发表机构
Central South University; Tsinghua University（中南大学; 清华大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出一种基于非均匀B样条的优化方法，通过分布函数选取特征点并反算控制点，在保证精度的同时减少控制点数量，实验表明控制点减少15.85%，平均误差降低51.35%。
AI 中文摘要
扫掠曲面构建在计算机辅助设计中广泛应用。我们提出了一种使用非均匀B样条的新型优化方法，以提高扫掠曲面的近似精度。首先，计算扫掠形状上的离散点，并利用表面积、离散曲率、一阶导数及其旋转角度等几何属性推导出表示曲面不规则性的分布函数，权重根据样本进行调整。然后，基于分布函数选择特征点，通过反算确定近似非均匀B样条曲面的控制点，从而产生优化近似。最后，根据估计的近似误差调整特征点的数量。在969个随机生成的扫掠样本和1个管道示例上的实验表明，所提出的算法在指定精度0.01下，以更少的控制点达到相似的精度，控制点数量减少了约15.85%。此外，在采样点充足的情况下，当特征点倍数为路径控制点的10倍时，平均误差降低了约51.35%，优于可比方法。
英文摘要
Swept surface construction is widely used in computer-aided design. We propose a novel optimization method using non-uniform B-splines to improve the approximate accuracy of swept surfaces. First, discrete points on the swept shape are computed, and geometric properties such as surface area, discrete curvature, first-order derivatives, and their rotation angles are used to derive a distribution function representing surface irregularity, with weights adjusted from samples. Then, feature points are selected based on the distribution function to determine control points for the approximate non-uniform B-spline surface via inverse calculation, producing an optimized approximation. Finally, the number of feature points is adjusted based on the estimated approximation error. Experiments on 969 randomly generated sweep samples and 1 pipe example show that the proposed algorithm achieves similar accuracy with fewer control points, reducing them by about 15.85% at a specified accuracy of 0.01. Moreover, with ample sampling points, it reduces the average error by approximately 51.35% when the feature point multiple is 10 times the path control points, outperforming comparable methods.
CommentsUpdated version of the paper accepted to BDDM 2025
Journal ref2025 International Conference on Big Data and Data Mining (BDDM)
