一种提取可展网格曲面的新方法

可展曲面是每一点高斯曲率为零的曲面,由于其具有优良性质,因此在工程实践中得到广泛应用。为便于各种网格处理,从一个整体表面网格模型中获取可展区域具有重要意义。针对目前相关方法中存在的不足,本文提出了一个提取可展网格面片的新方法。首先利用高斯曲率提取可展网格面片,接着对分割得到的层可展区域进行微分几何上的直纹面的拟合,然后根据拟合的直纹面方程来判断是否可展,最后根据每种可展类型的直母线性质来判定可展类型。获得的可展面片中包括连续柱面和连续锥面,而传统方法无法获得;另外,确定获得面片的可展类型便于下一步网格处理。与已有方法相比,此方法更具有可行性和优越性。     

一种三维模型形状检索描述符

为了解决基于关键字的搜索方式不能准确查找三维模型的问题,对三角网格形式的三维模型提出一种基于内容的模型搜索算法.首先将模型中的三角网格再次划分,增加形状函数的维度,定义了一种新的三维模型形状函数,以提高形状函数的准确性;然后确定三维模型的极轴,将三维模型绕任意轴的旋转转换为绕极轴旋转,增强了球面调和方法提取的形状描述符旋转不变性;最后根据形状描述符之间的欧氏距离来度量三维模型的相似程度.实验结果表明,该算法适用于基于内容的三维模型搜索,并且在准确性和时效性方面都令人满意.     

一种基于进化泛函网络的建模与函数逼近方法

提出了一种进化泛函网络的建模与函数逼近方法,该方法把泛函网络建模过程转变为结构和泛函参数的优化搜索过程,利用遗传规划设计泛函网络神经元函数,对网络结构和参数共存且相互影响的复杂解空间进行全局最优搜索,实现泛函网络结构和参数的共同学习,并用混合基函数实现目标函数的逼近,改变了人们通常用同类型基函数来实现目标函数逼近的方式.数值仿真结果表明,提出的网络建模与逼近方法具有较高的逼近精度.     

基于最小二乘RBF的含噪声散乱数据逼近

径向基函数能够有效的对散乱数据进行差值和逼近,因此在信号和图形处理等领域应用广泛,例如信号重构.针对从含有噪音的散乱数据中逼近原始数据,提出了一种基于最小二乘的变分模型,该模型由包含L2范数的拟合项和光滑项构成,光滑项通过三角网格上的拉普拉斯平滑方法来实现对函数梯度的约束,并应用最小二乘法求解该模型.最后通过数值实验对噪音数据进行逼近和误差分析来验证此方法的有效性.     

一种基于遗传算法的数字曲线多边形逼近方法

提出了一种基于遗传算法的数字曲线多边形改进逼近方法。该方法针对规则形状数字曲线的多边形逼近问题,以二进制向量序列表示的染色体作为每一个对应的逼近多边形候选解,将简化前后多边形质心偏移误差以及各被替换线段欧氏距离的方差引入到适应函数中,用迭代次数的sigmoid函数作为变异概率来控制遗传算法优化求解过程中的全局和局部搜索特性。实验结果表明,该方法对于保持曲线多边形简化逼近后的形状特征具有较好的效果。     

插值曲率线的直纹面可展设计

目的 曲率线在微分几何中起着非常重要的作用,它在曲面分析中是一个很有用的工具。可展曲面是曲面造型中最简单也最常用的一类曲面,目前大部分工作都是研究在给定曲面上寻找或者计算曲率线,而其反问题研究工作较少,为此,提出一种插值曲率线的可展曲面构造方法,并进一步将它应用到曲面造型中。方法 利用Frenet标架表示直纹面的母线,根据曲线为曲面曲率线以及曲面可展的充要条件,得到直纹面的母线需要满足的关系式。并引入控制函数控制曲面的形状。结果 给出了以给定曲线为曲率线的直纹面可展的具体表达式,根据可展曲面分类分析了设计曲面为柱面、锥面和空间曲线切线面的充要条件,并给出了两个代表性的实例验证该方法的有效性,实例结果表明,该方法不仅适用于一般参数曲线,对分段参数曲线也是有效的。结论 利用构造性的方法给出了插值曲率线的可展曲面的具体表达形式,并通过具体实例验证了该方法的有效性。     

