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作 者:王永澳 吕杭汀 陈小雕[1] Wang Yongao;Lyu Hangting;Chen Xiaodiao(College of Computer,Hangzhou Dianzi University,Hangzhou 310018)
机构地区:[1]杭州电子科技大学计算机学院,杭州310018
出 处:《计算机辅助设计与图形学学报》2024年第5期687-700,共14页Journal of Computer-Aided Design & Computer Graphics
基 金:国家自然科学基金面上项目(61972120).
摘 要:曲线曲面间求交计算在CG和CAD中有着广泛的应用.牛顿法等迭代法计算效率高但需要良好的初始值;裁剪法具有良好的鲁棒性但计算效率不理想,尤其是对于相切情况的求交问题.为此,提出一种计算2条B样条曲线交点的混合方法.首先提出一种高效的线性复杂度裁剪方法,用于获得良好的初始值;然后提出一种与导数无关且效率更高的改进的割线法,用于验证贯穿性相交情况;最后提出一个相切情况下收敛阶为2的迭代公式,其性能远优于现有的牛顿法和裁剪法.理论上,混合方法若与根隔离法相结合,可以应用于更多类型曲线间的求交问题.数值实验结果表明,与现有的同类方法相比,在贯穿情况下,所提方法的计算效率提高约10%,在相切情况下则提高约100%~300%.The intersection problem between curves and surfaces has wide applications in computer graphics and computer-aided design.Iterative methods,such as the Newton’s method,are efficient but need good ini-tial values,while clipping methods are robust to obtain all intersection points but their efficiency of compu-tation is not so good,especially for computing a contact intersection point.This paper presents a hybrid method for computing intersections between two B-spline curves.There are three main contributions.Firstly,it provides an efficient clipping method of linear complexity,which can be used to obtain good initial values.Secondly,it presents a simple method for verifying traversal cases,and provides a derivative-free method with a higher efficiency index which generalizes the secant method.Finally,it presents a new iterative for-mula of convergence rate 2 for a contact case,which achieves much better performance than those of pre-vailing Newton’s method and clipping methods.In principle,by combining with root-isolation method,it can be applied for the intersection problem of non-polynomial curves.Numerical experimental results show that,comparing with prevailing Newton’s method,the computational efficiency of the new method can be im-proved by about 10%and 100%‒300%for a traversal case and a contact case,respectively.
关 键 词:B样条曲线/曲线求交 裁剪法 线性包围法 相切 非多项式函数
分 类 号:TP391.41[自动化与计算机技术—计算机应用技术]
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