点集局部处处为凸的外包线自动生成

在海岸工程的数学模型中,原始地形数据一般表现为一系列平面点的坐标,而在数学建模过程中往往需要根据该点集(坐标)人工给定模拟区域的边界。可根据事先设定的搜索点数得到点集的外包线,不同的搜索点数可以得到不同的外包线。一般说来,随着搜索点数的增加,外包线内的面积也不断增大,直到得到该区域的凸包(该凸包一般不是所要寻找的)。外包线内的面积与凸包的面积比值,定义为该外包线的凸度。为了减少手工工作的劳动量,提出了一个根据给定点集,自动寻找其合适外包线的算法。同时给出了外包线的调整算法,使得寻找到的外包线更加贴近初始给定的情形。最后应用该程序对渤海区域边界点数据进行了边界寻找,效果良好。

Algorithm for automatically generating a locally convex envelope curve of a point set

In coastal engineering mathematical model,the original terrain data are a series of planar point data with its elevations.In the mathematical model,it is required to get the artificial boundary of the given model region from the points set.An algorithm can get the envelope curve based on pre-set number of searching points,and different number can get different envelope curve.With the number of search points increasing,the area bounded by the envelope curve is also increasing,until the convex hull of the region is got(in general,the convex hull is not what we are considering).The convex-concave degree of envelope curve is defined as the ratio of the area bounded by the envelope curve and the area bounded by the convex hull.In order to reduce the amount of manual labor work,an algorithm which could automatically generate the appropriate envelope curve of the given points set was presented in this paper.An adjustment algorithm which could make the envelope curve more coincidence of the actual situation was also given.Finally,this algorithm was used to generate the Bohai Sea region boundary.The computed boundary agrees reasonable well with the actual situation.