with boundary constraints
Computer-Aided Design
Interpolation function of generalized q−bernstein-type basis polynomials and applications
Proceedings of the 7th international conference on Curves and Surfaces
Journal of Computational and Applied Mathematics
Explicit G2-constrained degree reduction of Bézier curves by quadratic optimization
Journal of Computational and Applied Mathematics
An explicit method for G3 merging of two Bézier curves
Journal of Computational and Applied Mathematics
Construction of dual B-spline functions
Journal of Computational and Applied Mathematics
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We propose a novel approach to the problem of multi-degree reduction of Bezier triangular patches with prescribed boundary control points. We observe that the solution can be given in terms of bivariate dual discrete Bernstein polynomials. The algorithm is very efficient thanks to using the recursive properties of these polynomials. The complexity of the method is O(n^2m^2), n and m being the degrees of the input and output Bezier surfaces, respectively. If the approximation-with appropriate boundary constraints-is performed for each patch of several smoothly joined triangular Bezier surfaces, the result is a composite surface of global C^r continuity with a prescribed order r. Some illustrative examples are given.