改进的基于mean value重心坐标的多边形变形

对平面多边形的变形,为了避免变形过程中边界的退化和自交现象,目前主要采用将初始多边形与目标多边形分别嵌入到具有凸边界的同构三角网格中去,转化成三角网格的变形问题。但该方法在进行同构三角剖分时,增加的额外点数目较多,复杂度高,且不能实现刚性变形。论文提出一种基于多边形星形分解的同构三角网格剖分算法,使用较少的额外点,降低了算法复杂度。此外,文中选择正多边形作为三角网格的边界,并采用刚体变形技术以保持初始多边形和目标多边形尽可能刚性地变形,取得了较好的变形效果。

Improved Polygon Morphing Using Mean Value Coordinate

At present,for naturally and continuously morphing two simple planar polygons,the commen method to guaranteed the self-intersection free and non-degeneration properties is reducing the polygon morphing problem to the problem of morphing compatible planar triangulation of corresponding point sets,which is performed by embedding the initial polygon and the target polygon into compatible planar triangulations respectively.But in the method,a large number of extra points are used which increases computational complexity.In this paper,an algorithm based on star decomposition is introduced that triangulates two simple polygons into compatible triangulations,which uses smaller additional points to compatible triangulations,and rigid morphing is adopted for better morphing effects.