多截面形状要求的广义旋转曲面

旋转曲面在计算机辅助设计中有比较重要的作用 ,很多种类的曲面可以看作由曲线旋转而成 ,传统的旋转曲面在生成的过程中 ,母线的形状不发生变形 ,这样就大大地限制了旋转曲面的应用范围。因此 ,本文对旋转曲面的概念做了进一步的拓宽 ,使母线在旋转运动的过程中能够按照设计的要求发生一定的变形 ,这样就拓宽了其应用范围。曲线在发生变形前后一般要求其形状变化不大 ,本文根据自由曲线能量的概念 ,提出了变形应该使位移曲线的能量最小的假设 ,根据该假设 ,推出了相应的计算公式 ,经过实际计算表明该假设是比较合理的。最后 ,根据本文提出的方法 ,给出了一个有多个截面形状要求的广义旋转曲面造型的例子。

On Generalized Revolving Surface Based on Metamorphose Curve

Revolving surface is very important in CAD,many kinds of surfaces can be regarded as being made from the revolving of a curve. For traditional revolving surface, the shape of generatrix is not changed, its application is greatly limited. We extend the scope of revolving surface by allowing metamorphose to the generatrix. Usually the change of shape of the curve before metamorphose and after metamorphose is slight. According to the concept of the energy of free curve, we propose a hypothesis that the deform of the curve should make the displacement curve get lowest energy. According to this assumption we derived the formula. Calculation shows that the assumption is reasonable. Finally, an example of generalized revolving surface with different section shapes is given.