Journal of Computer Science and Technology

   

Quasi-Developable B-Spline Surface Design with Control Rulings

Zi-Xuan Hu1(胡梓轩), Peng-Bo Bo1,*(伯彭波), Member, CCF, and Cai-Ming Zhang2,3(张彩明), Senior Member, CCF   

  1. 1School of Computer Science and Technology, Harbin Institute of Technology, Weihai 264209, China
    2Shandong Co-Innovation Center of Future Intelligent Computing, Yantai 264005, China
    3Shandong Province Key Laboratory of Digital Media Technology, Shandong University of Finance and Economics, Jinan 250061, China

We propose a method for generating a ruled B-spline surface fitting to a sequence of pre-defined ruling lines and the generated surface is required to be as-developable-as-possible. Specifically, the terminal ruling lines are treated as hard constraints. Different from existing methods that compute a quasi-developable surface from two boundary curves and cannot achieve explicit ruling control, our method controls ruling lines in an intuitive way and serves as an effective tool for computing quasi-developable surfaces from freely designed rulings. We treat this problem from the point of view of numerical optimization and solve for surfaces meeting the distance error tolerance allowed in applications. The performance and efficacy of the proposed method are demonstrated by the experiments on a variety of models including an application of the method for path planning in 5-axis Computer Numerical Control (CNC) flank milling.


中文摘要

1、研究背景(context):
可展曲面能够不经拉伸和撕裂准确展开到平面,是纸张、木材、钢板等难拉伸、易弯曲材料的理想数学模型。可展曲面的设计方法得到了广泛的研究,其中一类方法采用数值优化技术,基于边界曲线和母线等设计要素,得到误差满足实际应用要求的近似可展曲面。可展曲面的表示形式有网格和样条曲面等多种形式,为了满足曲面表示的工业标准,本文研究B样条近似可展曲面的生成。
2、目的(Objective):
本文目的是提供一种直观的近似可展曲面设计方法,类似通过控制点进行曲线设计的理念,该方法通过给定一些设计曲面的母线作为控制母线,生成尽量经过给定母线的近似可展曲面。
3、方法(Method):
本文将要研究的问题描述为带约束的数值优化问题,提出控制母线约束条件的表示形式,研究了与可展曲面设计相关的其它约束条件,通过求解非线性优化问题得到结果。
4、结果(Result & Findings):
大量实验展示了本文方法得到的可展曲面能够很好逼近给定的控制母线,平均距离误差在模型大小的1%左右,并且得到的近似可展曲面的法向偏角小于6度,其可展性满足实际应用要求。本文实验也说明了在任意给定的控制母线附近存在有实际应用价值的近似可展曲面的解。本文方法的缺点是需要求解非线性优化问题,计算时间还达不到实时设计的要求。
5、结论(Conclusions):
本文方法是首个基于控制母线的近似可展曲面设计方法,相对于传统的基于曲面边界曲线的可展曲面设计方法,本文方法具有更好的几何直观性,如果能进一步提高计算效率,实时得到设计曲面,该类方法将称为一种新的有效的可展曲面设计方法。



Key words: developable surface, surface modeling, B-spline surface, numerical optimization

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ISSN 1000-9000(Print)

         1860-4749(Online)
CN 11-2296/TP

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