A rational interpolation surface model and visualization constraint

Abstract

This paper presents a new weighted bivariate blending rational spline interpolation based on function values and partial derivatives. The new spline has some characteristics comparing with the present interpolation. Firstly, the interpolation function can be simply expressed with symmetric basis functions. Secondly, the interpolating function is C 1 continuous for any positive parameters. Furthermore, the interpolation surfaces are smooth under the conditions that parameters is not limited. Thirdly, the interpolation functions has more freedom with parameters and a weighted coefficient λ. Fourthly, the interpolation surfaces could be varied as the parameters and weighted coefficient vary. This paper also deals with the properties of the interpolation surface, including the properties of basis function, the properties of integral weighted coefficients and bounded property of the interpolation. What is more important is that the value of the interpolation function at any point in the interpolating region can be modified under unchanged interpolating data by selecting suitable parameters and different coefficients, so the interpolation surfaces can be modified for the given interpolation data when needed in practical design. Experimental results illustrate the effective constraint of this spline interpolation.