Good degree reduction of Bézier curves using Jacobi polynomials

AbstractThe constrained Chebyshev polynomial is the error function of the best degree reduction of polynomial with C1-continuity. In this paper, we propose the constrained Jacobi polynomial as an alternative error function for good degree reduction. Although the degree reduction is not the best approximation, it is more useful than the constrained Chebyshev polynomial since its coefficients are represented explicitly, but the coefficients of the constrained Chebyshev polynomial are not. We present the uniform error bounds of the constrained Jacobi polynomials and subdivision scheme for degree reduction within given tolerance. We also apply our method to an example and compare its result to that of the best degree reduction