ICP Algorithm (Classic Implementation) with Moving Least-Squares Enhancement for Curve and Surface Fitting

This paper presents a curve and surface fitting methodology based on the Moving Least-Squares (MLS) algorithm. Compared to conventional Least-Squares (LS) methods, this approach incorporates significant improvements that result in generated curves and surfaces exhibiting enhanced precision and better smoothness properties. We provide a comprehensive explanation of the MLS algorithm's underlying principles, including its key differentiators from other fitting techniques through comparative analysis of their advantages and limitations. The implementation typically involves: 1) Local weight function calculation using Gaussian or polynomial kernels, 2) Iterative neighborhood point selection via k-d tree spatial partitioning, and 3) Solving local weighted least-squares problems for each evaluation point. Additionally, we present practical application case studies demonstrating the method's real-world performance, accompanied by thorough evaluation and analysis of its computational efficiency and fitting accuracy. In conclusion, this MLS-based curve and surface fitting technique proves to be a highly effective and practical solution with broad application prospects in computer graphics, reverse engineering, and scientific data visualization.