Multi-degree reduction of NURBS curves based on their explicit matrix representation and polynomial approximation theory

NURBS curve is one of the most commonly used tools in CAD systems and geometric modeling for its various specialties, which means that its shape is locally adjustable as well as its continuity order, and it can represent a conic curve precisely. But how to do degree reduction of NURBS curves in a fast and efficient way still remains a puzzling problem. By applying the theory of the best uniform approximation of Chebyshev polynomials and the explicit matrix representation of NURBS curves, this paper gives the necessary and sufficient condition for degree reducible NURBS curves in an explicit form. And a new way of doing degree reduction of NURBS curves is also presented, including the multi-degree reduction of a NURBS curve on each knot span and the multi-degree reduction of a whole NURBS curve. This method is easy to carry out, and only involves simple calculations. It provides a new way of doing degree reduction of NURBS curves, which can be widely used in computer graphics and industrial design.     

空间凸轮廓面侧铣加工及最小二乘优化刀位方法

通过对空间凸轮非等价加工方式下理论刀轴轨迹曲面微分几何特性的研究，表明加工空间凸轮工作廓面必然存在法矢异向误差。为寻求加工误差最小的最佳刀轴矢量，提出了数控侧铣加工空间凸轮廓面的方法。根据实际刀轴轨迹面是直纹面的性质，以NURBS直纹面重构理论刀轴轨迹面，采用最小二乘优化方法确定侧铣加工刀位，给出了理论加工误差模型，并通过实例的数值计算和加工实验结果证明了该方法的有效性。     

Curve interpolation with variable feedrate for surface requirement

Finish machining of a curved surface is often carried out by an NC system with curve interpolation in the field. This function, called a NURBS interpolation, adopts a feedrate optimizing strategy based on both the geometrical information of the curved path and dynamic properties such as the curvature of the curve, the allowable acceleration and the time constant. However, in the case of a finish cut using a ball-end mill, the curve interpolator needs to take the machining process into account for improved surface roughness, while reducing the polishing time. This surface roughness on high-speed machining is theoretically defined by the feed per tooth and the pickfeed at the given radius of the tool. In this study, the effect of low machinability at the bottom of a tool on surface roughness is also considered. A curve interpolation algorithm is proposed for generating particular feedrate commands that are able to control the roughness of a curved surface. The simulation of the machined surface by the proposed algorithm was carried out, and experimental results are presented. A feedrate scheme that depends on the inclination angle has important potential application in part finishes consistent with prescribed surface roughness. The results show that the proposed algorithm is potentially useful for roughness-controlled machining of curved surface products.     

一种基于曲面建模与多边形建模的混合人体建模方法

针对人体模型在服装行业的应用,提出了一种基于曲面建模与多边形建模的混合人体建模方法.该方法根据人体不同部位对于模型动态改变中的不同作用分为动态部位和静态部位.动态部位是指在系统中需要根据个体特征尺寸进行调整的部位;静态部位是指变动可以忽略的部位.动态部位采用基于切片的NURBS参数化曲面建模方法,可以满足这些部位根据个人特征尺寸进行调整;对于静态部位,采用多边形建模方法,能更快捷、方便地予以定性描述.实验证明该方法能高效地、快捷地实现人体模型的实时生成和实时调节.     

基于IGES接口的电磁计算模型数据交互

现今武器大多是利用非均匀有理B样条(non-uniform rational B-spline,NURBS)数学表述,在CAD/CAM系统下完成建模和重构.利用电磁计算软件运算武器模型的雷达散射截面(radar cross section,RCS)从而评估其隐身性能,就需要与CAD/CAM系统进行数据交互.通过对基本图形转换规范(initial graphics exchange specification,IGES)数据标准的分析,为电磁计算软件编译了IGES数据接口.该数据接口具备IGES文件数据导入和模型数据导出另存为IGES文件格式的功能,从而实现了自行开发的计算软件CRCS v1.2和CAD系统软件的数据交互,提高了软件处理复杂模型的能力进而使模型重构与计算趋于一体化.     

基于NURBS曲面的棉花器官建模

数字农业将工业可控生产和计算机辅助设计的思想引入农业。该文介绍了利用NURBS和OpenGl对虚拟棉花主要器官果枝、铃、主茎叶、果枝叶、花瓣、苞叶等进行建模的方法,得到了逼真的效果。与三维数字化方法相比,省去了大量精确数据的测量和数学表达式的拟合工作。     

NURBS边界曲面直接生成法

由于非均匀有理B样条(NURBS)曲面的复杂性,传统NURBS边界曲面的生成是先构造孔斯曲面,再由孔斯曲面向NURBS曲面转换得到,其操作过程比较烦琐。针对此问题,提出了NURBS边界曲面直接生成算法,该算法根据给定的四条NURBS边界曲线,结合孔斯曲面生成方法直接插值生成NURBS曲面,从而避免了通过孔斯曲面向NURBS曲面转换所带来的计算代价,因此同传统方法相比,具有较低的计算代价。实验结果表明:该算法简化了曲面生成步骤,减少了曲面转换过程的计算量,生成的曲面边界信息明确,且连续性好。     

圆弧的C-Bézier曲线表示

圆弧的表示一直是计算机辅助设计关心的问题.但是,现有的方法对用户并不友好.利用C-Bézier曲线,给出了圆弧的一系列表示方法,讨论了这些表示方法的相互关系.为度量其优劣,提出了特征比的概念.同时,发现了高次的C-Bézier表示要优于低次的表示,特别地,五次C-Bézier曲线能很好地表示整圆.     

NURBS双向蒙皮造型方法的研究与实现

本文通过对ＮＵＲＢＳ造型方法技术的研究，在自主开发的ＳｕｐｅｒＭａｎＣＡＤ／ＣＡＭ集成系统中成功地实现了基于复杂曲线的ＮＵＲＢＳ双向蒙皮曲面的造型功能，从而建立了完全基于ＮＵＲＢＳ方法的ＣＡＤ／ＣＡＭ系统．通过大量的工程应用和实例验证表明所研究的ＮＵＲＢＳ方法是一种适用于复杂外形产品设计与制造的、灵活有效的造型方法．     

改进的NURBS曲线预估校正插补方法

现行的NURBS曲线参数预估校正插补方法不能预估最开始的两个参数,而且不能控制预估参数迭代修正的次数。提出改进的NURBS预估校正插补方法,该方法预估插补点参数,根据最大进给步长约束、轮廓误差约束以及法向加速度约束,判定预估参数与实际参数的误差,当误差在允许范围内,则对参数步长增量进行调整,否则进行迭代修正。仿真实验结果表明,新方法通过对参数步长增量的调整,使得预估参数更加接近实际参数,较现有方法有效减少了参数迭代修正的次数,利于实时插补的实现。