具有两类形状参数的代数三角混合样条曲线的构造和调配

Construction and Blending of Algebraic-Trigonometric Spline Curves with Two Kinds of Shape Parameters

带形状参数的样条曲线曲面是外形设计的重要方法,形状参数不是全局性的就是局部的,大多数仅考虑参数连续性.为了更好地修改和调配曲线曲面,构造了满足几何连续的带两类形状参数的代数三角样条曲线,简称为ATB-spline.这种曲线不仅具有普通三角多项式函数的性质,还具有全局和局部的可调性.两类形状参数在给定的范围内取值时,带两类形状参数的ATB-spline曲线满足一阶的几何连续;当两个相邻曲线中的形状参数取特殊值时,带两类形状参数的ATB-spline曲线满足不同性质的连续.利用曲线的性质构造了旋转面,讨论了两类形状参数对旋转面外形的调配并给出了实例.该曲线还可精确表示椭圆曲线.上述结果表明该方法构造的曲线是有效而实用的,并具有交互性.

A spline curve with shape parameters is an important method in design. In ex- isting methods, however, shapes parameters are either global or local, and only parameter continuity are considered. To modify and blending the curves, an algebraic-trigonometric spline curve, called ATB-spline, is constructed with two kinds of shape parameters satisfy- ing geometric continuity. This curve not only has the properties of ordinary trigonometric polynomials, but also has global and local properties. When the two kinds of shape param- eters are taken in a given range, the ATB-spline curves with two kinds of shape parameters satisfy geometric continuity of the first order; when the shape parameter of the two adjacent curves is given a special value, the ATBJspline curve with two kinds of shape parameters can satisfy continuity of the different properties. The rotation surface is constructed based on the property of the curve. Blending of the two kinds of shape parameters on the sur- face of the rotating surface is given together with an example. In addition, this curve can accurately represent conic curves. The above results indicate that curves constructed with this method are practical and effective.