两个轴异面的管道拼接

Blending Tubes Whose Axes are Non-coplanar

证明二轴异面的圆管在其任意平面截口处通常不能用三次代数曲面 GC1拼接 ,提出构造轴线与给定二圆管的轴分别共面的辅助圆柱 ,并利用二轴共面的吴文俊公式实现了给定圆管的分两段的三次

In this paper, we prove that given two cylinders whose axes are non-coplanar, in general, there doesn't exist a cubic GC 1 blending surface for any clipping planes. We introduce a new trick, \{i.e.,\} to constructing an auxiliary cylinder whose axis is coplanar with each of the two axes of the two given cylinder respectively and then obtain the two-piece cubic GC 1 blending surfaces by using Wu Wen-tsn Formulae of two coplanar cylinders.