一种参数有理圆弧样条的保形性条件

The necessary and sufficient conditions for shape preserving of a kind of parametric rational circular arc spline

有文献表明利用向量值连分式插值,可在平面上构造一种GC′连续的参数有理圆弧样条,并且可通过调整端点切向量使其具有保形性,但没有给出如何调整端点切向量的一般原则,不便于实际应用。文章首先介绍参数有理圆弧样条的构造,并建立相邻两分段点切向量之间的递推关系式,然后再利用此关系式给出了此参数有理圆弧样条保形性的充要条件,为实际应用提供了理论依据。

In the literature related,the GC′ continuity parametric rational circular arc spline has been constructed in the plane by means of vector valued continued fractions interpolants,and the tangent vector of the first knot can be adjusted to preserve the shape of the spline,but the general principle of adjusting the tangent vector has not been given,which is inconvenient for practical use. In this paper,the construction of parametric rational circular arc spline is introduced briefly,the recurrence relation between the tangent vectors of adjacent knots is given,then using the relation,the necessary and sufficient conditions of shape preserving are provided.