满足约束的Gn连续过渡曲面的构造

在Erich Hartmann提出的由两基曲面线性组合构造G^n连续过渡曲面方法的基础上，针对该方法存在很难找到合适的参数变换的问题，提出了一种基于基曲面局部区域重新参数化构造G^n连续过渡曲面的方法。通过对基曲面上切触线附近区域部分曲面重新参数化，再由重新参数化局部基曲面线性组合构造G^n连续过渡曲面。这样将两基曲面间构造过渡曲面的问题转化为在重新参数化局部基曲面间构造过渡曲面。以构造G^1连续的翼身融合面为例，讨论了满足约束要求条件时G^2连续过渡面的构造方法。即先对基曲面上过渡切触线附近的局部区域进行重新参数化，后通过优化求解来确定比例因子和偏移量、平衡因子和调配因子，使过渡曲面满足前后边条线约束，最后利用线性组合来构造G^2连续的过渡面。约束过渡曲面的形状可通过改变重新参数化基曲面的大小来调整．

Generating Parametric Gn Blending Surface with Some Constraints

This paper presents a method of generating a parametric G n blending surface based on reparameterizing the partial surface patches in the base surfaces on the basis of Erich Hartmann method. This method is expressed as follows: Firstly, the partial region near contact curves in both base surfaces is reparameterized. The contact curves are used as the boundaries of the reparameterized partial region respectively. The reparameterized partial region in two base surfaces is called the reparameterized local base surfaces. Then the parametric G n blending surface is generated by a linear combination of the reparameterized local base surface patches depending on one of the common parameters. Therefore, generating a Parametric G n Blending Surface between two base surfaces is translated into generating a Parametric G n Blending Surface between the two reparameterized local base surfaces. This paper illustrates the method to generate the G n blending surface with some constraints by generating a G 2 blending surface between the aerofoil and the body of a missile with the constraints of the forward and rear fringe curves. When the G n blending surface with some constraints is generated, the partial region near contact curves in both base surfaces is reparameterized, and the scale factors, offset, balance factor and thumb weight are defined by meeting the constraints through using an optimization method. Then the parametric G n blending surface is generated by the linear combination of the reparameterized local base surface patches. The shape of the blending surface can be adjusted by changing the size of the reparameterized local base surface patches.