Abstract:

For the integral modeling of objects with composite surfaces, it is necessary to stitch up the single-sided patches with gaps. Traditional surface intersection technology has many shortcomings, which can not meet the requirements of intersection accuracy and intersection speed at the same time. Regarding this an optimal tracing method is proposed for surface intersection. Five degree non-uniform B-spline is used as a fitting curve. The tracing step size is correlated with the curvature at the end of the intersection line in the process of intersection, which can make the step size change in real time according to the specific environment. The intersection algorithm is stable, accurate and fast. The intersection process of different surfaces is realized in Surface Reverse, a self-developed reverse system. The experimental verification is carried out based on the fixed step tracking method and the improved step-adaptive tracking method. The results show that the improved tracking method not only has less computation and shorter time, but also has less intersection lines when the intersection line error is less than 0.001 mm. The accuracy can reach above micron level. This intersection algorithm is stable, accurate and fast.

Key words: non-uniform B-spline curve, adaptive step, tracking method, surface intersection

摘要：

对具有多种曲面特征的实体进行建模，必须对相邻的单面片进行拼接。传统曲面求交技术有很多缺陷，例如在求交精度、求交速度上不能同时满足要求。对此提出步长可自适应的追踪法进行曲面求交，将五次非均匀B样条作为拟合曲线，在求交过程中将追踪步长值与交线末端曲率相关联，可以使步长根据具体环境实时变化。限定精度阈值[ε]为0.001?mm，将曲面求交试验在自主研发的逆向系统Surface Reverse中进行，分别采用传统追踪法和基于步长自适应的追踪法进行曲面求交，结果表明，追踪步长可自适应的追踪法求取交线的计算量少、用时较短，且交线精度可达到μm级。这种相交算法稳定、准确且速度较快。

关键词: 非均匀B样条曲线, 步长自适应, 追踪法, 曲面求交