点集序列与分形生成的细化算法

On the Refined Algorithm for Generating Sequences of Set of Points and Fractals

提出了一种从初始的离散控制点集逐次细化生成曲线和分形的子分割算法．deRham算法是本文算法的简单特例．令是平面上初始点集．逐次细化的序列按如下规则计算：其中系数由设计者根据其需要选择．在计算机上，该细化格式能够生成几何设计中非常重要的规则图形和非规则的分形．特别对典型的诸如科赫曲线，谢尔宾斯基曲线，闵可夫斯基曲线及龙曲线的生成都是有效的，结果的一个有趣的应用是对所谓德灵格线画艺术进行绘制．

A new kind of subdivision algorithms of successive refinements of initial sets of discrete control points which are used to model curves and fractals is presented in this paper. The de Rham's algorithm is a simple and special case shown in the paper.Suppose is initial points in the plane. Successive refined sequences are computed by the following rule:where and the coefficients are chosen by users for their requirments. The refined scheme can generate regular graphs and irregular fractals which are important in geometric designs on computers. In particular, by using the scheme some classical examples such as von Koch, Seirpinski, Minkowshi and Dragen curves can also be generated easily. An interesting application is shown for rendering so called Dehlinger's Line Art.