复杂多边形中轴构建方法

Methods for Constructing Approximate Medial Axis for Planar Free-form Shapes

多边形中轴是指与多边形不同边(或边的延长线)上的两个或两个以上点等距离的点轨迹。多边形中轴的图形结构表明,在多边形凸顶点处存在中轴线,而在凹顶点处不存在中轴线(中轴线在多边形外)。采用左右点法实现对多边形顶点凹凸性的判断,进而定义和标注多边形不同边界线段。借助ArcGIS软件,提出了构建任意复杂多边形中轴的两种逼近方法:一种是基于Voronoi图的矢量方法;另一种是基于欧氏距离区域分配的栅格方法。实验表明这两种方法都是有效的、可行的。

The medial axis （or a topological skeleton） is a thinner version of a geometric object, which is equidistant from the object^s different edges. It can be seen from this definition that medial axis construction involves defining the ＂different edges＂ problem. Actually, the graph structure of polygon medial axis shows that there is a medial axis in polygon convex vertex, and no medial axis （outside the polygon） in a polygon concave vertex. In this paper, the left and right point method was adopted to judge if one vertex of a polygon is a concave vertex or not, and then the different boundary segments of such polygons were defined and labeled. With the aid of ArcGIS software, this paper presents two methods for constructing approximate a medial axis for planar free-form shapes： one is vector method based on the Voronoi diagram; another is raster method based on the regional distribution based on the Euclidean distance. Experimental results show that both methods are both effective and feasible.