NURBS曲线,曲面造型过程的可视化设计

由于ＮＵＲＢＳ曲面,曲线构造的复杂性,描述ＮＵＲＢＳ曲线,曲面必然采用复杂的数据结构,这样给人－机交互带来很大的困难。本文利用ＶＣ＋＋编写的ＮＵＲＢＳ曲线,曲面造型系统可以实时观察曲线等操作,这对ＮＵＲＢＳ曲线曲面造型无颖 会带来极大的方便。     

基于NURBS的扫描曲面造型方法的研究

由于非均匀有理Ｂ样条（ＮＵＲＢＳ）表示的曲线,曲面具有充分的灵活性,同时又统一了初等曲线,曲面和自由曲线曲面的表示,故在ＣＡＤ领域得到广泛应用。扫描曲面造型则是自由曲面造型的重要手段之一,介绍了ＮＵＲＢＳ表示曲线曲面的方法及特点,对扫描曲面造的各种情况进行了讨论,在此基础上给出了基于ＮＵＲＢＳ的扫描曲面造型算法。     

准D-NURBS摆转曲面在曲面造型中的应用

提出了基于物理型面设计的准Ｄ－ＮＵＲＢＳ摆转曲面的概念。建立了用于表达具有对称性和拓扑变化的一大类物体的动态的、自由表面模型。这一新的模型是基于摆转ＮＵＲＢＳ曲面之上的,继承了其有用的截面设计特性。在基于物理的框架之内,具有曲面设计的几何特征。用弹性曲面的拉格朗日动力学推导出了准ＤＮＵＲＢＳ摆转曲面的运动方程。举出了一些准ＤＮＵＲＢＳ摆转曲面的应用实例,如曲面倒圆角与调和、曲面拟合及交互式造型等。     

产品造型设计中的NURBS方法研究

适合计算机系统的复杂曲面表示是工业产品造型设计的关键，过去使用的Ｂｅｉｚｅｒ、Ｂ样条方法已不能满足目前设计形势的需要。本文探讨了目前ＣＡＤ／ＣＡＭ系统中利用ＮＵＲＢＳ进行产品复杂曲面设计的理论和方法，全面总结和归纳了ＮＵＲＢＳ曲面造型的基本形式，并对其中典型的造型方法给出了相应的数学表示，展示了其优越的设计几何能力。     

NURBS 曲线的形状调整

ＮＵＲＢＳ曲线、曲面在ＣＡＤ／ＣＡＭ、计算机图形学等领域占有重要的地位。本文通过齐次坐标从代数角度考虑ＮＵＲＢＳ曲线的形状调整，克服了从几何角度考虑的复杂性和有限性，其结果非常有利于翼型设计及气动性能分析。     

NURBS曲面造型中曲线曲面分割问题研究

提出一种基于ＮＵＲＢＳ齐次坐标表示来计算曲线曲面分割问题的方法，把ＮＵＲＢＳ问题转化为四维空间里非有理Ｂ样条问题，就可利用Ｂ样条分割算法来解决，其几何意义明确，求解过程简便易行，便于在ＣＡＤ／ＣＡＭ系统中实现。     

NURBS曲面造型中曲线曲面分割问题的研究

提出一种基于ＮＵＲＢＳ齐次坐标表示来计算曲线曲面分割问题的方法，把ＮＵＲＢＳ总是转化为四维空间非有理Ｂ样条问题，就用Ｂ样条分割算法来解决，其几何意义明确，求解过程简便易行，便于在ＣＡＤ／ＣＡＭ系统中实现。     

NURBS 曲面法矢量的理论探讨

从Ｂ样条曲线一阶导数公式出发,推导了非均匀Ｂ样条曲面、ＮＵＲＢＳ曲面单位法矢量的计算公式,并进行了实例验证,为复杂自由曲面数控加工系统设计以及刀具与工件相对运动轨迹的模拟奠定了基础。     

微机曲面造型软件AutoSurf简介

微机曲面造型软件ＡｕｔｏＳｕｒｆ简介北京金马正好软件技术开发公司汤志东，漆为民美国Ａｎｔｏｄｅｓｋ公司最新推出的基于ＮＵＲＢＳ技术的曲面造型软件ＡｕｔｏＳｕｒｆ使用户的微机变成了ＣＡＤ工作站．曲面造型在ＣＡＤ／ＣＡＭ领域中占据非常重要的位置。过去，这...     

基于NURBS方法的车身表面造型系统的研究与应用

指出非均匀有理Ｂ样条方法的一系列优良性质及其对车身曲面设计具有的良好适应性，建议应在车身曲面造型中尽快推广应用。文中还从ＮＵＲＢＳ方法的原始定义出发推导了具有实用意义的算法，并建立了用于车身曲面几何造型的系统。最后给出了设计实例。     

NURBS curve and surface fitting for reverse engineering

Reverse engineering is an approach for constructing a computer-aided design (CAD) model from a physical part through dimensional measurement and surface modelling. This paper presents alternatives for reverse engineering of free-form parts using Non-Uniform Rational B-Spline (NURBS) surfaces. A two-step linear approach is employed for fitting NURBS curves and surfaces using the measured points. During the first step, the weights of the control points are identified from a homogeneous system using symmetric eigenvalue decomposition. The control points are further processed in a way similar to B-spline curve and surface fitting. Some examples are presented to illustrate both the steps of reverse engineering and the process of NURBS curve and surface fitting.     

