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

Area of Science:

• Computer-aided geometric design (CAGD)
• Computational geometry
• Optimization algorithms

Background:

• Said-Ball curves are crucial in CAGD for 3D modeling, vascular repair, and path planning due to their geometric flexibility.
• Curve degree reduction is vital for optimizing computational and storage resources while preserving essential geometric properties.

Purpose of the Study:

• To develop a novel degree reduction model for Said-Ball curves that enhances geometric feature preservation.
• To introduce and evaluate a multi-strategy enhanced coati optimization algorithm (MSECOA) for improved performance in optimization tasks.

Main Methods:

• A new degree reduction model utilizing Euclidean distance and curvature data.
• Development of the multi-strategy enhanced coati optimization algorithm (MSECOA) incorporating opposition-based learning, fitness-distance equilibrium, dynamic spiral search, and adaptive differential evolution.
• Performance evaluation using IEEE CEC2017 and CEC2022 benchmark functions and constrained engineering optimization problems.

Main Results:

• The MSECOA algorithm demonstrated superior convergence, accuracy, and stability compared to nine other highly cited algorithms.
• The proposed degree reduction model significantly improved the preservation of geometric features in Said-Ball curves.
• The MSECOA algorithm showed strong practical utility in engineering optimization and effective application in multi-degree reduction approximation of Said-Ball curves.

Conclusions:

• The novel degree reduction model and the MSECOA algorithm offer a highly effective and accurate solution for complex curve degree reduction tasks in CAGD.
• The study validates the MSECOA's efficiency and precision, providing a valuable tool for geometric design and optimization challenges.