Aiming at the lack of traditional ploting method in the areas of three dimension graphics , the b - spline surface is adopted . in order to more easily build the b - spline surface the control points are replaced with one center point during the storage , and make it clear to simulate the curve of branches 在三维图形的绘制方面，针对传统绘制方法的不足，采用b样条曲面来构造三维几何模型，在曲面的生成及存储过程中用一个中心点代替多个控制顶点，将对曲面的控制转为对曲线的控制，使得对枝条形状的模拟更加方便直观，并且减少了存储空间。
The general idea behind the second one is approximation . the control mesh is subdivided until the error between the control vertices and corresponding subdivision surface is less than a given threshold . then the vertices substitute those points on the surface approximately . the last step is to calculate offset point for every vertex and connect them to form an offset surface 第二种算法采用逼近思想，首先通过对控制网格进行细分，当控制顶点和细分曲面的距离满足一定误差要求时，近似用控制顶点代替细分曲面上的点，然后对各个顶点分别求等距点。
The main difficulty along with approximating to object ' s surface with multi - nurbs patches is that one must deal with more control points , especially the control points around the jv - patch corner because of the intertwining of the geometric continuous constraints along the boundaries converging on the corner 用nurbs曲面分片逼近物体表面带来的问题就是要处理大量的控制顶点，特别是n面角附近的控制顶点更需要特别处理，因为曲面片之间的几何连续约束在角点处互相缠结。
By the means of optimization methods , degree reduction of rational bezier curves is changed to a optimization problem so that both weights and vertices are consider respectively . using programming method and genetic algorithms , a new method on rational bezier curves is presented 第四从最优化的思想出发，把有理b zier曲线的降阶转化为求最优化问题，这样也使得权因子和控制顶点被分开考虑，以保证权因子的非负性；同时结合智能计算中的仿生学方法和程序设计方法，给出了有理b zier曲线降阶的一种新方法。
It offers the idea according to problem faced , considering the good character of the ends , the ajusted cubic b - spline curve is used to fit ship lines . it finds out the control vertexs according to a sequence of given points , and then , through particular formula , each point in the curve could be worked out . it smoothes lines with the method based on small - paramter 针对面临的问题，提出了自己的思路，在数学计算方法上，由于三次准均匀b样条曲线良好的端部性质，这里用它来拟合船舶型线，首先根据所给的初步型值求出其控制顶点，然后根据相关公式进行插值便能得到曲线上的所有插值点。
