【摘要】 在本文中,作者们提出了一种新的超椭圆、亚椭圆、内摆线和特种曲线的递推算法。设:X_i=[（x_i-x_c）cosα+（y_i-y_c）sinα]ⁿY_i=（a/b）ⁿ[（y_i-y_c ）cosα-（x_i-x_c）sinα]ⁿ（1）则:[X_i+1 Y（i+1）]=[X_i Y_i)（?）（2）因此[X_i+1-X_c Y_i+1-Y_c]=[|X_i+1|^-n|Y_i+1|^-n]（?）（3）式中δ是每前进一步的微小旋转角这种递推算法的优点在于计算插值点非常简单,并且仅需少量计算机内存,即可求出数以百计的插值点。根据这种算法可以编制出一组产生曲线的软件。作者们还提出了一种构造超椭圆曲面的概念或原则,超椭圆曲面可以组成飞机机身或其它运载工具外形。这类机身的载面比由圆截面或椭圆截面有较大的使用空间。这种类型曲面也比其它曲面较易构造和处理,同时由超椭圆组成的机身的强度,比圆和椭圆截面组成的机身要高。更多还原

【Abstract】 In this paper the authors present a new recurrence algorithm for super ellipse,para ellipse,hypocycloid and special kind of curves. Suppose that x_i= [（x_i-x_c）cosα+（y_i-y_c）sinα]ⁿ Y_i= （a/b）ⁿ [（y_i-y_c）cosα-（x_i-x_c）sinα]ⁿ （1） then [X_i+1 Y（i+1）]=[X_i Y_i]（?）（2） therefore [x_i+1-x_c y_i+1-y_c]=[|X_i+1|^-n|Y_i+1|^-m（?） （3） where δ is a small rotation angle for furthering one step. The advantages of this recurrence algorithm is that it is very simple to calculate the interpolating points,and only fewer memory spaces of the computer are needed to find the severl hundrod interpolation points.Based on this recurrence algorithm a kind of ourve generation software canbe pro- grammed. The authors also propose a conception or a principle to constructa su- per ellipse surface.An aircraft fuselage or other vehicles can be composed of super ellipse surfaces.The cross sections of this kind of fuselage allow for bigger useful space than that composed by circles and ellipses.This type surface is much easier to construct and handle than other surfaces.The stre -ngth of the fuselage consisted of super ellipses is higher than that of the circular and elliptical sections.更多还原