遗传规划和进化策略混合算法及应用

文中把函数拟合建模看作是模型结构和参数的优化搜索过程,将遗传规划和进化策略结合起来对函数拟合的结构和参数共存且相互影响的复杂解空间进行全局最优搜索实现拟合结构和参数的共同识别。克服了传统的函数拟合完全依赖于数据、精度低、结构与参数分别确定这样一“串行”计算结构等缺陷。实验数据表明,该方法得到的拟合函数比传统方法得到的拟合函数,具有较高的精度和推广预测能力。     

网格曲面近似“最直路径”的快速计算

为实现网格模型两点间最短路径的近似逼近,提出一种网格曲面上近似"最直路径"的计算方法.利用起点与终点邻域特征获得初始切割面,对网格曲面上的三角片逐步切割求交,扩展"最直路径";在求交过程中逐步调整切割平面的方向,直至终点.实验结果表明,文中方法快速、有效.     

基于非精确图匹配的CAD模型搜索方法

为了弥补现有的三维CAD模型搜索方法难以搜索到不同近似程度的相似模型的缺陷,提出一种基于面属性化邻接图非精确匹配的CAD模型搜索方法.首先提取CAD模型中的B-rep信息将CAD模型转化为面属性化邻接图;然后计算目标模型与被搜索模型的面属性化邻接图之间的顶点相容程度矩阵和边相容程度矩阵,并由此建立2个模型相似程度的度量作为选择不同顶点匹配矩阵M的优化目标函数;在对匹配矩阵M进行连续化松弛后,运用Sinkhorn行列交替规范化方法求解匹配优化问题.实验结果表明,采用该方法能够搜索到不同近似程度的相似模型;并且由于避免了具有NP复杂性的精确图匹配过程,检索效率也能满足实际要求.     

基于多尺度高斯核的分布式正则化回归学习算法

针对工业、信息等领域出现的基于较大规模、非平稳变化复杂数据的回归问题,已有算法在计算成本及拟合效果方面无法同时满足要求.因此,文中提出基于多尺度高斯核的分布式正则化回归学习算法.算法中的假设空间为多个具有不同尺度的高斯核生成的再生核Hilbert空间的和空间.考虑到整个数据集划分的不同互斥子集波动程度不同,建立不同组合系数核函数逼近模型.利用最小二乘正则化方法同时独立求解各逼近模型.最后,通过对所得的各个局部估计子加权合成得到整体逼近模型.在2个模拟数据集和4个真实数据集上的实验表明,文中算法既能保证较优的拟合性能,又能降低运行时间.     

Cone spline approximation via fat conic spline fitting

Fat conic section and fat conic spline are defined. With well established properties of fat conic splines, the problem of approximating a ruled surface by a tangent smooth cone spline can then be changed as the problem of fitting a plane fat curve by a fat conic spline. Moreover, the fitting error between the ruled surface and the cone spline can be estimated explicitly via fat conic spline fitting. An efficient fitting algorithm is also proposed for fat conic spline fitting with controllable tolerances. Several examples about approximation of general developable surfaces or other types of ruled surfaces by cone spline surfaces are presented.     

Quasi-Developable B-Spline Surface Design with Control Rulings

We propose a method for generating a ruled B-spline surface fitting to a sequence of pre-defined ruling lines and the generated surface is required to be as-developable-as-possible. Specifically, the terminal ruling lines are treated as hard constraints. Different from existing methods that compute a quasi-developable surface from two boundary curves and cannot achieve explicit ruling control, our method controls ruling lines in an intuitive way and serves as an effective tool for computing quasi-developable surfaces from freely-designed rulings. We treat this problem from the point of view of numerical optimization and solve for surfaces meeting the distance error tolerance allowed in applications. The performance and the efficacy of the proposed method are demonstrated by the experiments on a variety of models including an application of the method for path planning in 5-axis computer numerical control (CNC) flank milling.     

Feature-Preserving Mesh Denoising via Anisotropic Surface Fitting

We propose in this paper a robust surface mesh denoising method that can effectively remove mesh noise while faithfully preserving sharp features. This method utilizes surface fitting and projection techniques. Sharp features are preserved in the surface fitting algorithm by considering an anisotropic neighborhood of each vertex detected by the normal-weighted distance. In addition, to handle the mesh with a high level of noise, we perform a pre-filtering of surface normals prior to the neighborhood searching. A number of experimental results and comparisons demonstrate the excellent performance of our method in preserving important surface geometries while filtering mesh noise.     

