插值点和法向的能量极小B样条曲线曲面

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

为了使插值点及法向的曲线曲面更加光顺,提出了一种基于弯曲能量极小的B样条曲线曲面插值点及法向的方法.首先根据插值点及法向列出约束方程,接着引入弯曲能量函数利用拉格朗日乘数法求出能量极小时约束方程的解,进而求出能量极小的B样条插值曲线曲面.实验给出了几种不同的曲线以及它们的曲率半径和对应的运算时间.数值结果表明,与没有能量约束的插值曲线相比,所提方法的曲线的曲率半径波动较小,运算时间较短,因此所提方法求出的曲线曲面更加光顺,且计算效率更高.

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.