四点插值细分算法极限曲线曲面C2连续的充分必要条件

Necessary and Sufficient Conditions for the C² Continuous Limit Curves and Surfaces of 4-Point Interpolatory Subdivision Scheme

摘要: 研究了四点插值细分算法的连续性.用若当标准形重新证明了Dyn的一个定理,从而得到了一个极限函数具有二阶导函数的充分必要条件及二阶导函数的解析表达式;并将结果推广到曲面的情形.

Abstract: The continuity of 4-point interpolatory subdivision scheme was studied. One of Dyn's theories was proved in a new way by using Jordan's normal form. Necessary and sufficient conditions for the second derivative of limit function were obtained, and expression of second derivative was acquired as well. The result was accordingly extended into the case of surfaces.