A weighted bivariate blending rational interpolation function and visualization control

摘要

A new weighted bivariate blending rational spline with parameters is con-structed based on function values of a function only. The interpolation is C ~1 in the whole interpolating region under the condition which free parame-ters is not limited. This paper deals with the properties of the interpolation surface, including the properties of basis function, the properties of integral weighted coeffcients 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 inter-polation 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.