Rational Many-Knot Spline Interpolating Curves and Surfaces
有理多结点样条插值曲线及曲面

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.