逆向工程中平面轮廓线数据的B样条曲面拟合

利用统计学的知识，对空间数据点参数值分布情况进行了分析，给出了曲面拟合过程中节点矢量的确定方法。在此基础上给出了曲面轮廓线数据的B样条曲面拟合算法以及应用该方法对平面轮廓线扫描数据进行B样条曲面拟合的算例。     

基于径向基函数与B样条的散乱数据拟合方法

针对散乱数据的曲面拟合问题,提出一种径向基函数与B样条插值结合使用的曲面拟合方法.通过分片径向基函数插值,三维散乱点,再从分片插值曲面上获取预先设定好的有序网格点的值,最后利用张量积B样条插值有序网格点,从而得到拟合曲面.该方法较好地解决散乱数据插值和拟合的计算不稳定性问题,最后给出算法实例.     

一种基于NURBS理论的曲面逼近优化算法

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NURBS曲面构造方法,该方法根据已知数据点逼近目标曲面.通过实际系统应用验证,该方法是一种行之有效的曲面拟合方法.     

基于逼近理论的曲面重构方法的研究

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NURBS曲面构造方法。该方法根据已知数据点逼近目标曲面。通过实际系统应用验证，该方法是一种行之有效的曲面拟合方法。     

基于组合方法对图像的双三次多项式拟合

提出了基于图像数据构造拟合曲面的新方法.假设给定的图像数据所对应的原场景曲面能用分片二次多项式曲面表示,原场景曲面称为原曲面.现有方法通常是用图像数据作为插值数据构造原曲面的拟合曲面,而新方法以图像数据生成公式为约束,通过反向采样过程来构造对图像数据拟合的曲面,从而使拟合曲面具有更好的逼近精度.由于图像边缘处的质量对图像的视觉效果起着关键的作用,我们也把图像边缘做为约束条件用于拟合曲面的构造.对于每一个数据点及其邻近区域,新方法以采样公式和图像边缘作为约束条件局部地构造一张二次多项式曲面片,该曲面片具有二次多项式精度.所有的二次多项式曲面片的加权组合形成逼近原曲面的拟合曲面.对算法比较的实验表明,由新方法生成的放大图像具有较高的精度和较好的视觉效果.     

非矩形定义域上的散乱数据曲面重建的Multiquadric基函数拟合法

传统的Multiquadric基函数拟合散乱数据方法,只能用于定义域呈矩形拓扑的散乱数据集上,而逆向工程中通常遇到的是非矩形定义域上的散乱数据集,因此不能用传统方法。文章提出一种新的Multiquadric基函数拟合非矩形定义域上的散乱数据集。该方法首先找到一个与该散乱数据集所在曲面拓扑等价的参数曲面,通过将散乱数据点(xi,yi,zi)一一映射到此参数曲面,反求出其对应参数(ui,vi),由于(ui,vi)∈犤0,1犦×犤0,1犦,从而将非矩形定义域上的Multiquadric基函数拟合方法转化为传统的方法。将Multiquadric曲面与B-样条曲面进行了比较,指出了Multiquadric曲面优于B-样条曲面之处。     

基于轮廓数据的B样条曲面重建

针对B样条曲面拟合中出现的问题和困难,提出了一种基于行组织的轮廓数据（截面数据）的曲面重建方法。该方法避免了数据点的参数化问题,使得逼近曲面拥有较好的形状和合理的控制顶点数量。该方法的基本思想是：首先构造易于控制的低阶曲面拟合数据点,此曲面称控制曲面,然后利用高次曲面逼近该曲面,此高次曲面称为逼近曲面,为所需要的重建曲面。在曲面重建中利用最佳平方逼近和光顺函数,减少了逼近曲面的控制顶点冗余,较有效地防止了逼近曲面的形状突变和曲面的扭曲,很大程度地提高了曲面的质量。     

基于局部曲面拟合的散乱点云简化方法

随着数据获取手段的进步,散乱点云数据在三维重建中获得越来越广泛的应用,然而庞大的数据量往往影响重建的效率。现有简化算法中采用的曲率计算方法精度不高,导致模型特征模糊。本文在分析曲面特征的基础上给出了一种曲面特征的定量描述方法。该方法采用局部曲面拟合得到曲面在一点处的近似曲面,然后用法曲率在360度范围内的平均值代替平均曲率来描述曲面在一点处的特征。简化时采用K-D树剖分点云数据,根据子节点所包含的采样点数、空间区域大小和曲面特征大小控制简化过程。实验结果表明,该方法能够更好地保持曲面的几何特征,从而证明了算法的有效性。     

