A Kind Of Rational Interpolating Spline Surface And Its Convesity

This paper is the expansion and the improvement of literature [38]. At first, some properties arestudied for a(3,2)1-order bivariate rational spline interpolating function using only values of thefunction being interpolated, for example, boundaries, limits, analysis and canonical etc. This paperpoints out that the limit surface graph is hyperbolic paraboloid, and reveals the influence ofparameters on the rational spline interpolating surfaces. Second, the necessary and sufficientconditions for the rational interpolation surface to be local convex are derived. Under the conditions,examples are given to show how the parameters can be chosen and the shapes of the surfaceschanged.Particularly for the interpolation method in literature [38], it is found that this interpolationsurface convexity at a certain point is relatively rigid defects even if the data type value is convex.They are greatly restricted on the applications particularly the applications in Computer AidedGeometric Design (CAGD). In response to this shortage, the paper presented an new interpolationmethod for rational spline interpolating surface whose accuracy isO (k~3)(k is the measure of arectangular grid). Improved the interpolation method in literature [38] whose accuracy isO (k~2).This interpolation method of(3,2)~1-order rational spline interpolating surface still has a simplepiecewise explicit representation and good geometric properties. Under the premise of unchanged theinterpolation conditions, it can achieve the goal of controlling surface shape simply by adjusting theshape parameters to march local modification of the surface. Several full conditions are elicited out bychanging the representation of Gauss curvature into rational function whose denominator is double8times, molecular is also double8times and using the theory of zero points for polynomial with realcoefficient. Thus it can priori judgment the convexity for interpolating surface just through adjustmentshape parameter. Assigned examples validate the methods of this paper.