Point-Normal Interpolatory B-Spline Curve and Surface with Minimal Energy

In order to make the curved surface of interpolation points and normals smoother, an algorithm based on the interpolation points and normals of B-spline surfaces with minimal bending energy is proposed. Firstly, the constraint equations are listed according to the interpolation points and normals, and then the bending energy function is introduced to solve the solution of the energy pole hour constraint equation by the Lagrange multiplier method, and then the B-spline interpolation curve surface with very small energy is obtained. Several different curves are given experimentally, along with their radius of curvature and corresponding operation time. The numerical results show that compared with the interpolation curve without energy constraint, the curve radius fluctuation of the proposed method is smaller and the operation time is shorter, so the curve surface obtained by the proposed method is smoother and the calculation efficiency is higher.