摘要： 在交互设计系统中曲率(包括高斯曲率和平均曲率)评价是分析曲线曲面质量的重要工具。对于B样条曲线的光顺算法已经比较成熟。但对于如何基于曲率（包括高斯曲率和平均曲率）的曲面光顺算法则还有许多工作要做。该文提出了一种基于最小二乘的曲面优化算法，可以得到比较好的结果。该光顺算法主要包括两个步骤：依据曲率光顺准则修改曲面的曲率和修改后的曲率基于原曲面优化反向求出新的控制顶点。

关键词: 高斯曲率, 最小二乘法, 高斯-牛顿法

Abstract: Assessment of curvature is an important tool for the analysis of curves and surface in the interactive design system. The fairing algorithm by curvature for B-spline curves has been perfect. But fairing algorithm by curvature (including Gaussian and mean curvature)for B-spline surface is no more maturity. This paper presents a new algorithm based on the least square optimal method. That should lead to a desired result. This algorithm includes two steps: modifying the curvature of surface by curvature criterion of fairing surface, a new surface obtained by utilizing the least square optimal method based on result of the first step.

Key words: Gaussian curvature, Least square, Gaussian-Newton method

中图分类号: 

• TP391.72