Cubic B样条旋转曲面的自由绘制技术

随着基于样条曲线的模型逐渐成为CAGD的主要研究对象,进一步带动了高度自由曲面建模技术的发展.本文描述一个新颖、直观的旋转曲面绘制技术,它支持三次B样条的自由输入作为轮廓线,并通过提取的样点矢量以及最小方差逼近方法形成旋转轴,利用轴上测量点的切线方向确定各个圆平面,从而建立了平面上旋转坐标矩阵,最终插值空间球面样点生成双三次B样条曲面.实验结果有效地验证了此技术的高效性.     

过测地线的B样条曲面优化设计

给定一组不相交B样条曲线或满足一定约束的相交B样条曲线,提出了插值已知B样条曲线且以这组曲线为等参测地线的B样条曲面构造方法.插值曲面上的控制顶点分2步确定:首先利用B样条乘积和升阶理论显式计算曲面上与插值条件相关的控制顶点,其次由极小化Dirichlet能量确定曲面上其他自由控制顶点.采用文中方法构造的插值测地线曲面具有次数低、形状易控制等优点,并通过计算实例验证了该方法的正确性和有效性.     

基于区域分割的三维自由曲面相似性评价算法

为了在工程应用中检索已有的三维CAD模型,以便重用相应零件的设计信息,节省设计和加工成本,提出一种基于曲面分割技术的CAD自由曲面相似性评价算法.依据曲面的曲率将自由曲面分割成具有相对固定曲率特征的不同区域;对每个分割得到的区域用一个7维向量表达其形状的几何特征和拓扑特征,一个自由曲面形状特征即可通过各分割区域所对应的7维向量组成的向量组表达;将该向量组作为自由曲面的形状描述子,2个自由曲面的相似性可通过相对应的形状描述子间的相似性表达.在评价2个曲面形状描述子的相似性时,将描述子中的每个向量看成是一个带有属性的节点,2个形状描述子所对应的2组属性节点可看成是一个二分图,2组属性节点间相应节点距离看成是二分图的权值,并利用赋权二分图最优匹配的算法求出2组属性节点的相似性,实现2个自由曲面之间的相似性评价.实验结果表明,该算法是有效、可行的.     

形状可调的5次组合样条及其参数选择

目的 为了克服3次参数B样条在形状调整与局部性方面的不足,提出带参数的5次多项式组合样条。方法 首先构造一组带参数的5次多项式基函数;然后采用与3次B样条曲线相同的组合方式定义带参数的5次多项式组合样条曲线,并讨论基于能量优化法的5次组合样条曲线参数最佳取值问题;最后定义相应的组合样条曲面,并研究利用粒子群算法求解曲面的最佳参数取值。结果 5次组合样条不仅继承了3次B样条的诸多性质,而且还比3次B样条具有更强的局部性及形状可调性。由于5次组合样条仍为多项式模型,因此方程结构相对较为简单,符合实际工程的需要。利用能量优化法可获得光顺的5次组合样条曲线与曲面。结论 所提出5次多项式组合样条克服了3次参数B样条在形状调整与局部性方面的不足,是一种实用的自由曲线曲面造型方法。     

基于多分辨率模型的三角曲面特征线辨识技术

由于特征线在反求工程 CAD建模中具有非常重要的作用 ,因此利用图形图象处理中的多分辨率模型概念 ,通过研究三角曲面模型的特征线 ,提出了一种三角曲面特征线的计算方法 .将计算得到的初始特征线通过编辑、修改等手段进行处理 ,得到清晰的特征线 ,并将其作为进一步划分重构 B样条曲面边界的依据和参考 ,从而为实现基于三角曲面模型的 B样条曲面重构奠定了基础 .实验结果证明 ,该算法能够在三角曲面上提取出令人满意的特征线 ,并据此重构出拓扑划分合理的 B样条曲面 .     

