三角曲面数字样品的特征提取与再现技术

针对特征技术在反求工程 CAD建模中的重要作用 ,提出基于三角 Bézier曲面数字样品的特征提取和计算方法 ,研究了将特征曲线嵌入到原始测量数据中并且作为三角化约束条件的特征再现技术 ;同时基于反求工程的产品再创新设计思想 ,给出在已有三角 Bézier曲面模型中局部再造特征的算法 .应用实例表明 ,利用特征提取与再现技术能够有效地改善三角 Bézier曲面模型的品质 ,为最终获得高品质的 CAD曲面模型打下良好的基础     

器官反求CAD建模中的虚拟测量

针对基于断层轮廓数据反求CAD建模中曲面品质较差的问题，提出一种基于复合三角Bezier曲面的局部虚拟测量方法。首先分离品质较差的局部曲面，然后拟合局部曲面的散乱点得到光顺的中间曲面模型，最后将中间曲面离散得到修正的曲面模型。算例表明，利用局部虚拟测量方法可以明显提高器官重构曲面模型的品质。该方法也可以用于改善零件反求CAD中曲面局部特征的品质。     

复合三角Bèzier曲面的裁剪

利用三角Ｂèｚｉｅｒ曲面片的保凸性和可分割性,解决了初始交点计算、迭代收敛等问题;通过求近曲面点、边界点跨越等过程,由一个初始交点出发跟踪计算跨越许多曲面片的整条交线;将各交点作为型值点插入曲面中,对三角网格进行局域三角化,以交线为界限进行分离,重新生成两张复合曲面,实现了裁剪的目的;基于次边界环和重新分布边界点的计算,改善了狭长三角形对整张曲面的性态影响．测试显示,上述方法简单可靠,满足了反求工程ＣＡＤ建模的要求     

反求工程中的隐式曲面快速自适应性多边形算法

论文给出一种反求工程中基于三角形细分的隐式曲面快速自适应性多边形化方法。该文先由输入的三维扫描数据点利用空间延展的MarchingCubes方法得到隐式曲面较为粗糙的三角形表面网格形状,再利用该文的自适应性优化方法对粗糙网格从三个方面自适应性调整,即调整网格顶点法向,控制曲率,再补偿网格抽样率。从而生成的三角网格和采样点具有局部适应性,能随着曲率的变化自动控制采样点的疏密程度,消除了逼近网格中的T-形边。实验表明,恢复的隐式曲面能很好地反映形状特征,能满足反求工程的实时需求。     

三角网格模型的特征线提取

在反求工程中，散乱数据点云的曲面重构常采用三角网格模型，若将其转换成曲面实体模型则有更广泛的应用，从三角网格模型中提取特征线是转换过程中的重要步骤．在讨论反求工程中数据点云分块方法的基础上，采取“基于边”的方法来提取特征线：先提取特征点，再连接成特征线．根据相邻三角片的法矢夹角和各点主曲率是否为极值，分两次提取特征点，利用三角顶点加权和均匀化等方法减少狭长三角片对特征点提取的计算误差影响，再将特征点分组连接成B样条曲线．文中算法的结果可为B样条曲面分片拟合和建立B-rep曲面实体模型提供依据。     

细分曲面求交裁剪算法研究

基于细分曲面的参数化表示,研究了细分曲面的精确求交、裁剪算法。首先对控制网格建立局部坐标系,将细分曲面表示为一系列小的面片,并对每个控制顶点赋予参数值。然后用改进的轮廓删除法细分控制网格,在关联曲面间进行相交性检测,得到近似交点及其参数值,再用迭代法求得精确解。根据用户指定的裁剪区域确定交线的走向,将被裁剪曲面的控制网格面分为保留面、裁剪面和删除面,设置每个裁剪面的裁剪域,从而实现细分曲面的精确裁剪。算例表明,该文的方法简单、有效。     

运用多项式曲线在多项式曲面上裁剪Bézier曲面

在多项式曲面的定义域上,以两多项式曲线及两直线段围成的简单区域作为裁剪区域,运用参数变换将该区域变换到标准正方形区域,以多项式开花为工具,将裁剪区域对应的子曲面片表示成Bézier曲面形式。对于参数平面上的复杂裁剪区域,则分割为若干简单区域来进行。该裁剪算法能处理形状较为复杂的曲面裁剪,方法对任意多项式曲面适用,而且能推广到有理情况。     

基于解析法的裁剪PDE曲面的生成技术

为解决基于偏微分方程的曲面裁剪问题,研究一种广泛应用于偏微分方程曲面的裁剪方法.首先介绍基于偏微分方程的曲面生成方法,其次由参数域内的曲线在曲面上的投影,得到所求裁剪曲面的边界,然后利用解析法求得裁剪后的PDE曲面,最后列举一系列的实例来说明该裁剪方法的应用并且专门研究多个裁剪区域的问题.     

