有理多结点样条插值曲线及曲面

Rational Many-Knot Spline Interpolating Curves and Surfaces

鉴于多结点样条曲线 (MSIC)是一种点点通过的插值样条曲线 ,因此在对多结点样条插值曲线研究的基础上 ,给出了有理多结点样条插值曲线和有理多结点样条插值曲面的定义 ,并讨论了有理多结点样条的性质 ,对有理多结点样条曲线和有理多结点样条曲面的光滑拼接问题进行了讨论 .此外 。

Many knot spline interpolating curves (MSIC) are a kind of spline curves that precisely pass through every interpolating point on the curves, many knot spline interpolating surfaces (MSIS) also pass through every interpolating point on the surfaces. Many knot spline interpolating curves have been successful applied in many fields, such as computer animation, computer font design and wavelet analysis, etc. Based on studying of many knot spline interpolating curves, some definitions and properties of rational many knot spline interpolating curves and those of rational many knot spline interpolating surfaces are taken into account in this paper. All the concepts and properties discussed in this paper are the first step to research rational many knot spline interpolating curves and rationl many knote interpolating surfaces. Following the properties and definations, some applications of these rational curves and surfaces are introduced. The Problem of continuity of many knot spline interpolating curves and that of rational many knot spline interpolating curves are discussed by the end of this paper.