分形理论在曲线插值中的应用

摘要

T he linear interpolation methods commonly used have their ow n advantages and disadvantages and applicability .But they can’t give consideration to the irregularity of the linear object itself very well as keeping its inner characteristics . T he paper has three main aspects like the initial point selection , the number of iterations and the fractal dimension are considered , and experiment on the effect of the implementation of the fractal interpolation algorithm is done and have got some beneficial conclusions after comparison and analysis of the results .They have certain reference value for Fractal to be applied to the linear feature interpolation in topography .Finally it proves that fractal interpolation is better than other interpolation methods and has great advantages through an example .%传统的线性插值方法具有各自的优缺点及适用性，但都不能很好地兼顾线性地物本身的不规则性。故从初始点选择、迭代次数和分形维度这三个主要方面考虑，对分形插值算法进行实验。通过对结果的比较分析，得到一些有益的结论，它们对于分形理论应用于地形中的线状地物的插值具有一定的参考价值。最后，通过一个实例证明分形插值比其它插值方法具有很大优势。