棱边特征曲面拓扑逼近重建算法

针对含有棱边特征的曲面模型难以正确重建这一问题,提出一种基于网格曲面延拓求交重建棱边特征区域的算法.首先对点云进行邻域高斯映射聚类分析,剔除棱边特征点,对剩余点云以种子点增长算法实现平坦连通区域的分割;然后将增益优化后的边界样点邻域点集作为曲面局部样本,采用三次Bézier曲线延伸方向为制导对点云进行扩展,提高曲面延拓区域的光滑性;最后对延拓后的平坦区域重建结果进行求交,采用曲面裁剪的方法重建棱边特征.以斯坦福大学提供的采样点云作为曲面重建数据,实验结果表明,在重建含有棱边特征曲面的过程中,该算法可有效地避免孔洞与棱边凹痕等错误的出现,且对非均匀采样数据具有良好的适应性.     

一种实用的曲面求交算法

一、前言随着自由曲面在几何造型、CAD/CAM、RP（反向工程）等领域中的广泛应用,针对自由曲面的几何处理,如曲面求交、曲面裁剪等成为计算几何中的热门研究课题,并作为完成复杂产品造型及产生数控或RP加工数据的基本手段和衡量曲面造型系统设计能力的主要指标而倍受重视。其中,作为曲面裁剪、曲面过渡等基础的曲面求交是最基本和最重要的问题之一。曲面求交算法是曲面编辑操作中最基本的一种算法,是曲面造型、曲面加工的基础。通常要求算法效率高,计算稳定,且精度易于控制。由于曲面与曲面求交问题的非常复杂,至今还未得到圆满…     

Smooth multiple B-spline surface fitting with Catmull%ndash;Clark subdivision surfaces for extraordinary corner patches

This paper presents an algorithm for simultaneously fitting smoothly connected multiple surfaces from unorganized measured data. A hybrid mathematical model of B-spline surfaces and Catmull–Clark subdivision surfaces is introduced to represent objects with general quadrilateral topology. The interconnected multiple surfaces are G ² continuous across all surface boundaries except at a finite number of extraordinary corner points where G ¹ continuity is obtained. The algorithm is purely a linear least-squares fitting procedure without any constraint for maintaining the required geometric continuity. In case of general uniform knots for all surfaces, the final fitted multiple surfaces can also be exported as a set of Catmull–Clark subdivision surfaces with global C ² continuity and local C ¹ continuity at extraordinary corner points. Published online: 14 May 2002 Correspondence to: W. Ma     

Curvature estimation scheme for triangle meshes using biquadratic Bézier patches

When dealing with triangle meshes, it is often important to compute curvature information for the purposes of feature recognition, segmentation, or shape analysis. Since a triangle mesh is a piecewise linear surface, curvature has to be estimated. Several different schemes have been proposed, both discrete and continuous, i.e. based on fitting surfaces locally. This paper compares commonly used discrete and continuous curvature estimation schemes. We also present a novel method which uses biquadratic Bézier patches as a local surface fitting technique.     

Sharp feature preserving MLS surface reconstruction based on local feature line approximations

Sharp features in manufactured and designed objects require particular attention when reconstructing surfaces from unorganized scan point sets using moving least squares (MLS) fitting. It is an inherent property of MLS fitting that sharp features are smoothed out. Instead of searching for appropriate new fitting functions our approach computes a modified local point neighborhood so that a standard MLS fitting can be applied enhanced by sharp features reconstruction.We present a two-stage algorithm. In a pre-processing step sharp feature points are marked first. This algorithm is robust to noise since it is based on Gauss map clustering. In the main phase, the selected feature points are used to locally approximate the feature curve and to segment and enhance the local point neighborhood. The MLS projection thus leads to a piecewise smooth surface preserving all sharp features. The method is simple to implement and able to preserve line-type features as well as corner-type features during reconstruction.     

Partitioning 3D surface meshes using watershed segmentation

This paper describes a method for partitioning 3D surface meshes into useful segments. The proposed method generalizes morphological watersheds, an image segmentation technique, to 3D surfaces. This surface segmentation uses the total curvature of the surface as an indication of region boundaries. The surface is segmented into patches, where each patch has a relatively consistent curvature throughout, and is bounded by areas of higher, or drastically different, curvature. This algorithm has applications for a variety of important problems in visualization and geometrical modeling including 3D feature extraction, mesh reduction, texture mapping 3D surfaces, and computer aided design     

As‐Conformal‐As‐Possible Surface Registration

We present a non‐rigid surface registration technique that can align surfaces with sizes and shapes that are different from each other, while avoiding mesh distortions during deformation. The registration is constrained locally as conformal as possible such that the angles of triangle meshes are preserved, yet local scales are allowed to change. Based on our conformal registration technique, we devise an automatic registration and interactive registration technique, which can reduce user interventions during template fitting. We demonstrate the versatility of our technique on a wide range of surfaces.     

