Research on Medial Axis Between One Point and Multiline Set

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.