顾及海岸线地理弯曲特征约束的可控分形插值方法

针对海岸线分形插值缺乏地理特征约束和分形过程不可控的局限，提出了一种顾及海岸线地理弯曲特征约束的可控分形插值方法。首先，根据不同海岸地貌类型所呈现的不同弯曲特征和分形特征，对海岸线进行地貌单元划分，将传统的整体分形插值变换为以海岸线地貌弯曲特征为划分单元的分段插值组合；其次，利用一维随机中点移位法对各划分单元分别进行插值，并结合各划分单元的弯曲特征对分形参量分别进行约束控制，以保持海岸线不同地貌单元的弯曲特征；最后，将各插值单元顺次连接起来得到最终插值曲线。实验结果表明，所提方法能够很好地顾及海岸线不同地貌单元的弯曲特征和分形特征，且分形插值过程可控。

A Controlled Fractal Interpolation Method for Coastline Considering Bending Characteristic Constraints

To overcome the shortcoming of the existing fractal interpolation methods that don't take into account the constraints of geographical bending characteristics and the fractal interpolation process is uncontrollable for coastline. A controlled fractal interpolation method for coastline is proposed by considering its geographical bending characteristic constraints. Firstly, the coastline is divided into several parts according to the bending characteristics and fractal characteristics of different coastal landform types, which will change the traditional integral fractal interpolation into a combination of several piecewise landform bending interpolation units. Secondly, the one-dimensional random midpoint displacement method is used as a fractal interpolation function for each divided unit of the coastline, and in order to maintain the bending characteristics of different landform units in the coastline, the fractal parameters of the interpolation function are restricted by the constraints of each unit fractal characteristics. Finally, the result curve is got by linking the interpolation units in order. The experiments show that this method can keep well the geographical bending characteristics and fractal characteristics of different landform units of coastline, and the process of fractal interpolation is controllable.