An efficient bivariate three-point Lagrange interpolation method based on coordinate transformation

Abstract

This paper proposes a bivariate three-point interpolation method based on coordinate transformation. The transformation significantly improves computational efficiency by converting radial sampling points into interpolation nodes, while enabling high-precision computation of coordinates and normal vectors for any surface point. Numerical experiments validate the effectiveness of the bivariate three-point interpolation method based on coordinate transformation. Although its accuracy is slightly lower than that of the NURBS surface method, it still meets the requirement for high precision. In particular, the proposed method drastically reduces the computation time by more than 50% compared to the NURBS surface method. In addition, it seamlessly computes coordinates and normal vectors for any surface point. It is significantly helpful for the improvement of computational efficiency in engineering for the measurement and evaluation of aircraft radomes.