基于角度分割的截面线数据匹配点对建立算法

研究了从截面线数据到B样条曲面拟合的过程中,建立最佳匹配数据点对的问题。提出了一种基于角度分割建立截面线数据匹配点对的算法,该算法利用各层截面线的公共几何中心,计算各点到中心的斜率,再利用基于斜率的插值获取给定角度在原参数曲线上的参数值。最后运用德布尔点的递推公式得到参数对应的坐标。当处理完所有的截面线数据,就得到了一组采样个数统一的匹配点对。该算法在进行截面线数据重采样的同时就完成了对数据点的对正处理,不仅适用于对凸轮廓的处理,而且也能处理层间形状变化较大的截面线数据。     

基于轮廓约束点的B样条曲面拟合算法

提出了一种面向截面测量数据的B样条曲面拟合算法。首先对原始数据点列进行降噪处理,然后遴选出曲率优势点,并将其作为初始的轮廓约束点,得到插值于约束点的初始曲线。再在需改善拟合精度的区域增加约束点,直至获得满足精度要求的B样条曲线。最后以约束点数目最多的曲线为准,在其余的曲线上增加差额数目的约束点,并进行平均弦长参数化,构造出B样条曲线簇,最终获得B样条拟合曲面。仿真实验结果表明,该方法可显著压缩曲面模型的控制顶点数目,具有较高的曲面重构效率。     

散乱测量数据多层次B样条逼近曲面拟合算法

提出了一种散乱测量数据的快速曲面拟合方法。该方法使用由粗到精的有继承关系的控制网格分级，从而产生相应的拟合逼近函数，每一级都比前一级更加逼近测量数据。拟合曲面的精度与光顺性可通过适当选择分级层数得到控制。当控制网格分级足够多，密度足够大时，最后拟合结果是插值于测量数据的C2连续曲面。     

散乱点曲面拟合及在车身曲面中的应用

提出了一种基于NURBS 曲面的散乱点参数曲面拟合方法,可以对散乱点云数据进行插值或基于最小二乘意义下的光顺拟合。完成了软件开发并在汽车车身外形曲面设计中得到了应用。NURBS曲面的优良品质保证了这种方法计算稳定,生成的曲面满足光顺要求。     

抽样点对基于Zernike多项式曲面拟合精度的影响

在光学测量中,常以Zernike多项式作为基底函数对测量得到的离散数据进行拟合,把实际波面或面形表示为Zernike多项式各项的线性组合,用拟合得到的曲面方程去反应实际波面或面形的属性。现研究了用不同精度的测量设备得到的抽样数据进行基于Zernike多项式的曲面拟合,研究了测量设备精度和抽样点数目对拟合精度的影响,得出通过增加抽样点可以对由较低精度设备测得的抽样数据进行较高精度拟合的结论。     

采用截面特征点云的NURBS自由曲面构建

结合NURBS曲面的构建理论,以工程软件UG为平台,探讨了基于截面特征点云的NURBS自由曲面构建的工程实现方法.实现了由截面特征点云进行NURBS曲线拟合,再由拟合曲线进行自由曲面的构建过程,并从曲面的表面状态与误差两个方面对构建的自由曲面进行评估.实践表明:采用该方法构建的自由曲面能保证NURBS曲面拟合质量,且精度高,能有效地反映实物原型.     

截面数据的B样条曲面重建研究

针对截面数据 ,研究其B样条曲面重建问题。给定节点矢量、依据最小二乘方法生成初始拟合曲面 ;为了提高拟合精度 ,采用迭代最近点方法优化修正数据点的参数 ,进而生成符合精度要求的拟合曲面。实际算例表明该算法简单、实用、可靠     

基于径向基函数的离散数据重建方法

针对离散数据的曲面拟合问题,提出一种基于八叉树分割的径向基函数曲面拟合方法。通过对给定的曲面点集构造相应的离面约束点集及对应非零函数值,对包含所有曲面约束点和离面约束点的点云数据进行八叉树空间分割,然后在八叉树分割的每个叶结点建立相应的方程组并求解,从而构造出插值或逼近属于该叶结点的数据点的三次样条径向基函数,最后提取该基函数的零等值面,并绘制得到最终的重建曲面。方法较好的解决了离散数据插值和拟合的计算速度和稳定性问题。     

