Abstract: Geometric iteration method has been widely used in computer aided geometric design (CAGD). In order to improve the convergence speed and iterative accuracy of the traditional B-spline curve interpolation in geometric iterations, this study proposes the geometric iteration method based on many-knot spline polishing functions, which introduces many-knot spline polishing functions, and combines many-knot spline polishing functions method and geometric iteration method in curve fitting. After polishing operator and iterating, the curve fitting method with high approximation under the optimal solution of L-BFGS iterative algorithm is constructed. Experimental results show that the proposed method not only reduces the times of iterations, but also improves the iterative speed under the same accuracy. The proposed geometric iteration method can be used in the shape design of airplanes, automobiles, etc. It can also be used to reconstruct and rebuild the shape of cultural relic houses and satellite image processing.

Key words: geometric iteration method, many-knot spline polishing functions, limited-memory BFGS algorithm, B-splines