Fast High-Precision Bisection Feedback Search Algorithm and Its Application in Flattening the NURBS Curve

It is important to accurately calculate flattening points when reconstructing ship hull models, which require fast and high-precision computation. However, some search algorithms, such as the bisection method, iterate near the optimal value too many times before converging in high-precision computation. The paper proposes a fast high-precision bisection feedback search (FHP-BFS) algorithm to solve the problem. In the FHP-BFS algorithm, the Newton–Raphson (NR) method is adopted to accelerate the convergence speed by considering the iteration characteristics of subintervals. Furthermore, a new feedback mechanism is proposed to control the feedback directions. In addition, an acceleration algorithm, called the interval reformation method, is used to guide the FHP-BFS algorithm for fast convergence. Finally, the flattening algorithm is improved by the FHP-BFS algorithm. In the comparative experiments, the practical efficacy of the FHP-BFS algorithm is first demonstrated, and then the optimal range of the threshold precision is determined. Next the FHP-BFS algorithm is compared to the best existing algorithms. Finally, the performance of the improved flattening algorithm is verified. The experiments demonstrate that the FHP-BFS algorithm has optimal performance among the compared algorithms, and it has an improved computation efficiency while maintaining robustness. The improved flattening algorithm reduces the computation time, ensures smoothness and meets practical engineering requirements.