Patch layout from feature graphs

The structuring of surface meshes is a labor intensive task in reverse engineering. For example, in CAD, scanned triangle meshes must be divided into characteristic/uniform patches to enable conversion into high-level spline surfaces. Typical industrial techniques, like rolling ball blends, are very labor intensive.We provide a novel, robust and quick algorithm for the automatic generation of a patch layout based on a topology consistent feature graph. The graph separates the surface along feature lines into functional and geometric building blocks. Our algorithm then thickens the edges of the feature graph and forms new regions with low varying curvature. Further, these new regions-so-called fillets and node patches-will have highly smooth boundary curves, making the algorithm an ideal preprocessor for a subsequent spline fitting algorithm.     

A data-driven intermediate level feature extraction algorithm

An algorithm is presented that is based on the regression updating theory for fitting linearly parameterizable curves without prior classification of edge data. An initial estimate of a hypothesized curve is first obtained by a statistical windowing technique. A search region is determined and iteratively grown. Edge points in the search region are tested for their goodness-of-fit to the previous estimate. The estimate is iteratively updated with the edge points that have favorable goodness-of-fit measures. The edge points having poor goodness-of-fit measures are rejected as outliers. The algorithm drives the estimate to converge to a final solution. By repeatedly applying this procedure to the edge data excluded from the previous fitting, all the underlying curves are reconstructed. The major feature that distinguishes this approach from that of others is that classifying the edge data prior to fitting is not required. Advantages of this algorithm are: (1) the fitting procedure achieves higher robustness and accuracy by dynamically analyzing the data consistency; (2) the computational complexity increases only linearly with the number of edge data; (3) the algorithm readily extends to reconstruct surfaces from range data. Thus the algorithm provides a powerful technique enabling a data-driven intermediate-level vision module to extract parametric features needed for higher-level processing     

分组渐进迭代逼近算法拟合数据点集

目的 在计算机辅助设计领域里,曲线或曲面的渐进迭代逼近（PIA）性质在插值与拟合问题中有着广泛的应用。如果直接使用PIA方法对所有的数据点集进行拟合,那么在拟合大规模数据点时就缺少一定的灵活性。为了进一步提高渐进迭代逼近方法在拟合大规模点集时的灵活性,提出基于分组的渐进迭代逼近方法。方法 首先对待拟合点集进行分组;其次对分组后的点集采用PIA方法或是基于最小二乘的渐进迭代逼近方法（LSPIA）来得到一组插值或拟合精度不断改善的曲线/曲面;最后运用曲线/曲面拼接算法保证曲线/曲面的连续性,得到1条/张插值或拟合于给定点集的曲线/曲面。结果 给定相同的数据点集,分别采用分组PIA方法,PIA方法和LSPIA方法进行拟合。分组PIA方法与PIA方法相比误差减少的倍数与组数相当;分组PIA方法与LSPIA方法相比误差减少一半。结论 本文将分组思想引入渐进迭代逼近方法之中,提出了基于分组的渐进迭代逼近方法。该分组算法适用于拟合大规模数据点集,在拟合过程中,可以提高渐进迭代逼近方法在拟合大规模点集时的灵活性;经过理论推导证明了曲线/曲面的迭代效率有所提高,且与PIA方法相比误差有较大的改善。     

三次B样条插值曲面及其实现

目前在ＣＡＭ／ＣＡＭ的自由曲面构造方法中，较流行的有Ｂ样条曲面，Ｂｅｚｉｅｒ曲面、Ｂａｌｌ曲面等方法，但由这几种方法和成都是拟合曲面，而百插值曲面，常常不能满足一些工程实际中严格插值的要求，本文构造了一种自由插值曲面生成方法－Ｂ样条母线法，所生成曲面达到Ｃ＾２级光滑，适用机械，模具、汽车、造船等制造加工行业的复杂曲面设计。     

非规则三维数据的曲面拟合方法

给出了一种非规则三维数据的曲面拟合方法,该方法给出的网络模型不需要删除奇异数据,从而可以保持数据信息的完整性,此外,该方法给出的拟合曲面平滑,连续性好,局部细节丰富,且处处可偏导。