基于蚁群的数据点NURBS曲面快速拟合研究

研究数据点的NURBS曲面拟合问题,提高拟合速率。针对所要拟合的数据点分布散乱,传统的基于遗传算法多次迭代,造成曲面拟合速率不高的问题。为解决上述问题,提出一种基于蚁群的数据点NURBS曲面拟合算法。通过采用蚁群寻址算法搜索出控制顶点和边界数据点集,计算曲面的权因子后完成NURBS曲面的拟合,并使用蚁群算法对拟合曲面进行优化,避免了传统方法多代遗传迭代造成的拟合速率不高的问题。实验表明,这种方法能够快速完成散乱数据点的NURBS曲面拟合,并且具有一定的拟合效率,取得了满意的结果。     

基于B样条的平面轮廓重构闭合曲面算法

由一组平行轮廓线重构三维闭合表面是三维可视化研究的主要内容之一。文中通过对B样条插值算法的研究,提出了一种新的公共节点矢量确定方法,利用该方法首先对经过预处理的CT牙齿图片提取轮廓线获得三维数据点,之后对轮廓线数据点进行B样条曲线的拟合,在每条拟合曲线上根据所确定的节点矢量值重新采样,由重新采样的三维数据点利用B样条曲面插值算法构造闭合曲面．所构造的闭合曲面是对原始轮廓数据的拟合。通过实例验证可看出该方法可获得较好的拟合曲面,经过误差分析检测,满足拟合条件,因此该方法可以保证几何重建的准确性。     

Adaptive coding of generic 3D triangular meshes based on octree decomposition

In this paper, we present an adaptive-coding method for generic triangular meshes including both regular and irregular meshes. Though it is also based on iterative octree decomposition of the object space for the original mesh, as some prior arts, it has novelties in the following two aspects. First, it mathematically models the occupancy codes containing only a single–“1” bit for accurate initialization of the arithmetic coder at each octree level. Second, it adaptively prioritizes the bits in an occupancy code using a local surface smoothness measure that is based on triangle areas and therefore mitigates the effect of non-uniform vertex sampling over the surface. As a result, the proposed 3D mesh coder yields outstanding coding performance for both regular and irregular meshes and especially for the latter, as demonstrated by the experiments.     

基于Marching cubes的三维目标表面积估算方法

三维目标表面积参数广泛应用于石油地质,医学,制造行业等领域。在介绍一种基于Marching cubes的局域配置方法来估算三维目标的表面积的过程中,针对Marching cubes分类的14种模型元,给出了一种简单和易于实现的分类方法,避免了重新实现Marching cubes算法或者使用一系列复杂的三维表面探测算法。基于Marching cubes的表面积估算方法对于规则和不规则目标表面积的估算均适用。通过实验数据对比几种不同的估算方法结果的精确度,说明基于Marching cubes的估算方法精确度是非常高的,可以应用于实际工程中。     

离散点云原始形状及边界曲线提取算法

大规模离散点云包含多种类型的扫描缺陷:噪声、异常数据、孔洞及不规则的各向异性采样,大部分现有的算法不能够很好地处理这些缺陷,这对点云拓扑关系的恢复及特征提取带来了困难.针对此问题,提出了一种健壮有效的点云重构算法,首先,计算每个数据点的局部属性;然后利用局部属性探测点云中包含的原始形状;最后利用统计优化方法对原始形状中...     

Robust feature detection and local classification for surfaces based on moment analysis

The stable local classification of discrete surfaces with respect to features such as edges and corners or concave and convex regions, respectively, is as quite difficult as well as indispensable for many surface processing applications. Usually, the feature detection is done via a local curvature analysis. If concerned with large triangular and irregular grids, e.g., generated via a marching cube algorithm, the detectors are tedious to treat and a robust classification is hard to achieve. Here, a local classification method on surfaces is presented which avoids the evaluation of discretized curvature quantities. Moreover, it provides an indicator for smoothness of a given discrete surface and comes together with a built-in multiscale. The proposed classification tool is based on local zero and first moments on the discrete surface. The corresponding integral quantities are stable to compute and they give less noisy results compared to discrete curvature quantities. The stencil width for the integration of the moments turns out to be the scale parameter. Prospective surface processing applications are the segmentation on surfaces, surface comparison, and matching and surface modeling. Here, a method for feature preserving fairing of surfaces is discussed to underline the applicability of the presented approach.     

