Abstract: Because of the complexity of Non-Uniform Rational B-splines (NURBS) surface, the conventional NURBS surface generation method usually first constructs a Coons surface and then changes it into NURBS surface, which adds the operation complexity. To address this problem, an NURBS boundary surface direct generation method was proposed, which can directly construct a NURBS boundary surface by using four NURBS boundary curves. Compared with the traditional method，it need not convert Coons surface to NURBS surface and have a low computing cost. The experiments show the proposed method is simple and convenient, but the generated surface still has a high quality and good continuity.

Key words: Coons surface, knot vector, NURBS, boundary surface

摘要： 由于非均匀有理B样条(NURBS)曲面的复杂性，传统NURBS边界曲面的生成是先构造孔斯曲面，再由孔斯曲面向NURBS曲面转换得到，其操作过程比较烦琐。针对此问题，提出了NURBS边界曲面直接生成算法，该算法根据给定的四条NURBS边界曲线，结合孔斯曲面生成方法直接插值生成NURBS曲面，从而避免了通过孔斯曲面向NURBS曲面转换所带来的计算代价，因此同传统方法相比，具有较低的计算代价。实验结果表明:该算法简化了曲面生成步骤，减少了曲面转换过程的计算量,生成的曲面边界信息明确，且连续性好。

关键词: 孔斯曲面, 节点矢量, NURBS, 边界曲面