一种类四次三角样条曲线

针对B样条曲线相对于其控制多边形形状固定，以及不能描述除抛物线以外的圆锥曲线的不足进行改进。将形状参数与三角函数进行有机结合，构造了一组含参数的三角基，由这组基定义了带形状参数的三角样条曲线，其每一段由相继的5个控制顶点生成。新曲线在继承B样条曲线主要优点的同时，既具有形状可调性，又能精确表示椭圆，对于等距节点，在一般情况下曲线C³连续，当形状参数取特殊值时曲线可达C⁵连续。采用张量积方法，将曲线推广后所得到的曲面具有与曲线类似的性质，给出了用曲面表示椭球面的方法。

Trigonometric spline curves on five-points piecewise scheme

Because the disadvantages of the B-spline curve＇s shape is fixed to its control polygon, as well as it cannot describe the conic section besides the parabola, the shape parameter and the trigonometric function are combined.One kind of trigonometric basis with parameter is constructed in this paper.Based on this basis, one kind of trigonometric spline curve is defined.Each piece of the curves is generated by five consecutive control points.The new curve not only inherits the major advantages of the B-spline curve,but also with shape adjustability, and it can express ellipse exactly.For equidistant knots,the curves are C3 continuous,and they are C5 continuous when being with special parameter.Using the tensor product method, the curve can be extended to surface.The surface has properties similar to the curve.The way to represent ellipse surface using the new surface is given.