Non-uniform B-spline optimization method for generating swept surfaces

2026-09-12

AI Summary

提出了一种使用非均匀B样条的优化方法，通过选取特征点和调整控制点来提高扫掠面的逼近精度，减少了控制点数量并降低了平均误差。

Abstract

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.

Problem

• swept surfaces
• non-uniform B-splines
• approximate accuracy
• computer-aided design
• optimization method

Innovation

• non-uniform B-splines
• swept surfaces
• approximation accuracy
• control points optimization
• feature point selection