一种加权剖分简单多边形为三角形和凸四边形子域的算法

针对计算几何与有限元网格自动剖分中多边形子域剖分问题，给出了一种适用于有限元网格子域单元（即大单元）剖分的标准，并提出了一种通过在可视点对之间引进适当的多边形剖分和根据子域单元的形状质量判定因子来引导剖分的算法。由于建立的权函数和凹角（凸角）本身有关，因此对同属于凹角（凸角）的权函数也可以加以权值上的区分。该算法通过分步进行剖分，即先将简单多边形剖分为凸多边形，然后再将凸多边形剖分为凸六边形和凸五边形，最后将凸六边形和凸五边形剖分为三角形和凸四边形，以得到满足要求的剖分结果。在以上的每个剖分过程中，都引进了权重来引导剖分，使得剖分结果更加优化、合理。

A Weighting Algorithm for Decomposing a Simple Polygon into Set of Triangles and Convex Quadrilaterals

According to the basic problem of the sub domains decomposition of simple polygon in the computational geometry and the finite element mesh generation of computational mechanics, an algorithm for decomposing a simple polygon into set of triangles and convex quadrilaterals is proposed in this paper in which rules of decomposition are developed. And these rules are propitious to the finite element mesh generation. The algorithm is guided by a weighting function for pairs of visible vertexes of the given polygon and the estimation factor of shape quality. The created weighting functions are related with the concave (convex) angles, so the function values are different for any two different concave (convex) angles. The algorithm is composed of three steps: (1) Decomposing the simple polygon into set of convex polygons step by step, (2) Decomposing the over six convex polygons into set of under six ones (include six ones), (3). Decomposing the six and five convex polygons into set of triangles and convex quadrilaterals.