关于有理Bézier曲面片的几何连续拼接问题

本文深入研究了有理Bézier曲面片的几何连续拼接问题,给出了GC~1拼接条件的显式表示和判断两曲面片GC~1拼接状况的判定条件。用此条件可编写一简单程序,通过输入两曲面片的控制顶点及权因子,便可以“YES”或“NO”的输出回答两曲面片的拼接是否为GC~1连续。在非GC~1拼接时,可对称地修改两曲面片使其GC~1拼接。最后,本文给出了几种CAD/CAM工程中实用的充分条件。

On the Geometric Continuity between Adjacent Rational Bezier Surface Patches

Geometric continuity (GCk-Continuity) is widely recognized as the appropriate way to fit together two adjacent surface patches in CAGD. It avoids dependence on the parametrizetion and provides additional parameters for modelling the shapes. This paper considers two adjacent rational Bezier surface patches with a common boundary edge along which they have to join smoothly. We give the explicit representations of GC1 continuity conditions,and GC1 adjudging conditions. In terms of these conditions,a simple and small program can be written that takes as input the Bezier points and weights of the two patches, and produces as output either "Yes" or "No".indicating the presence or absence of a common tangent plane. For the case of non-GC1 continuity,the given conditions provide an approach which can be used to modify the two patches symmetrically so as to obtain GC1 smoothly compositive surf aces. Furthermore, some sufficient conditions for practical application are developed.