A weighted bivariate blending rational interpolation function and visualization control
A new weighted bivariate blending rational spline with parameters is constructed based on function values of a function only. The interpolation is C-1 in the whole interpolating region under the condition which free parameters is not limited. This paper 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. In order to meet the needs of practical design, an interpolation technique is employed to control the shape of surfaces. The method of value control of the interpolation at any point in the interpolating region is developed. This control method can be applied to modify the local shape of an interpolating surface by selecting suitable parameters simply.
rational spline bivariate blending interpolation weighted interpolation computer-aided geometric design