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。     

应用NURBS实现飞机叶片的三维重构

针对光学叶片表面测量系统的三维重构问题,提出采用NURBS(非均匀有理B样条)重构叶片断层曲线以及叶片曲面,并介绍了NURBS的基本理论.同时应用三维图形标准以及图形函数库在VC6.0平台上完成该软件的编制.     

逆向工程中B样条拟合曲线与曲面的算法与实现

利用产品原形的三维测量数据,通过逆向工程设计新产品、改进或生产旧产品的过程中,曲线拟合及曲面重构是关键。采用B样条曲线拟合及B样条曲面重构,曲线更改灵活,曲面连接光滑,在逆向工程中具有广泛的实用性。     

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。     

基于实时重构的自由曲面自适应布点方法

针对现有的自适应算法计算量庞大、在工程中可应用性不强的缺陷,提出在等距法布点的基础上,对测量点进行实时重构来指导三坐标测量机根据曲面本身特性自动增加测量点的方法。测量过程中,当通过拟合五次B样条曲线、三次B样条曲面判断现有测量点不满足精度时,利用两侧测量点的曲率半径,计算出需增加测量点的准确位置,重新拟合包含新检测点的检测样本,直到满足精度要求。以曲面样件为例,辅以计算机图形可视化验证该算法,实验结果表明该方法测量精度及重构精度均可满足数字化检测要求,且在工程应用中相比曲率自适应算法其计算量大幅下降,有效提高了曲面检测效率。     

超声检测中复杂曲面数字化方法研究

提出了利用超声波检测探头实现自由曲面的路径受控仿形测量方法。针对数据压缩处理引起的各截面曲线上数据点数的不同，提出了一种蒙皮B样条曲面插值方法，该方法在保持插值精度的情况下，减少了曲面重构所需的控制顶点。应用表明，算法计算效率较高。     

反求工程技术在复杂曲面重构系统中的应用

论述了针对注塑零件复杂曲面的反求设计,提出运用CCD白光光栅非接触工业相机采集点云数据,将点云数据加载到Geometric软件中,利用NURBS曲面重构方法和插值算法,进行点云数据筛选,构造点云特征网格和曲面拟合,得到点云曲面的三维重构.实践证明,基于Geometric系统的NURBS曲面重构方法,在复杂曲面为原型实体重构的反求设计中具有理想的应用价值.     

半正交B样条小波及其在曲线曲面光顺中的应用

基于B样条基函数及其对应的小波不具有平移正交性,因而不能用现有Mallat快速算法进行小波分析的特点,从B样条基函数以及多分辨分析的定义出发,用严格的数学推导实现半正交B样条小波的分解重构算法。详细阐述该算法在准均匀三次B样条曲线中的运用,并给出一条复杂曲线及一个复杂曲面的分解重构实例,表明该方法能够在复杂曲线曲面的光顺中取得良好效果。     

发动机气道逆向工程及其砂芯模具设计

以发动机气道为研究对象,探讨了逆向工程在汽车发动机设计开发中的应用.利用光学扫描测量系统得到发动机气道曲面的点云数据,并进行数据处理和曲面重构得到三维数模,最后利用逆向工程得到的三维数模进行模具设计.     

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     

基于交互的B样条曲面重建与误差计算

基于三角网格模型的B样条曲面重建技术得到深入发展，计算与显示重建后的B样条曲面与原始测量三角网格之间的误差对分析曲面重建品质有重要作用。一种较为实用的B样条曲面重建方法是对三角网格模型进行四边界区域划分后进行栅格式采样，再根据采样点进行B样条曲面拟合。针对这种重建方法，研究了一种建立三角网格顶点与四边界区域对应关系的算法，再用离散的方法计算点到对应曲面的距离误差，最后用线性插值方法实现误差彩色．云图的显示。     

