Curvature-driven optimization of Bézier curve construction via Particle Swarm Optimization

Constructing Bézier curves with smooth shapes and specific curvature profiles is often challenging, as the process of selecting suitable control points is not straightforward. Curvature strongly influences the overall behavior of curves, and achieving a target curvature requires a systematic optimization strategy rather than a trial-and-error approach. This work proposes a curvature-driven framework based on Particle Swarm Optimization to search for optimal control points that satisfy a desired curvature profile. The study demonstrates the effectiveness of swarm intelligence in geometric modeling problems. Convergence analysis and statistical visualization are used to identify suitable Particle Swarm Optimization parameter settings, improving optimization efficiency and curvature accuracy. Based on the analysis of the proposed method, suitable parameter ranges for the three target curvature profiles are identified, including swarm sizes of 70–100, inertia weights between 0.4 and 0.8, and acceleration coefficients in the range of 0.5 to 2. The proposed approach enables the construction of Bézier curves that satisfy curvature constraints and offers practical value and insights for applications in Computer-Aided Design, robotics, and path planning.