径向基函数网络在虚拟加工对象重构中的应用

针对虚拟制造中无加工对象数据的加工过程仿真,提出适用于离散无规则边界测量数据的径向基函数网络方法,以重构加工对象曲面,阐述了径向基函数网络曲面重构的基本理论,分析了径向基函数网络宽度参数的确定方法;给出了径向基函数网络曲面重构函数的具体实现过程,计算了重构的误差.以实例验证了该方法的可行性,并与传统曲面拟合方法相比较,得出该方法的重构精度高,改进了传统曲面拟合在处理非均匀截面数据点时曲面形状的失真和运算的不稳定现象,从而显示了径向基函数网络重构曲面的优越性.     

反求工程自由曲面测量规划及重建技术的研究

反求工程中曲面的测量应遵循采样点密度随曲面曲率变化而疏密不断变化原则,并应根据离散采样点的分布确定自由曲面的重建工作。基于曲面Z向细化分层的测量技术和NURBS曲面方程拟合重建,能有效获取原曲面特征的最少测量点,并进行曲线数学重建,最终获得准确反映表面特征的NURBS曲面方程。     

A new approach for lofted B-spline surface interpolation to serial contours

This paper addresses the problem of B-spline surface interpolation to serial contours, where the number of points varies from contour to contour. A traditional approach to the problem creates a set of B-spline curves via B-spline curve interpolation to each contour, makes them compatible via degree elevation and knot insertion and performs B-spline surface lofting to get a B-spline surface that interpolates them. The approach tends to result in an astonishing number of control points in the lofted B-spline surface. This situation arises mainly from the inevitable process of progressively merging different knot vectors to make the B-spline curves compatible. This paper presents a new approach for fixing this problem. The approach includes a novel process of obtaining a set of compatible B-spline curves from the given contours. The process is based on universal parameterisation [1, 2], allowing the knots to be selected freely but leading to a more stable linear system for B-spline curve interpolation. Since the number of control points in each compatible B-spline curve is equal to the highest number of contour points, the proposed approach can realise efficient data reduction and provide a compact representation of a lofted B-spline surface while keeping the desired surface shape. Some experimental results demonstrate its usefulness and quality.     

逆向工程中扫描数据点的曲面重构

针对三维扫描数据点的曲面重构技术在实际系统中的应用，提出了一种以B样条曲面为基础的曲面构造算法。已知数据点按简明行方式排列，算法产生一个连续的B样条曲面，该曲面的参数化过程不受每行数据点分布的影响。根据所传递的候选节点矢量，采用柔性间距选择，有效地减少了控制顶点数，同时应用三维图形标准以及图形函数库，在VC 6．0平台上完成了该软件的编制。通过实际系统应用验证，该算法改进了传统曲面重构方法在处理非均匀扫描数据点时曲线曲面形状的失真和运算的不稳定现象，计算简单，易于编程实现。     

A New Parameterisation Method for NURBS Surface Interpolation

A new method is proposed for the parameterisation of data points in NURBS surface global interpolation. In this method, the parameter value at the maximum of each rational B-spline basis function is defined as the parameter value of the associated data point. Some advantages of this method in geometric modelling are: 1. It selects the knot vectors freely, regardless of the distribution of data points. 2. It is invariant under affine transformations of the data points. 3. It allows multiple data points.     

RECONSTRUCTION OF SYMMETRIC B-SPLINE CURVES AND SURFACES

A method to reconstruct symmetric B-spline curves and surfaces is presented.The symme- try property is realized by using symmetric knot vector and symmetric control points.Firstly,data points are divided into two parts based on the symmetry axis or symmetry plane extracted from data points.Then the divided data points are pararaeterized and a symmetric knot vector is selected in order to get symmetric B-spline basis functions.Constraint equations regarding the control points are deduced to keep the control points of the B-spline curve or surface to be symmetric with respect to the extracted symmetry axis or symmetry plane.Lastly,the constrained least squares fitting problem is solved with the Lagrange multiplier method.Two examples from industry are given to show that the proposed method is efficient,robust and able to meet the general engineering requirements.     

