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

RESUMO

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.