Multi-Degree Reduction of Said-Ball Curves and Engineering Design Using Multi-Strategy Enhanced Coati Optimization Algorithm.

Within computer-aided geometric design (CAGD), Said-Ball curves are primarily adopted in domains such as 3D object skeleton modeling, vascular structure repair, and path planning, owing to their flexible geometric properties. Techniques for curve degree reduction seek to reduce computational and storage demands while striving to maintain the essential geometric attributes of the original curve. This study presents a novel degree reduction model leveraging Euclidean distance and curvature data, markedly improving the preservation of geometric features throughout the reduction process. To enhance performance further, we propose a multi-strategy enhanced coati optimization algorithm (MSECOA). This algorithm utilizes a good point set combined with opposition-based learning to refine the initial population distribution, employs a fitness-distance equilibrium approach alongside a dynamic spiral search strategy to harmonize global exploration with local exploitation, and integrates an adaptive differential evolution mechanism to boost convergence rates and robustness. Experimental results demonstrate that the MSECOA outperforms nine highly cited agorithms in terms of convergence performance, solution accuracy, and stability. The algorithm exhibits superior behavior on the IEEE CEC2017 and CEC2022 benchmark functions and demonstrates strong practical utility across four engineering optimization problems with constraints. When applied to multi-degree reduction approximation of Said-Ball curves, the algorithm's effectiveness is substantiated through four reduction cases, highlighting its superior precision and computational efficiency, thus providing a highly effective and accurate solution for complex curve degree reduction tasks.