Improving geometric iterative approximation methods using local approximations

In this study, we propose improvements to Geometric Iterative Methods (GIM) for curve and surface approximation. Our key contributions include introducing an error vector function and deriving new error vectors, which enhance the approximation quality compared to the Least Squared Progressive and Iterative Approximation (LSPIA) methods. Additionally, we integrate parameter correction and control points update based on local approximations, achieving comparable accuracy to Geometric Approximation (GA) methods while being more computationally efficient. Extensive experiments demonstrate the superior accuracy and computational efficiency of our method.