引用本文: 王新生, 谢凯, 姜友华, 郭光毅. 复杂多边形中轴构建方法![J]. 武汉大学学报 ( 信息科学版), 2014, 39(2): 181-185.
WANG Xinsheng, XIE Kai, JIANG Youhua, GUO Guangyi. Methods for Constructing Approximate MedialAxis for Planar Free-form Shapes[J]. Geomatics and Information Science of Wuhan University, 2014, 39(2): 181-185.
 Citation: WANG Xinsheng, XIE Kai, JIANG Youhua, GUO Guangyi. Methods for Constructing Approximate MedialAxis for Planar Free-form Shapes[J]. Geomatics and Information Science of Wuhan University, 2014, 39(2): 181-185.

## Methods for Constructing Approximate MedialAxis for Planar Free-form Shapes

• 摘要: 目的 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。

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

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