Using of the generalized inverse theory and the definition of local fine point to extend this theorem,given the rank theorem for Fredholm map between Ck-Banach manifolds.

It has been studied that the local linearization of the unlinear mapping between Banach spaces by using of the generalized inverse theory and the definition of local fine point.

In addition,the local mesh subdivision method can be also applied to the research .

PD-LS algorithm for constructing product prototype based on location subdivision;

This paper introduces the Charles Loop’s scheme into the synthesis of realistic animated facial images drove by sound-driver,and proposes a Face-LS algorithm based on location subdivision module.