插值曲率线与特征线的B样条曲面构造

插值三维线框模型的曲面构造是几何建模中的一个重要研究问题.对于给定的三维线框模型,利用B样条乘积理论、微分几何的基础知识以及薄板样条能量,提出一种构造插值三维线框模型的B样条曲面的算法.首先将线框模型中的曲线分为曲率线(曲面以该线为曲率线)、特征线(曲面在该线处为G0连续)及光滑拼接线(曲面在该线处为G1连续),并对于曲率线及光滑拼接线推导了B样条曲面控制顶点所满足的条件;然后利用薄板样条能量求解出满足约束条件的光顺B样条曲面.上述算法能够构造出更光顺的曲面,被广泛地应用于B样条曲面构造领域.通过对若干模型进行测试,结果验证了文中算法的正确性与有效性.     

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.     

基于曲率优化的机器人砂带磨削轨迹规划

针对复杂曲面零件砂带磨削编程效率低、精度差的问题,基于B样条曲线曲面重构和机器人离线编程技术,提出了一种根据关键接触点曲率值生成工业机器人磨削轨迹的方法.首先,利用零件表面上需要进行砂带磨削的关键接触点和积累弦长参数化法构造节点矢量,从而计算出磨削轨迹的B样条基函数;其次,根据控制顶点反求矩阵得到全部未知控制点和3次B样条加工曲线;然后,分析关键接触点之间的曲率变化率和弧长,对关键点细化生成符合磨削工艺要求的目标点;最后,通过求解双3次B样条插值曲面方程获得目标点的加工姿态.以水龙头磨削为例进行试验,结果表明曲率优化算法磨削的零件表面轮廓形状明显优于截面法,且其粗糙度值能稳定在0.082 μm左右,可以有效提高工件表面加工质量.     

以多条离散曲线为测地线构造离散曲面

为了解决CAD中逆向主动设计问题,提出以任意多条空间离散曲线为测地线构造离散曲面的算法.首先通过密切圆思想离散化曲线相关几何变量;其次利用局部插值思想和测地线蕴涵特征,推导出满足约束条件的离散曲面公式;最后给出以B样条为度量函数的离散曲面构造公式.逆向主动设计实例表明,该算法是可行的并有较强的交互性,可以通过调整B样条度量函数的节点向量或控制顶点来调节曲面形状,设计出满足各种不同需求的曲面,在服装、鞋帽、义齿设计等领域有很好的应用前景.     

非均匀B样条曲面的自适应节点设置方法

针对非均匀B样条的节点设置问题,提出一种利用非均匀B样条曲面拟合离散数据的迭代算法,通过优化节点分布来改进拟合曲面的质量.该算法以带参数化的三角网格曲面为输入,在首次迭代中根据输入曲面的几何特征将其对应的参数域划分成若干个子区域,并使得每个子区域上累积的几何特征信息量近似相等,子区域的重心坐标将取为首次迭代的节点;在随后的迭代中,保证前次迭代生成的重心位置固定不变,并根据前次迭代得到的曲面拟合误差再次将区域划分成累积误差接近相等的子区域,新增加的子区域重心的坐标选为拟加入的节点.文中算法自适应地在曲面形状复杂或拟合误差大的区域引入更多的控制顶点,使得拟合曲面的质量得以逐步改进.实验结果表明,该算法快速有效,在拟合具有明显几何特征的输入数据时具有优势.     

自由特征模型参数化研究

为了更高效直观地对自由特征形状进行建模,对自由特征形体及自由特征定义点进行参数化,提出了一种通过封装参数和约束创建自由特征体特征的方法。在自由特征形状的定义中,建立数值参数和最终特征形状几何属性的映射关系。在轨迹线上提取特征定义点,在各点处建立横截面,对横截面进行蒙皮和扫掠运算,生成和基曲面无缝连接的自由形状体特征。     

Creation of user-defined freeform feature from surface models based on characteristic curves

