A NURBS Curve Approximation Method Based on GA-PSO Hybrid Optimization

Non-uniform rational B-splines (NURBS) find extensive applications in computer-aided design (CAD), reverse engineering, and robot path planning due to their powerful geometric expressiveness and flexible local control capabilities. However, traditional NURBS fitting methods often suffer from insufficient accuracy and susceptibility to local optima. To address these challenges, this paper proposes a hybrid optimization method combining genetic algorithms with particle swarm optimization to enhance the fitting accuracy and stability of NURBS curves. By optimizing the control point positions and weighting factors of NURBS curves, this method resolves the accuracy limitations encountered by conventional fitting approaches when handling high curvature. Multiple experiments, particularly simulations of PCR (Polymerase Chain Reaction) amplification curves, validate that this method effectively reduces fitting errors and improves accuracy when handling curves with non-uniform data distribution and increasing characteristics. Compared to traditional B-spline curve fitting methods and single optimization algorithms, the proposed method demonstrates significant advantages in both fitting performance and computational efficiency.