目的　研究自由曲面数学模型的建立和光滑拼接． 方法　分别利用网格法空间曲面、单线性曲面ＣＯＯＮＳ曲面、Ｂｅｚｉｅｒ 曲面构造曲面， 推导自由曲面的数学方程式． 并利用Ｂｅｚｉｅｒ 曲面的连续性条件和圆弧面补加点的办法实现曲面块光滑拼接． 结果　提出了自由曲面数学模型的建立方法和光滑拼接技术． 结论对数控编程中自由曲面的处理问题具有一定的实用价值 Objective To study the establishment of mathematical model of freeform surface and smooth splicing. Methods The mathematical equations of free-form surfaces were deduced by using the grid-based space surface, the single-line surface COONS surface and the Bezier surface, respectively. The smoothness of curved surfaces is achieved by using the continuity condition of Bezier surface and adding points of circular surfaces. Results The establishment method of mathematical model of freeform surface and the smooth splicing technique are put forward. Conclusion The problem of free-form surface processing in NC programming has some practical value