任意阶参数连续的三角多项式样条曲线曲面调配

Blending of the trigonometric polynomial spline curve and surface with arbitrary continuous order

为了进一步研究三角多项式样条曲线曲面的理论和探讨闭曲线曲面的表示方法,利用曲线曲面混合法,对三角多项式样条曲线曲面进行形状调配.所选调配基函数形式简单,通过调节调配因子可调配曲线曲面的局部形状.所得调配曲线曲面除了具备原有曲线曲面的基本性质和保持原有曲线曲面次数不变外,还能表示闭曲线曲面和精确表示二次曲线曲面,比原有的曲线曲面具有更好的表达能力.

In order to develop the theory of trigonometric polynomial spline curves, the representation of trigonometric polynomial spline curves is blended to a general form based on the blending of trigonometric polynomialones. Moreover, some properties of the blending curves and surfaces are discussed in details. The research shows that the ba sis of the trigonometric polynomial curves and surfaces is relative simple, and the blending curves and surfaces includes the original trigonometric polynomial spline curves and surfaces show much better shape-control capability than the original ones. Meanwhile, the blending curves keep the same degree as the original ones. It is easy to find that the curves and surfaces can be reshaped by adjusting the shape factor. At the same time, the new method of the representation of closed curves and surfaces is given which can also accurately represent conic curves and surfaces.