Improvement on constrained multi-degree reduction of Bezier surfaces using Jacobi polynomials

摘要

In 2009, proposed an explicit method for unconstrained and constrained multi-degree reduction of tensor product Bézier surfaces using Jacobi polynomials. For the unconstrained case, this method achieves the optimal result with respect to theL2-error.In this paper, we first point out that for the constrained case the result by is not optimal with respect to theL2-error. Then we present an improved method to achieve the optimal constrained multi-degree reduction using Jacobi polynomials as well, but in a slightly different way. Finally, we extend the improved method to solve another optimal constrained multi-degree reduction problem with general boundary constraints. Some examples are included to verify the improvement by our method.