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.