用三角Bézier曲面片的特征网格快速逼近矩形Bézier曲面片

CAD Geometrical-Property Calculation with Triangular Bézier Patch Mesh

提出了一种将矩形Ｂｅｚｉｅｒ曲面片的特征网格转化为相应三角Ｂｅｚｉｅｒ曲面片的特征网格的显式公式（表示相同的曲面片）。并利用三角Ｂｅｚｉｅｒ曲面片的特征网格的递推公式，生成更为密集的特征网格，该特征网格将是曲面片的近似表示。本方法已成功地应用于飞机总体外形的设计之中，它还可广泛用于力学分析、图形显示、数控加工、实物测量等领域。

In CAD calculation of geometrical properties, rectangular Bezier patch method is not easy to deal with. We utilize recent advances in research on triangular Bezier patch to make such calculation easier. We propose to transform rectangular Bener patch mesh into an equivalent triangular Bezier patch one.Such transformation can be explicitly accomplished with the aid of eq. (8). To make the triangular Bezier patch mesh denser, a recursion equation, eq. (9), can be used.Finally the usual example of unit sphere is taken. Table 1 showes the times required for generating 1380- point meshes. It can be seen that, though precision is a little lower, the time required for the equivalent triangular Bezier patch mesh (0.5s) is much lower than that required for the rectangular Bezier patch mesh (1. 5 s)