中文摘要：

为了在计算机动画中可以得到较好的图形过渡效果，提出了一保持平面多边形内部相似性的形状混合算法，从而有效地避免了中间多边形发生局部萎缩或者膨胀的现象．此方法从源和目标多边形的同构三角剖分出发，对同构三角网格每一个夹角处表示边角关系的几何量线性插值得到相对应的中间几何量，通过这些中间几何量以及它们与顶点坐标之间的关系来建立线性方程组，给定初始条件后用现成的程序库快速求解来得到中间三角网格（其边界即为中间多边形）．还通过引入特征多边形来保持混合多边形的全局视觉特征．该算法计算量小、运行效率高，对形状复杂的多边形仍然可以得到满意的结果．适合于实际应用中实时的要求．

英文摘要：

Planar shape blending or morphing, which involves the creation of a smooth transition from a source planar polygon to a target one, has gained widespread use in recent years. In order to obtain good effects in computer animation, a novel and efficient algorithm for planar shape blending is presented, which can preserve the similarity of the interiors of the polygons and avoid local expansion or shrinkage. First, the high quality compatible triangulations between the source and target polygons are constructed. Then, the geometric quantities including the angle and edge ratio at every interior angle of the intermediate triangulation are computed by interpolating the counterparts of the source and target triangulations. Finally, the intermediate triangulation is constructed by solving a linear sparse system, which can be efficiently solved by some solver library. The intermediate polygon is obtained by the boundaries of intermediate triangulation. Planar shape blending is formulated as solving a linear sparse system finally. The feature polygon is introduced to preserve the global visual features of the source and target polygons. This approach is simple and fast and can be used in practical applications in real-time. Many experimental results are presented to show that the approach is applicable and flexible and can obtain satisfactory results for complex polygons.