基于活动标架对Gosper曲线的研究

The Study of Gosper Curve on Moving Frame

基于活动标架定义离散曲率[1-3],并借此研究了Peano-Gosper分形曲线,得出一种新的生成Peano-Gosper空间填充曲线算法。通过建立曲线弯曲点位置号码与弯曲点曲率的映射,对于任意正整数n,能够输出对应弯曲点的曲率并画出相应弯曲点图象结构。相比于传统生成Peano-Gosper分形曲线的方法,本文算法减少迭代次数提高效率。

The Peano-Gosper fractal curve is studied based on the definition of discrete curvature from the moving frame and a new Peano-Gosper space flling curve algorithm is obtained.By establishing the mapping between the position number of the curve bending point and the curvature of the curve,for any real number n,the curvature of the corresponding bending point can be output and the image structure of the corresponding bending point can be drawn.Compared with the traditional method of generating Peano-Gosper fractal curve,the new algorithm can reduce the number of iterations and improve the speed of the algorithm.