Key-frame animation is the common mode for making 3D animation

and twecn-frame interpolation is the most important part. This paper presents a non-linear interpolation algorithm aiming at the non-skeleton 3D mesh mode. This algorithm is used to carry on auto-interpolation to key-frame posture and to form twccn-framc animation serial. This algorithm firstly calculates the affine transformation of each triangle of mesh mode in adjacent key-frame and then creates deformation gradient vector. The deformation gradient vector is regarded as deforming information of mesh mode which reveals the local correlation between mesh vertices in deformation. In the following

each affine transformation is decomposed to rotation component and stretch scale component. The latter is made linear interpolation

while the former is made non-linear interpolation using quaternion interpolation algorithm. By this strategy

the deformation gradient vector of tween-frame posture is composed

according to which the tween-frame mesh mode is calculated. This algorithm can make stable and vivid key-frame animation when there is great difference in posture between adjacent key-frame. This algorithm can reduce the number of key-frame and improve the efficiency of animation making.