The redefinition of B-spline curve

This paper proposes a new formula of B-spline curve. The new formula generates exact same shape as that of the original B-spline curve formula but has different basic functions and knot vector. This formula requires the number of knots to be the same as the number of control points. This property of the new formula enables us to select the knot vector automatically even in case of nonuniform and to generate spline with relative constant speed. Some experimental results demonstrate its usefulness and quality.     

基于逆向工程的蒙皮曲面重构技术研究

针对蒙皮曲面生成时截面线相容性处理所带来的数据量过大问题,提出一种蒙皮曲面重构方法.从三次B样条曲线插值入手,基于垂距对自由曲面自适应数据采样,构建物体外形轮廓曲面.该方法可以有效去除截面线相容性处理所产生的大量的冗余控制顶点,在用户定义的精度内实现数据压缩和光滑的曲面造型.最后,应用该方法给出一个完整的基于逆向工程的蒙皮曲面构造过程.     

基于非均匀B样条小波的NURBS曲面光顺

将非均匀B样条小波分解方法用于曲面光顺。通过整体光顺度量确定曲面整体光顺的方向，进而通过曲面整体小波分解实现曲面的整体光顺；通过曲面在节点对处的局部光顺度量，确定要光顺的节点及方向，然后用最小区域算法实现曲面的局部光顺；给出了一种由用户交互指定光顺区域的区域光顺方法；用细节部分的再次分解控制曲面的光顺误差；通过施加约束解决光顺前后曲面边界位置和切矢不变的问题；对于计算的稳定性及可能出现的奇异情况给出了论述。这些光顺算法在浙江大学开发的反求工程CAD软件RE-SOFT中的实际应用效果表明，基于非均匀B样条小波分解的NURBS曲面光顺算法能够有效地去除曲面上的坏点，改善曲面的品质。     

基于特征点自动识别的B样条曲线逼近技术

提出一种实用的用三次B样条曲线逼近稠密且带噪声的二维断面数据点列的算法。剔除数据点列中的重合点并对其进行均匀弧长重采样处理后,利用相邻点拟合圆弧的方法来近似计算各数据点的离散曲率值,并根据相邻点之间的离散曲率符号变化情况及相近点之间的曲率值和曲率差分关系自动识别出断面数据中绝大多数的特征点(拐点、折痕点、曲率极值点)。构造插值于特征点的B样条曲线,并在逼近误差最大处插入新的插值点。重复这一过程,直到逼近误差小于预先给定值,从而得到最终插值点列并构造相应的B样条曲线。试验结果表明,所构造的曲线节点数目及其分布合理,能够很好地反映原始断面数据点列中的细小特征部分。该算法具有速度快、逼近精度高等特点,可广泛应用于二维断面数据的曲线重建。     

Degree reduction of NURBS curves

Higher degree curves are used in applications because they are easier to manipulate interactively but require heavy computation. Most of the equations for curves used popularly in CAD software are of degree 2 and 3, because two curves of degree 3 can guarantee 2nd derivative continuity at the connection point. This study proposes a different but simpler method than any put forward before to deal with degree reduction of free-form curves. The reduced curves use the simplest knot vector type, i.e., the open uniform knot vector. Unlike other methods, this study does not modify or refine the knot vectors but perturb the control points globally. After obtaining an initial condition, a radiating web-like search algorithm is applied to detect the optimum positions. These NURBS curve formats reach basic industrial standards for CAD/CAM/CNC applications. By defining a global bound error function, this algorithm can achieve an optimum solution not only for NURBS curves but also Bézier/B-spline curves.     

An integrated surface modeling and machining approach for a marine propeller

For given data points on different cylindrical section curves of marine propeller during the design period, the fair fitting method with the least squares of the cubic B-spline curve has been used to form cylindrical section curves with different radius. Then the control points of the cylindrical section curves were used as new data points to process fair fitting in another direction, and the pressure surface and the suction surface of the propeller can be acquired at last. Aims to overcome disadvantages of the present machining method of propeller, such as lower machining precision and efficiency, repeated clamping, and limited machining scope, a new machining method—the second order osculating machining method—has been presented. By using this method, not only the cylindrical cutter and the machined surface can keep line contact, but also the propeller can be machined with one clamping. It’s very suitable for the machining of propeller with larger projected area ratio and the machining precision and efficiency will be improved.