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.