学术
摘 要:
给出一种用显式方程精确表示NURBS曲面上曲线的方法,利用该方法NURBS曲面上曲线仍然用NURBS形式来表示,此外,可用显式公式来计算该曲线的控制顶点、权因子和节点矢量。基本思想是：运用代数基本定理避免通常B样条基函数复合所采用的极形式（Polar form）以及非常烦琐复杂的开花（Blossom）运算,把B样条基函数的复合、乘积运算转化为求解线性方程组。通过实例验证了该方法的有效性,可用于CAD/CAM领域中的曲面求交、剪裁以及数控加工刀轨生成等。[著者文摘]
文章出处:
《南京航空航天大学学报》-2008年40卷1期 -85-88页
分 类 号:
文献标识码:
A
文章编号:
1005-2615（2008）01-0085-04
Exact Representation of Curves on NURBS Surfaces
Wei Wei, Zhou Laishui, Wang Zhiguo （College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics ＆ Astronautics, Nanjing, 210016, China）
Abstract:
A method is presented for representing a curve on a non-uniform rational B-spline （NURBS） surface exactly and explicitly and the curve on the NURBS surface is still represented in NURBS form. In addition, its control vertices, weight factors and knot vector can be computed by explicit formulas. The basic idea of the method is as follows： an algebraic theorem is used to avoid computing the composition and multiplication of B-spline basis function by Blossom and Polar form, and to reduce the computa- tion by solving linear equations. Experimental results show that the method is feasible and applicable to CAD/CAM, such as surface trimming, surface intersection and NC tool path generation, etc.[著者文摘]
Key words:
surfaces; curves; non-uniform rational B-spline; Blossom; polar form
基金资助:
教育部优秀青年教师教学科研奖励计划资助项目.
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