An Advanced Geometric Segmentation Approach for High-Precision and High-Efficiency Curve Fitting

This paper presents the Geometric Segmentation Curve Fitting (GSCF) method for NURBS curve fitting. By analyzing geometric characteristics, the method identifies optimal segmentation points, fitting each segment independently to ensure accuracy. Given that excessive control points increase computational complexity, GSCF reduces control points while maintaining or improving fitting accuracy, producing a smoother curve. The study first examines three key issues in curve fitting without segmentation: excessive control points, large corner errors, and path distortion. It then identifies feature points using chord error, curvature variation, and path length differences for precise segmentation. Based on accuracy requirements, the method selects either global fitting or approximation with the Least Squares Progressive Iterative Approximation (LSPIA) algorithm to optimize control point distribution. Simulation results show that GSCF reduces control points by over 85% while improving accuracy by more than 90%. The method applies to various curve-fitting applications, including CAD/CAM, robotic path planning, and CNC machining, demonstrating broad engineering potential.