EXACT EVALUATION OF THE INTERPOLATORY SUBDIVISION CURVES AT RATIONAL PARAMETER VALUES
插值细分曲线有理参数点的精确求值

An algorithm for exact evaluation of interpolatory subdivision curves at arbitrary rational points is proposed. The algorithm is designed based on the parametric m-ary expansion and construction of associated matrix sequence. The weights of the control points on the initial polygon can be obtained, through computation by multiplying the finite matrix sequence corresponding to the expansion sequence and eigen decomposition of the contraction operator related to the period of rational numbers. Two examples of evaluation of four-point subdivision scheme and four-point ternary one are given. The algorithm proposed in this paper can be generalized to evaluation of other non-polynomial subdivision schemes.