给定(N-1)条边界曲线及其跨界导矢构造N边域曲面

Constructing N-sided patches in terms of(N-1)boundary curves and their corresponding cross derivatives

在ＣＡＤ／ＣＡＭ系统的曲面设计中，常常需要根据给定的（Ｎ－１）条边界曲线及其跨界导矢构造Ｎ边域曲面。通过将Ｃｏｏｎｓ曲面的设计思想和Ｂ样条方法相结合，对任意的Ｎ（Ｎ≥４）边域曲面，提出了一种根据给定的（Ｎ－１）条边界曲线及其跨界导矢构造边域曲面的新方法，讨论了所构造曲面奇异性的消除，研究了其向ＮＵＲＢＳ曲面的转换方法。这种方法的优点在于：１）Ｎ边域曲面整体Ｃ１连续；２）Ｎ边域曲面的跨界导矢可以独立给定，不需要满足兼容性条件；３）可以用Ｎ片ＮＵＲＢＳ曲面来形成与相邻曲面近似Ｇ１拼接的Ｎ边域曲面。由于ＮＵＲＢＳ已成为ＣＡＤ／ＣＡＭ系统中曲面的基本表示形式和数据转换的标准，从而本方法易于在现有的ＣＡＤ／ＣＡＭ系统中实现。

? In the surface modeling of CAD/CAM systems, it is often needed to construct an N sided surface in terms of ( N- 1) boundary curves and their cross derivatives. Combining Coons' strategy and B spline method, a method is proposed to construct N sided surface in terms of ( N- 1) boundary curves and their cross derivatives. A strategy is suggested to remove the singularity of the constructed N sided surface. An approach is offered to form the constructed N sided surface using N pieces of NURBS surfaces of degrees 7×7 with nearly C 1 continuity. The advantages of the proposed method are: (1) The N sided surface is of global G 1 continuity; (2) the cross derivatives interpolated by the N sided surface can be given independently and need not meet the compatibility condition; (3) The N sided surface can be formed with N pieces of NURBS surfaces with nearly G 1 continuity. Since NURBS has become the standard of data exchanges and the basic expression form in many CAD/CAM systems, the constructed N sided surface can be easily incorporated into the existing CAD/CAM systems. 