Best multi-degree reduction of bernstein polynomial in L2 -norm based on an explicit termination criterion

Based on the properties of orthogonal polynomials, we derive an explicit constrained degree reduction criterion for Bernstein-Bézier polynomials in L₂ -norm. The criterion can be used to determine whether a further degree reduction can be applied to the polynomial in advance with a given tolerance ε. An efficient algorithm is also presented for obtaining the best Bernstein-Bézier polynomial after degree reduction. With the proposed algorithm, one can avoid the blind procedure for degree reduction and terminate the procedure in advance when the estimated error is larger than the given tolerance.