引用本文: 韩元利, 胡鹏, 杜爽. 关于点与折线集的中轴线问题研究[J]. 武汉大学学报 ( 信息科学版), 2005, 30(5): 421-425.
HAN Yuanli, HU Peng, DU Shuang. Research on Medial Axis Between One Point and Multiline Set[J]. Geomatics and Information Science of Wuhan University, 2005, 30(5): 421-425.
 Citation: HAN Yuanli, HU Peng, DU Shuang. Research on Medial Axis Between One Point and Multiline Set[J]. Geomatics and Information Science of Wuhan University, 2005, 30(5): 421-425.

## Research on Medial Axis Between One Point and Multiline Set

• 摘要: 运用离散观点,将折线集分解为独立点、线要素,并且基于点的方位检索法、路径检索法和要素的作用域概念,对各个要素中轴检索序列的分布规律与性质进行了深入剖析。通过对各要素中轴检索序列有序综合,引入回归环的概念来简化中轴检索序列,得到点与折线集中轴线的有序点集,揭示了中轴线的构成实质与相关性质特征。论证了中轴线的连续性,并且针对封闭折线集的特殊性进行了简要分析与论证。

Abstract: Firstly, this paper points out the conception error and the difficulty of current ways of outlining the polygon medial axis by analysis and comparison. With a discrete view, multiline set is decomposed into many monotone point factors and line factors, then we mark out the effect area for each element and get each element's counterpart medial axis point set independently through orientation-index and route-index which based on point and line respectively. With the aid of these single elements, medial axis’ distributing rule and its character is also revealed deeply. At last, we can outline the final medial axis between a single point and multiline set by the synthesis of each element’s index point-set in order. During this course reversion circle is used to simplify the structure of medial axis and to illustrate the essence of medial axis. The continuity and singleness identification is also argued in this paper and some typical case such as closed multiline set is given in brief to prove our thoughts or to list as special case.

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