回转体外形的参函数逼近

在文献4]的基础上,进一步讨论了回转体外形的参函数逼近方法。利用这种方法可以自然满足边界条件,简化逼近计算;可以对给定的型值进行直观的检查和光顺,提高逼近精度;可以显示出节点的合理部位,减少节点选择的盲目性。 作为文献4]的继续和补充,还给出了圆锥端头截体和平端头截体的数学表达式。

A PARAMETRIC FUNCTION METHOD FOR APPROXIMATION OF BODIES OF REVOLUTION

On the basis of the mathematical expression of bodies of revolation given in the author's previous paper4], a new method, which reduces the approximation of given shapes of bodies of revolution to that of the so-called parametric functions is presented. The boundary conditions will be satisfied automatically and thereby the calculations will be significantly simplified. It's interest to show that the transformation between the original function and the parametric function is very helpful to the approximation, so that the errors in the given data, upon which the calculations are based, may be detected audiovisually, and that a rough approximation of the parametric function will lead to a rather accurate approximation of the given shape.The method described in this paper may be applied equally to the two-dimensional shapes.