The Pre-Processing of Data Points for Curve Fitting in Reverse Engineering

Reverse engineering has become an important tool for CAD model construction from the data points, measured by a coordinate measuring machine (CMM), of an existing part. A major problem in reverse engineering is that the measured points having an irregular format and unequal distribution are difficult to fit into a B-spline curve or surface. The paper presents a method for pre-processing data points for curve fitting in reverse engineering. The proposed method has been developed to process the measured data points before fitting into a B-spline form. The format of the new data points regenerated by the proposed method is suitable for the requirements for fitting into a smooth B-spline curve with a good shape. The entire procedure of this method involves filtering, curvature analysis, segmentation, regressing, and regenerating steps. The method is implemented and used for a practical application in reverse engineering. The result of the reconstruction proves the viability of the proposed method for integration with current commercial CAD systems.     

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。     

RECONSTRUCTION OF LAYER DATA WITH DEFORMABLE B-SPLINES

0 INTRODUCTIONReverse engineering is a technology to establish CAD mod-els from samples, prototype, molds or manufacturing parts bydigitization. In many research and application areas such asmedical science, biomedical engineering, and CAD/CAM, anobject i…     

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.     

基于散乱数据点的B样条曲线反求方法

逆向工程中,由3D散乱数据点反求B样条线,常用的方法是用最小二乘法通过B样条曲线逼近来拟合出B样条线,因而存在拟合误差,更无法提前预知需要多少控制顶点才能达到所要求的逼近精度.我们从B样条曲线的数学定义出发,对B样条线的重构进行了研究,通过反求B样条多边形控制顶点的方法,来反求得到插值B样条线,并以三次均匀B样条线的反求为例,通过编程加以实现验证.     

基于OPENGL的曲面零件三维图形系统开发

针对具有大规模数据点的曲面零件,提出了一种基于OpenGL的三维曲面零件实体的图形开发方法,有效解决了由大量三维数据点构建三维图形中所遇到的难题。上述方法已经成功应用于激光测量中的图形显示系统。     

Prediction of surface reconstruction uncertainties for freeform surface inspection

A method is introduced to predict uncertainties of the B-spline freeform surfaces that are reconstructed from the measurement points for inspection of freeform surfaces. The uncertainties of a reconstructed B-spline surface are modeled by variances of coordinates of points on this freeform surface. Prediction of the uncertainty at any location on the reconstructed B-spline surface is carried out in two steps: (1) estimation of variances of the B-spline surface’s control points introduced by the surface reconstruction process, and (2) propagation of the variances from the control points to the points on the B-spline freeform surface. In this research, the variances of the control points of the reconstructed B-spline surface in all three directions are considered to improve the accuracy of uncertainty prediction in the regions with significant changes of geometric shapes. Both the errors and uncertainties at different locations on the reconstructed surface are considered in freeform surface inspection to compare the manufactured surface against the design surface and its tolerance. The developed method has been applied to two case studies to demonstrate its effectiveness.     

3-D measurement and evaluation of surface texture produced by scraping process

The scraping process involves traditional manual work and is an important technique for producing flat bearing surfaces with lubricating grooves on a sliding surface. In order to meet the requirements of precision engineering, the scraped surface should have an equally distributed pattern with a required number of high points per unit area while retaining good flatness. In the machine tool manufacturer’s workshop, however, the quality inspection of scraped surfaces still depends on human eyes. In this study, a 2-D evaluation system is first developed using image processing so that the peak points per area of square inch (PPI) and the percentage of points (POP) can be quantified as parameters. A vision-assisted laser focus probe system is then developed to measure the 3-D form of the scraped profiles. The laser probe is made of a DVD pickup head based on the astigmatic principle. Driven by an XY stage, the entire scraped profile can rapidly be scanned. The quality of the scraped surface can thus be interpreted in a more scientific manner. Based on the measured 3-D data, new evaluation methods are proposed for five parameters, namely the PPI, POP, height of points (HOP) or depth of surroundings (DOS), flatness, and oil retention volume. Experiments show that the 3-D system is consistent with the 2-D system. It not only reveals more surface quality parameters but also uncovers more characteristic surface phenomena than the 2-D image system.