一种3维动画中间帧非线性插值算法

关键帧动画是3维动画制作的常用模式，中间帧插值又是关键帧动画中最为繁琐的环节。提出了一种针对无骨架3维网格模型的非线性插值算法，用于对网格模型的关键帧姿态进行插补，自动生成中间帧动画序列。该算法首先计算动画角色的网格模型各三角片在相邻关键帧中的仿射变换，并据此生成变形梯度向量，作为3维网格模型的形变信息，这种表示形式体现了变形过程中网格顶点之间的局部互相关关系。随后将各仿射变换分解为旋转成分与拉伸缩放成分，对拉伸缩放成分进行线性插值，而对旋转成分采用四元数插值算法进行非线性插值，合成中间帧姿态的变形梯度向量，并据此计算出中间帧网格模型。当相邻关键帧姿态存在较大差异时，该算法也能快速生成平稳而生动的中间帧动画，可有效减少关键帧的数量，提高动画制作效率。

A Non-linear Interpolation Algorithm for Tweenframes of 3D Animation

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.