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

Fast Reconstruction Model of the Ship Hull NURBS Surface with Uniform Continuity for Calculating the Hydrostatic Elements

“…In the case of the stepwise knot refinement method applied to the flattening algorithm, different inserting knots produce different deformations to the original curve [44]. These deformations eventually affect the changes in curve curvature and other characteristics [48].…”

“…The algorithm has three accuracy thresholds α, β, γ, where α is used to assess whether the knot interval space reaches the preset accuracy, β is used to assess whether the algorithm performs iteration on the current interval or the next subinterval, and γ is used to determine the time required for the algorithm to execute the NR method. The design and parameter setting of the FHP-BFS and IR-BFS algorithms are described in detail in the study by Zhu et al [44].…”

“…In the inversion algorithm, the parameters are set as α = β = 10 −5 and γ = 10 −3 based on the recommendation of Zhu et al [43]. Similarly, based on the value of γ in the study by Zhu et al [44], the parameter in the UCG algorithm is set as ς = 10 −3 , t = 10 3 in the stepwise knot refinement method, and ξ = 10 3 in the HSG algorithm following a previous study [48].…”

“…Zhu et al [43] proposed the IR-BFS algorithm to solve the problem of the slow parameter inversion of NURBS curve points, which can ensure that the calculation accuracy meets the threshold conditions while improving the calculation efficiency. Subsequently, Zhu et al [44] constructed the FHP-BFS algorithm by introducing the NR algorithm into the IR-BFS algorithm, which improved the computational efficiency under the threshold of high inverse accuracy. These two studies allow for the quick construction of accurate and uniform continuous NURBS curves.…”