A process for surface fairing in irregular meshes

This paper describes a stepwise, automatic fairing process to construct a smooth surface by optimizing suitably chosen quantitative fairness measures. The input consists of given point and/or curve data, each designated to be interpolated or approximated. These data may stem from digitizing drawings or mockup models or from prior individual curve fairing. The data are arranged in an arbitrary irregular mesh topology. The irregular, n-sided mesh cells are converted by midpoint subdivision into aggregates of quadrilateral patches (Peters, 1994), for which a biquartic Bézier surface representation is chosen everywhere. The resulting C¹ surface minimizes the fairness measure, which is selected from a variety of geometrically relevant quadratic forms, including second and higher order derivative norms. This variational formulation of the fairing problem is of Quadratic Programming type and has a unique solution. Two algorithms are described, one for global, simultaneous and another for local, iterative solution of the corresponding large linear system of equations. This surface fairing technique will be illustrated by two main examples, viz., a car hood and a twisted tripod, demonstrating the performance of the fairing algorithms and the effects of the chosen fairness measures on the character of the resulting shapes.     

密集散乱测量数据点的B样条曲面拟合研究

回顾了密集散乱数量数据点面拟合研究发展情况,针对异形边界自由曲面密集散乱测量数据点,提出一种B样条曲面多步拟合算法,其中涉及边界插值B样条曲面生成、Hardy′s双二次局部插值、规则网格数据点B样条曲面最小二乘拟合等关键技术,通过一个工程实例,对文中提出的B样条曲面多步拟合算法进行了实验验证。     

一种数据流中的频繁模式挖掘算法

时序数据流的无限性、流动性和不规则性使得传统的频繁模式挖掘算法难以适用。针对时序数据流的特点,提出了一类特殊非规则数据流频繁模式挖掘的新算法。新算法采用时序数据分段的思想,逐段挖掘局部频繁模式,然后依据局部频繁模式有效地挖掘出所有的全局频繁模式。将新算法应用于电信领域的收入保障项目之中,结果表明,新算法具有良好的性能,能有效发现挖掘时序数据流中的频繁模式。     

DigitalSculpture: a subdivision-based approach to interactive implicit surface modeling

This paper presents DigitalSculpture, an interactive sculpting framework founded upon iso-surfaces extracted from recursively subdivided, 3D irregular grids. Our unique implicit surface model arises from an interpolatory, volumetric subdivision scheme that is C¹ continuous across the domains defined by arbitrary 3D irregular grids. We assign scalar coefficients and color to each control vertex and allow these quantities to participate in the volumetric subdivision of irregular grids. In the subdivision limit, a virtual sculpture is obtained by extracting the zero-level from the volumetric, scalar field defined over the irregular grid. This novel shape geometry extends concepts from solid modeling, recursive subdivision, and implicit surfaces; facilitates many techniques for interactive sculpting; permits rapid, local evaluation of iso-surfaces; and affords level-of-detail control of the sculpted surfaces.     

Multiresolution analysis on irregular surface meshes

Wavelet-based methods have proven their efficiency for visualization at different levels of detail, progressive transmission, and compression of large data sets. The required core of all wavelet-based methods is a hierarchy of meshes that satisfies subdivision-connectivity. This hierarchy has to be the result of a subdivision process starting from a base mesh. Examples include quadtree uniform 2D meshes, octree uniform 3D meshes, or 4-to-1 split triangular meshes. In particular, the necessity of subdivision-connectivity prevents the application of wavelet-based methods on irregular triangular meshes. In this paper, a “wavelet-like” decomposition is introduced that works on piecewise constant data sets over irregular triangular surface meshes. The decomposition/reconstruction algorithms are based on an extension of wavelet-theory allowing hierarchical meshes without property. Among others, this approach has the following features: it allows exact reconstruction of the data set, even for nonregular triangulations, and it extends previous results on Haar-wavelets over 4-to-1 split triangulations     

DSACNN: Dynamically local self-attention CNN for 3D point cloud analysis

The point cloud is a common 3D representation widely applied in CAX engineering due to its simple data representation and rich semantic information. However, discrete and unordered 3D data structures make it difficult for point clouds to understand semantic information and make them unsuitable for applying standard operators. In this paper, to enhance machine perception of 3D semantic information, we propose a novel approach that can not only directly process point cloud data by a novel convolution-like operator but also dynamically pay attention to local semantic information. First, we design a novel dynamic local self-attention mechanism that can dynamically and flexibly focus on top-level information of the receptive field to learn and understand subtle features. Second, we propose a dynamic self-attention learning block, which adopts the proposed dynamic local self-attention learning convolution operation to directly deal with disordered and irregular point clouds to learn global and local point features while dynamically learning the important local semantic information. Third, the proposed operation can be compatibly applied as an independent component in popular architectures to improve the perception of local semantic information. Numerous experiments demonstrate the advantage of our method for point cloud tasks on datasets from both CAD data and scan data of complex real-world scenes.