Multiple Degree Reduction of Wang-Ball Curves by Using Dual Basis Polynomials

摘要

A new method of multi-degree reduction of Wang-Ball curves with constraints is presented by using basis transformation and the constrained dual basis polynomials, associated with the Jacobi scalar product. Favorable qualities of dual basis polynomials are also given, including the explicit orthogonal representations, and the degree elevation formula. The complexity of the method is O(mn), if the input and output curves are of degree n and m(m < n), respectively. Some numerical examples are also given to show the effectiveness of the algorithm.