过渡曲面构造方法探索

针对模具过渡曲面构造过程中存在的问题，提出了运用NURBS曲线、曲面构造方法，在缺少一条边信息的条件下构造过渡曲面，用这种方法构造的曲面能够满足过渡曲面的工艺要求。     

基于边界控制的Gn连续过渡曲面的构造

讨论了基于重新参数化局部基曲面线性组合构造G^n连续过渡曲面时重新参数化局部基曲面的形状对于过渡曲面的边界和形状的影响；提出了采用能量最小法使过渡曲面的边界弯曲最小来确定重新参数化局部基曲面参数域的方法，并提出相应的重新参数化局部基曲面的确定方法，从而构造较好的过渡曲面。     

反求工程中复杂曲面重构算法研究与实现

针对复杂曲面的精密制造与检测，提出了一种有效实用的曲面重构算法。系统地论述了该方法重构复杂曲面的实现全过程。实例表明，该方法具有采样效率高、重构曲面精度高、曲面光顺等特点。     

NURBS自由型曲面延展和过渡功能的开发

根据曲面的延展量进行曲面分割，对分割后曲面进行控制点的反射对称，得到满足G^2连续的延展曲面。给出了散乱控制点的有序化的方法，有效地防止了拓展曲面产生折叠、起皱，实现了曲面延展设计的算法。     

自由曲面孔域数据的拟实填补与曲面重建

为解决具有孔域的自由曲面在逆向设计中存在的数据空洞，提出了孔域测量数据的填实方法，通过孔域边界数据的光顺，截面测量曲线的端点 闭合处理，孔域的截面数据延拓，母面设计和曲面裁剪等技术，解决了自由曲面孔域数据填补和曲面的重建问题，实例应用表明，该方法可应用于逆向工程中对具有孔域的自由曲面的测量和造型，并能保证曲面重建的品质。     

基于重采样技术的三角Bezier曲面局部特征逼近

针对反求工程中基于初始测量点直接构造的三角Bezier曲面难以对曲面特征进行正确描述的问题，提出了一种通过局部重采样技术重构曲面特征的方法。从原三角曲面中提取并分离重采样区域，基于区域内测量点拟合B样条曲面，在垂直过渡特征脊线的截面轮廓线上均匀重采样，重新三角化后即可以构造具有良好品质的曲面特征。实例表明提出的方法可以明显改善曲面局部特征的品质。     

固定边界Coons曲面的造型

以汽车覆盖件的曲面造形为例，对Coons曲面的造型方法进行了研究。提出了在固定边界条件下通过改变Coons曲面的混合函数来使曲面变形，并达到预期变形目的的方法。指出混合函数对Coons曲面形状的影响要受到包括边界曲线在内的边界条件的制约，缺乏必要的边界条件就无法仅凭混合函数来获得所需要的变形。     

固定边界Coons曲面的造型方法研究

提出了在固定边界务件下，通过改变Coons曲面的混合函数来使曲面变形，并达到预期变形目的的方法。指孝混合函数对Coons曲面形状的影响，要受到包括边界曲线在内的边界条件的制约，缺乏必要的边界条件就无法仅凭混合函数来获得所需的变形。     

共轭曲面求解理论与方法研究

分别介绍了基于解析曲面和数字曲面的共轭曲面求解理论与方法 ,对各种求解方法的基本思想、关键技术作了简要说明和评述 ;提出了基于数字曲面的求解策略 ,预测了该领域今后的研究重点和方向。     

一种自由曲面加工步长和行距确定的修正方法

基于曲面理论和零件表面残余高度的理论分析，对曲面加工步长和行距的合理确定进行了研究，提出了一种曲面加工步长和行距确定的修正方法。     

基于广义延拓逼近法的复杂曲面重构研究

针对逆向工程中复杂曲面重构,基于广义延拓逼近法,提出一种逼近算法.该算法一方面能在分片边界点上满足插值条件,使得各分片之间的变化具有一定的协调性;另一方面,利用分片插值区域周围结点(包括内点)的信息,实现分片区域内部的最佳逼近,同时算法又使曲面形状具有局部可控性、变差减少性和凸包性等特性.仿真实例证实,该算法改善了传统逼近算法方法在重构曲面时产生的失真和运算的不稳定现象,并且得到较高的曲面重构精度,具有计算稳定、快速和方便的优点.     

基于散乱数据的罐车曲面重建与容积检定系统

针对目前铁路罐车容积测量技术在可操作性、准确性等方面存在的问题,提出一种简捷、准确的罐车容积检定方法。该方法通过罐车序列图像三维重构,获取罐车表面测量数据。进而借助提出的散乱数据序化方法,构造罐车的系列截面轮廓线,并以蒙皮操作为基础实现罐车曲面的精确重建。最后利用参数曲面的离散表达,完成罐车容积的快速检定。对比试验表明,所提检定方法的结果符合"JJ140-1998铁路罐车容积"中"铁路罐车容积扩展不确定度小于0.4%(k=2)"的要求。     

