Inversion Approximation for Polynomials by the Constrained Jacobi Basis and its Application

To solve the inverse function of polynomial is a fundamental problem in CAGD.An algorithm about approximating the inverse function with C^k constrains is proposed.By using the constrained Jacobi basis and a derived transformation formula for it to Bernstein basis,and using the degree elevation,arithmetic and composition algorithms for Bernstein polynomials,the specific method for solving the coefficients of inverse function is given.The approximation method is convenient and steady.Moreover,the defect that the corresponding coefficients must be recalculated when approximating every inverse function one by one was overcame.Finally,the experimental results show that the approximation methods are correctness and effective.As an application,generating quasi arc-length parameterization of PH curves is also discussed.