用双三次Coons曲面构造工程曲面的方法

本文从研究角点信息对双三次Coons曲面片的形状及连接的影响入手,提出了用双三次Coons曲面片构造工程曲面时提供角点信息的办法,同时给出了在保证连接达到二阶连续的条件下角点切矢的自动生成方法。

Construction of Engineering Surface with Double Cubic Coons Surface Patches

The procedure for determining the corner point information when the double cubic Coons surface patches are used to construct an engineering surface is proposed as follows:1. Divide the surface patches properly, that is, the patch areas should be small where the curvature is large and vice versa. However, the change of area from small to large should be gradual. This is the basis for the determination of the corner position vector;2. A set of equations are to be written based on the condition of the second-order continuity when the surface patches are connected. From the equation set the corner tangential vector within the engineering surface boundary can then be calculated. The solution is used as the initial value for constructing the surface. When the shape is found to be unsatisfactory, the direction and the magnitude of the tangential vector should be modified. If it is desired that the surface be more convex, then the tangential vector should be made longer. Otherwise, it should be shortened;3. At corner points 00 and 11, the twisting vector can make the surface convex near the corner points in the direction of the vector while at 01 and 10, the direction of surface convex is opposite to that of the vector. Modify the twisting vector until the surface shape is in conformity with what is required. When the curvature of surface patches is small, the twisting vector is usually equal to zero.