Implementation of online NURBS curve fitting process on CNC machines

The study aims to develop a method for implementing an online non-uniform rational B-spline (NURBS) curve fitting process on CNC machines for improving the quality and efficiency of machining. Conventional CAD/CAM/CNC systems usually induce some machining difficulties and limit the machining results in real applications. Therefore, some researchers have proposed various methods for improving the machining results. An online NURBS curve fitting process consists of the fetching and fitting stages for CNC machines is developed in this paper. The fetching stage fetches a block of NC code and generates motion commands for obtaining data points. The fitting stage executes the NURBS curve fitting method along with a given set of data points. Moreover, the optimal search method is designed for obtaining good results in the NURBS curve fitting process. Simulations and machining tests carried out on a vertical machining center show that the proposed approach reduces the machining time to about 23% while maintaining the machining quality for the sample test.     

Fast and accurate NURBS fitting for reverse engineering

Fast and accurate fitting of non-uniform rational B-spline (NURBS) curves and surfaces through large sets of measured data is an important problem in applications such as reverse engineering and geometric modelling. This paper presents a method for realising significant improvements in the computational efficiency of this task. The basic idea is that the sparsity structures of the relevant matrices that are specific to the problem of NURBS fitting can be precisely defined and that full exploitation of these structures leads to significant savings in both computational and storage requirements. These savings allow for a large number of control points to be used in order to define the surface and consequently to improve the accuracy of shape representation. The achieved computational complexity is linear in both the number of measured points and the number of control points while the storage requirements of the algorithm are linear with the number of control points only. The complexity analysis, as well as the analysis of actual running times is presented. The results demonstrate that, using this approach, highly complex shapes may be modelled accurately with a single NURBS surface.     

基于前瞻算法的高效非均匀有理B样条曲线插补器

根据计算机数字控制系统的实际性能和非均匀有理B样条曲线的几何特性,设计了一种能够实现加速度平滑过渡的高效非均匀有理B样条曲线插补器。首先,该插补器利用快速插补计算模拟实际加工过程,找到加速度不连续的点;然后,采用S曲线加减速方法向后逆求减速点,并通过约束速度和加速度的方法,预估S曲线加减速第三阶段起点,不仅提高了所求减速点位置的精度,还实现了减速点处加速度的连续性。仿真结果表明,该插补器能在保证加工精度的前提下,以较高效率实现加速度的平滑过渡。     

基于Foley参数法反算三次NURBS曲线的算法研究

非均匀有理B样条(NURBS)方法已成为定义工业产品几何形状的唯一数学描述方法.工程实践中,常需要通过曲线已知的一批型值点反算曲线.针对三次NURBS曲线反算问题,采用矩阵形式来表示三次NURBS曲线,由已知的型值点及其权因子,利用Foley参数法确定节点矢量,并推导出以抛物条件即贝塞尔条件作为边界条件构造附加方程,反算出三次NURBS曲线的控制点及其权因子.曲线拟合结果表明,该方法生成的插值曲线具有良好的光滑性,很好地适用于工程实践.     

利用ARX构造反求近似曲面

面对反求工程中仅仅具有少量测量点构造近似曲面的要求,通过利用Ob ject ARX的内置类库,提出了采用NURBS曲线构造近似曲面的方法。该方法简单有效,可以满足一般少量测量点近似曲面构造的要求。     

An Approximate Lofting Approach for B-Spline Surface Fitting to Functional Surfaces

Owing to their specific functionality, surfaces are often given as bivariate functions including non-polynomial or higher-orde polynomial terms. It is necessary to represent them in standard formats such as non-uniform rational B-splines (NURBS) for approximation. As most such surfaces require fine quality of surfacing and high precision of manufacturing, accuracy should be guaranteed in their representations. As high accuracy is likely to result in bulky and redundant representations, it is also important to make them more com-pact. For NURBS surfaces, control points must be reduced without sacrificing accuracy. This paper presents an approximate lofting method for B-spline surface fitting to a functional surface within a specified accuracy. It adopts adaptive sampling and multiple B-spline curve fitting. The method is very effective when the surface shape is longish or the cross-sectional curves vary regularly in shape along a specific direction. Some experimental results demonstrate its usefulness and quality.This revised version with a corrected online cover date was published online in April 2004.     

NURBS及其自由变形

在分析 NURBS曲线、曲面与其参数域之间映射关系的基础上 ,建立了 NURBS实体和其参数域之间的映射关系 ,并进一步发现了基于 URBS的由变形与三参数 NU RBS实体之间的联系和自由变形的实质 ,即对三参数 NURBS实体的参数施了形状约束。将这一思想进一步推广到控制晶格顶点和权因子 ,则是我们下一步的工作     

基于型值点拟合的非均匀有理B样条曲线曲面延拓算法

提出了一种用于非均匀有理B样条曲线曲面延拓的算法,采用＂先离后合＂的思想,首先对需要延拓的非均匀有理B样条基线进行分析,构造出一系列的基线型值点;然后将延拓点加入到型值点序列中,再对新的型值点序列进行插值,创建出延拓曲线;最后对生成的延拓曲线的控制顶点序列进行优化操作,以保证所创建的延拓曲线拥有最佳的几何数据结构,从而为下一次延拓打下坚实的基础。算法通过在型值点构造过程中调节容差检验值,使得延拓操作能够适应任意精度的运算场合,从而在运算速度与精度之间达到最佳平衡。讨论了非均匀有理B样条曲线曲面延拓的几种不同形式,以及相应延拓点的计算方式,并给出了运用该算法的运行结果。     

基于NURBS理论的叶轮五坐标CAD／CAM技术研究

本文采用当今国际流行的NURBS理论，对叶片及叶轮等五坐标零件进行曲线拟合，曲面造型，曲线及曲面求变，加工刀具迹求解等技术难题的研究，并开发了后置处置，加工轨迹仿真等模块。以DNC方式控制CNC机床进行零件加工，为建立叶片，叶轮等五坐标零件的CAD／CAM集成系统奠定了基础。