A practical sampling method for profile measurement of complex blades

Blade is one of the most important parts in turbine machinery. The complex geometry of blades not only makes them difficult to fabricate, but also leads them difficult to inspect. Typically, the surface of blades is measured by using coordinate measuring machine (CMM). Since the measurement time and cost increase proportionally as the increase of measurement points, it is essential to sample measurement points which can represent entire blade with sufficient confidence and accuracy. In order to achieve a certain allowable deviation with a suitable set of points, a practical sampling method for surface measurement of blades was studied. Firstly, the leading edge curve and trailing edge curve were supposed to represent the twisted and bend information of blades. A sampling method based on maximum chordal deviation for leading edge curve and trailing edge curve was researched. Further, a fusion approach for sampling points on both edge curves, which determine the cross-sections, was proposed. Secondly, the inspection points sampling method for sectional curves were investigated. Finally, two simulation and one experimental examples were used to demonstrate the sampling methodology. The results indicated that the approach of this study can ensure the measurement precision at high curvature potion by measuring a small number of points.     

<Emphasis Type="Bold">Determination of the Optimal Parameters for Freeform Surface Measurement and Data Processing in Reverse Engineering</Emphasis>

One objective of this work is to determine the optimal combination of the probe diameter and grid distance for freeform surface measurement, and another is to determine the optimal parameters for the local Shepard interpolation. The optimal combination of the probe diameter and grid distance for freeform surface measurement was determined through a Taguchi matrix experiment. The smaller the probe diameter and grid distance, the better the accuracy of the surface normal based on the configured matrix experimental result. The optimal parameters, namely the exponent and the radius R, for the local Shepard interpolation were determined by using the minimisation method of the root-mean-square normalised error (RMSNE) between the measured data points and the theoretical data points on a standard steel ball surface. The optimal parameters determined were actually applied to the measurement of a freeform surface (mouse surface) on a coordinate measuring machine (CMM). The local Shepard interpolation method was used to interpolate 16 control points from 1054 measured data points. Bi-cubic Bezier- and B-spline surface CAD models were constructed through these interpolated control points.     

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.     

Calculation of the Normal Vector using the 3 × 3 Moving Mask Method for Freeform Surface Measurement and its Application

The concept of a 3 × 3 moving mask operation image-processing technique is proposed to calculate the normal vector of measuring points in this study. The method developed reduces greatly the calculation time of matrix operation and memory space in comparison with the traditional composite Ferguson-spline method. The methodology for calculating the normal vector is to select eight neighbouring points at equal distances in the vicinity of an arbitrary node on the surface, from which a small surface patch can then be constructed from the nine selected points. Different analytical methods are used to calculate the unit normal vector, namely the Bezier method with uniform parameters and the Bezier method with non-uniform parameters, and are discussed in this study. The accuracy of these two methods in calculating the unit normal vector was also verified by calculating different positions on a spherical surface. The Shepard interpolation method was adopted to interpolate a few control points from a massive number of measured data points to establish the CAD model of a freeform surface using a rectangular grid. The method developed was applied for the measurement of a freeform surface (mouse surface) using a coordinate measuring machine. The local Shepard interpolation method was used to interpolate 16 control points from 1054 measured data points. A bi-cubic Bezier- and B-spline surface CAD model were constructed through these interpolated control points.     

基于像散原理的并行共焦检测的微形貌参数的可视化测量

为实现对微结构表面轮廓参数的精确测量,用基于像散原理的并行共焦检测系统获取微结构表面的三维信息,进而实现对微结构表面参数的可视化测量。考虑到微结构表面特点,采用累加弦长双三次样条插值曲面对其表面进行重构。并选择高的插值细分倍率获得连续光顺廓形表面,通过拾取拟合曲面上的点而不是廓形局部三角面片上的点实现三维廓形参数评定。由重构曲面模拟结果显示:累加弦长双三次样条重构微结构表面可以有效地实现对微结构表面参数的精确测量。     

裁剪B样条曲面重建算法研究

提出了具有不规则边界的裁剪B样条曲面重建方法。采用基准平面对数据点进行参数化，并建立以B样条曲面控制顶点为未知量的超定方程组；提出了基于有效点判别条件的孔洞识别算法，通过对孔洞区域的控制顶点施加顶点形状保持约束,确保方程组最小二乘解的存在；基于误差控制重构B样条曲面整体覆盖数据区域，通过边界线提取或曲面求交剪裁来重构裁剪曲面的边界。该方法具有符合设计意图、曲面在孔洞区域具有良好的形状一致性、曲面重构精度高等特点。     

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。     

一种基于机器人的曲面测量、建模和加工方法

提出了一种基于机器人的卷曲类自由曲面的测最、建模和加T路径生成方法.本文采用结构光测量方法设计了一种基于机器人的自动测量系统,实现了自由曲面零件的表面测量.根据测量数据和零件的形状特点提出了一种新的建模方法,该方法首先采用提出的截面法直接提取点云的边界,然后利用射线与局部拟合曲面的交点获得有序的精整数据点,实现了NURBS曲面的精确拟合.最后,对重构的自由曲面采用等参数线法生成了加工路径.实际的算例和应用验证了本文方法的有效性和精确性.