A New Algorithm for Polynomial Interpolation in Complex Surface Modeling

High-fidelity modeling of complex surfaces is the basis for accurate characterization of surface quality and realistic analysis of performance in the fields of digital process design of products and digital twin. This paper proposes to improve the new polynomial interpolation algorithm to improve the effect of the polynomial interpolation algorithm fitting in complex surface modeling through the center variable, and combines the moving least squares approximation function with the new polynomial interpolation algorithm to further optimize the effect of the complex surface modeling through the regular moving construction of the fitting surface by the local approximation method. It is found that the overall average error and standard deviation between the turbine blade surface roughness modeled based on the new polynomial interpolation algorithm and the roughness meter measurements are within 1.7 μm (0.7580-1.6715 μm), and the error is within the acceptable range. It is also found that using the method of this paper can save a lot of time and realize the rapid modeling of complex surfaces of the body. It also has good smoothness, which provides convenience for the subsequent processing of complex surface modeling. The new polynomial interpolation algorithm proposed in this paper provides a new idea for the research in the field of complex surface modeling, and can be applied to the actual production to assist the design and production of related products.