Improved flattening algorithm for NURBS curve based on bisection feedback search algorithm and interval reformation method

Deformation of flattening is one of the difficulties in ship reconstruction, which requires inversion of spline curves to accurately calculate the knots of end points of flattening line segment. To reduce the error of spline knot in the flattening algorithm caused by unstable inversion, the bisection feedback search (BFS) algorithm is proposed to stably achieve the global optimum. The feedback object of feedback operation, which is recorded by a bisection table, is judged using convergence criteria. Considering the strong convex hull property of the spline curve, the IR-FBS algorithm is proposed, which is the BFS algorithm accelerated by the proposed interval reformation (IR) method by reducing the feedback time and the number of iterations. Finally, the flattening algorithm of the spline curve is improved based on the IR-BFS algorithm, considering both stability and accuracy. To verify the effectiveness of the algorithms, comparative experiments are designed. First, the BFS algorithm and Newton–Raphson (NR) method are compared to verify the stability of solutions. Then, the IR-FBS algorithm is compared with FBS and the best existing three compound algorithms to check the acceleration effects and computational efficiency. Next, the improved flattening algorithm is used to process spline curves, and the flattening effect is investigated through the change of curve curvature. The experiments demonstrate that the BFS algorithm can ensure both accuracy and stability of solutions. In addition, the IR-BFS has the optimal performance among compound algorithms by the accelerated effects of IR method, and the improved flattening algorithm can ensure the high smoothness and meets the requirements of practical engineering. •A new global spline inversion algorithm (BFS) provides accurate and stable results.•The interval reformation method reduces the computation time of the BFS algorithm.•The spline curve flattening algorithm is improved by BFS and interval reformation.•The proposed methods can be used for the deformation of ship reconstruction.•The results can be applied to ship dynamic damage stability.