Abstract: NURBS surfaces are one of the most crucial techniques in surface modeling，which has extensive applications in various aspects of CAGD/CG.This paper is devoted to the shape modification of NURBS surfaces，in which a method based on energy optimization is proposed.Specifically，geometric features（such as position，partial derivative or normal vector） of the selected parametric points on a given NURBS surface are modified，by minimizing the strain energy of the error surface.The numerical examples show that this method can realize miscellaneous modification effects and is convenient for interactive design.

Key words: Non-Uniform Rational B-Splines（NURBS） surfaces, energy optimization, geometric features, shape modification

摘要： NURBS作为曲面造型技术中的重要方法之一，在计算机辅助几何设计和计算机图形学领域中有着广泛的应用。针对NURBS曲面的几何特征修改，提出了基于能量优化的修改方法。通过对NURBS曲面的控制顶点进行扰动，以曲面的应力能改变为目标函数并使之最小化，实现了NURBS曲面上给定多个点处的位置、一阶偏导矢、二阶偏导矢和法矢等几何特征的修改。数值实例表明该方法用于微调时，可实现对曲面局部形状的多种修改效果，便于交互设计。

关键词: 非统一有理B样条曲面, 能量优化, 几何特征, 形状修改