在计算机绘图中，一般来说，曲线实际上是由折线代替，而曲面实为小平面拼接而成，在使计算量降到最低的情况下画出真正的曲线方面，已有许多文章研究了曲线的逐点生成方法，并取得了一定的进展，但是尚无有效的快速逐点生成曲面的方法，为了快速逐点生成曲面，在建立多项式函数递推计算公式和算法的基础上，给出了一种逐点生成参数多项式曲面片的算法，由于此算法中只用到整数加法运算，且点数的适当选取可使计算量达到极小，因此是一种很有效的算法，该方法还可以加以改进，而用于有理函数，这无疑对有理曲线曲面（如NURBS曲线曲面）的快速生成以及对计算机图形学的其他一些领域都是有意义的。

In computer drawing, generally, curves are represented by line segments and surfaces are tessellated up with small plane patches. To draw genuine curve and reduce computational costs as much as possible, curve-generating point-by-point has been studied in many papers, some good results have been achieved. But there is lack of effective approaches for fast surface-generating. If we suppose that surfaces consist of points of space lattice and the coordinates of points on a surface could be calculated one by one, then we would obtain the surface. There are already some algorithms for calculating polynomial curves on a plane, we can generalized them to space curves and surfaces. This paper presents an algorithm based on recursive formulas and algorithms for polynomial to generate a parametric polynomial surface patch point-by-point, in which only integral additive operation is employed, and properly choosing point number minimizes the computational costs, so it is quite efficient. The method in the algorithm can be modified for rational function, therefore it is of significance in fast generating parametric rational curve and surface(such as NURBS curve and surface), as well as in many other areas of Computer Graphics.