一种全局优化的多边形变形方法及应用

通过对多边形的凸部分，并建立２种不同多边形的凸子集映射，提出了一种全新的基于凸多边形的全局优化方法，解决了任意非同拓扑结构（包括有孔及凸边形）的变形问题。理论上证明了此方法的正确性，讨论了不同凸剖分对变形的影响。实验证明此方法变形效果自然、质量好、速度快、自动化程度高，并可用于汉字的合成与二维动画关键帧的内插。

A NEW GENERAL OPTIMIZATION METHOD OF POLYGON METAMORPHOSIS AND ITS APPLICATIONS

A new method of polygon metamorphosis based on morphology and general optimization is proposed in this paper. By decomposing each polygon into a set of several individual convex sub polygons and constructing the map between the two sets, this method can solve the metamorphosis problem of two polygons which have not same topology(including concave polygon and holey polygon). The principle of it is proved theoretically and the results of polygon metamorphosis created by different convex decomposition is discussed. It is proved in the experiment that this method can generate natural, high quality metamorphosis with simple computation. This method can also be used in font composition and interpolation between two keyframes in 2D computer animation.