2D动画制作是一个劳动密集型的过程，如何自动进行关键帧插值是研究的难点。关键帧插值的核心环节是2D形体渐变，现有2D形体渐变算法大多针对闭合的单一多边形，在应用到包含多个区域的复杂形体时，可能出现区域之间的重叠。本文算法获取输入关键帧的封闭区域，并迭代计算区域间的匹配关系；对每个子区域建立相对于父区域的局部坐标系，施加层次间的约束关系进行插值，以消除父子区域插值过程中“运动”的不匹配现象。实验结果表明，该算法合成结果自然光滑，具有一定的实用价值。

Two-dimensional animation is a labor-intensive process， where automatic keyframe in terpolation (inbetweening) is a research focus.Two-dimensional shape-blending plays a key role in keyframe inbetweening. Most of the existing 2D shape-blending algorithms are designed for a single closed polygon. When they are applied to complex shapes containing multiple regions， overlaps between different regions may occur. Our algorithm first obtains closed regions of input keyframes and calculates the matching relations between these regions. Then we iteratively construct a local coordinate system relative to its parent region for each child region. Then the hierarchical constraint relation can be used to get rid of “motion” mismatches between parent-child areas. Experimental results show that our algorithm can synthesize naturally smooth inbetweens and is efficient enough for practical demands.