A Fast Algorithm of Normal Vector Calculation for NURBS Surface Based on Taylor Expansion

In order to improve the efficiency of normal vector calculation for NURBS surface in complex surface modeling, this paper proposes a fast calculation algorithm for NURBS surface and its normal unit vector based on Taylor expansion (FCNN). When using FCNN to calculate the normal unit vector of a NURBS surface, it is only necessary to calculate the derivative vector of the iso-parametric line of the B-spline surface at each node from 0 to its order in the NURBS surface fraction expression. Then the Taylor formula can be used to calculate the corresponding parameters in the normal unit vector of the NURBS surface, and the corresponding points on the surface can be calculated in this process. In order to illustrate the feasibility and efficiency of the proposed algorithm, this paper carried out simulation verification, and compared the calculation results and code running time. The simulation results show that the FCNN algorithm is accurate and feasible, which is of great significance for improving the calculation efficiency of the points on the NURBS surface and the normal unit vector.