一种带噪声的密集三角网格细分曲面拟合算法

实现了一个从带噪声的密集三角形拟合出带尖锐特征的细分曲面拟合系统.该系统包括了一种改进的基于图像双边滤波器的网格噪声去除方法,模型的尖锐特征提取以及保持尖锐特征的网格简化和拓扑优化.为了处理局部细节特征和模型数据量问题,提出了自适应细分方法,并将根据给定精度估计最少细分深度引入到细分曲面拟合系统中,使得拟合得到的细分曲面模型具有良好的细节特征和数据量小等特点.大量3D模型实验结果和实际工程应用结果表明了该细分曲面拟合系统的有效性.     

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.     

自适应T样条曲面重建

为了进行快速高精度的曲面重建,提出了一种新的基于T样条的曲面自动重建算法。由于T样条控制网格具有特殊性质,因此在使用T样条进行曲面重建时,一个关键的问题是如何构造好一个T网格。该新算法在进行曲面重建时,用三角网格的参数化方法,先将数据点同胚映射到平面,然后再利用平面四叉树细分的方法将无结构散乱数据自动生成合理有效的T网格,最后将曲面重构模型转化为最优化问题,并由最小二乘法求解,同时在误差较大的区域辅以T样条的局部修正,以使重建曲面与原网格面的最大误差小于指定的误差值。由于该新的曲面重建方法是一个基于细节的重建方法,因此采样点密集区域所插入的T网格点也就相应地增多,这样既抓住了网格曲面的特征,又能很好地减少过多的T网格控制顶点,这就提高了算法效率。另外,该新算法还具有高效、易操作、能适应复杂曲面重建、曲面自动生成且满足相应精度要求等优点。重构结果显示,该新的曲面重建算法不仅重构应用范围广,且重构精度高。     

Direct Reconstruction of a Displaced Subdivision Surface from Unorganized Points

In this paper we describe the generation of a displaced subdivision surface directly from a set of unorganized points. The displaced subdivision surface is an efficient mesh representation that defines a detailed mesh with a displacement map over a smooth domain surface and has many benefits including compression, rendering, and animation, which overcome limitations of an irregular mesh produced by an ordinary mesh reconstruction scheme. Unlike previous displaced subdivision surface reconstruction methods, our method does not rely on a highly detailed reconstructed mesh. Instead, we efficiently create a coarse base mesh, which is used to sample displacements directly from unorganized points, and this results in a simple process and fast calculation. We suggest a shrink-wrapping-like shape approximation and a point-based mesh simplification method that uses the distance between a set of points and a mesh as an error metric to generate a domain surface that optimally approximates the given points. We avoid time-consuming energy minimization by employing a local subdivision surface fitting scheme. Finally, we show several reconstruction results that demonstrate the usability of our algorithm.     

A new feature-preserving mesh-smoothing algorithm

We present a novel mesh denoising and smoothing method in this paper. Our approach starts by estimating the principal curvatures and mesh saliency value for each vertex. Then, we calculate the uniform principal curvature of each vertex based on the weighted average of local principal curvatures. After that, we use the weighted bi-quadratic Bézier surface to fit the neighborhood of each vertex using the least-square method and obtain the new vertex position by adjusting the parameters of the fitting surface. Experiments show that our smoothing method preserves the geometric feature of the original mesh model efficiently. Our approach also prevents the volume shrinkage of the input mesh and obtains smooth boundaries for non-closed mesh models.     

基于投影变换的Sweep曲面构造方法

Sweep曲面通常用沿脊线的局部活动标架来刻划，但是活动标架的构造在很大程序上由脊线的几何性质决定。因此提出：构造Sweep曲面是否一定需要用活动标架来确定截线的位置？为解决这个问题，提出了一种投影方法，它有两个优点：首先，当脊线是直线段和圆弧时，Sweep曲面可以精确表示；第二，Sweep曲面可以直接用投影变换方法来构造，从而可以避免使用活动标架，进而可以不必考虑脊线的连续性Sweep曲面形状的影响。另外，曲面的误差控制可以通过对脊线的offset的误差控制来实现。通过实例验证了所提算法的稳定性和有效性。