Curve and surface fairing is crucial in computer-aided geometric design, influencing product quality, physical performance, and aesthetics. Traditional methods often apply global modifications, lacking fine-grained control. This paper introduces a novel progressive-iterative fairing method based on control point adjustment. By assigning independent weights to each control point, our approach enables precise, localized shape adjustments. The method functions both globally and locally, allowing for comprehensive shape fairing and fine control over the fairing effect. Furthermore, this paper provides an automatic control point selection method to adjust shapes, thereby eliminating the reliance on manual interaction. Numerical experiments demonstrate the efficiency and effectiveness of our approach.

翻译：曲线与曲面的光顺在计算机辅助几何设计中至关重要，直接影响产品质量、物理性能和美观性。传统方法通常采用全局修改，缺乏细粒度的控制。本文提出一种基于控制点调整的新型渐进迭代光顺方法。通过为每个控制点分配独立权重，该方法能够实现精确的局部形状调整。该方法兼具全局与局部功能，既可用于整体形状光顺，又可对光顺效果进行精细控制。此外，本文还提供了一种自动控制点选择方法用于形状调整，从而消除对人工交互的依赖。数值实验证明了该方法的有效性与高效性。