This paper proposes a novel method for the creation of user-defined freeform feature (UDFFF) from existing surface model. The developed methodology has four major steps: selecting the region of interest (ROI), obtaining the characteristic curves from the surface model, reconstructing the ROI surface, and parameterizing the UDFFF. To quickly create UDFFF on the ROI, the representation of freeform feature based on characteristic curves is proposed. First, the characteristic curves of ROI are obtained automatically or by a small amount of human–computer interaction. In particular, user can directly and easily draw the curves on surface to satisfy the designer's requirements. Second, from the set of characteristic curves that is obtained, freeform surface is reconstructed by a suitable surface generation method, e.g., sweeping, revolving, skinning, and filling. Finally, parameterization of the freeform feature is configured, which primarily involves establishing parameters and building the mappings between feature parameters and shape data. Moreover, according to the degrees of freedom, two types of parameterization of freeform features may be described: one (low degrees of freedom) can be accurately described by the characteristic curves and the other (high degrees of freedom) can be approximated with these curves. The proposed UDFFF creation method has been tested with examples based on the surface models. Experience with our prototype system indicates that it allows untrained users to create UDFFFs from the surface models.     

附加自由曲面构造框架及其有效性维护的研究*

在对HUST-CAID(哈尔滨理工大学计算机辅助工业造型设计)系统进行研究的基础上,首先引入了自由曲面特征,然后结合HUST-CAID系统定义了自由曲面特征的分类和参数化,应用这种分类和参数化的方法创建了一个自由曲面特征,提出了一种基于FFDP配置的附加自由曲面特征的构造框架。此框架可以使自由曲面整体模型的构造完全参数化。最后建立了基于这个框架构造的自由曲面附加特征的有效性维护机制,从而达到对自由曲面附加特征进行有效性维护的目的。     

自由曲面特征的定义与识别技术的研究

结合自主开发的HUST-CAID（哈尔滨理工大学计算机辅助工业造型设计）系统的特点,引入自由曲面特征,给出了自由曲面特征的参数化定义,并在此基础上对自由曲面特征识别进行研究,先是给出自由曲面特征识别的定义,接着提出了基于曲线的特征识别的算法。该方法将基于曲线的特征以二维参数的形式给出定义,使其能在二维平面上研究,通过重构特征的剖面模板库,从而利用目标特征与模板特征匹配实现了特征识别。     

A surface based approach to recognition of geometric features for quality freeform surface machining

The paper presents a surface-based approach for geometric feature recognition for the purpose of automating the process planning of freeform surface machining. The proposed approach consists of the following four steps for recognition of the geometric features: conversion and preprocessing of the surface geometry data, subdivision of NURBS surface, reconstruction of surface orientation areas, and recognition of geometric features. The proposed scheme assumes that the input geometry data form is based on an IGES CAD model and the surface model can be represented in the form of trimmed NURBS surfaces. The connectivity relations of the product surfaces are analyzed and each surface is subdivided into orientation regions based on the surface normal vector over a certain point density grid, and then all the connected regions with the same orientation type are grouped into surface orientation areas. After that, the geometric feature will be recognized through the analysis of area connectivity and relationship. The paper describes the developed algorithms on surface orientation region subdivision, surface orientation area reconstruction, and geometric feature recognition. The verified feasibility study of the developed method is also presented.     

Local parameterization of freeform shapes using freeform feature recognition

Form feature modeling is a much used shape modeling technique that offers high-level control over a shape. When a feature-based interpretation of shape data is not available, e.g. when a shape is obtained by a laser range scanner or from a database of shapes, then the features must be reconstructed through feature recognition. Many methods for the recognition of machining features exist, but these methods cannot be used for freeform feature recognition, of which the complexity is much larger. In this paper, a new freeform feature recognition method is presented that is based on a new definition of the freeform feature concept. The method uses a three-step approach to feature recognition, in which first the global shape of a feature is matched to the target shape model. In a second step, this global shape is locally adapted to the target shape by adapting the definition of the feature. Finally, if the desired configuration of the feature has been determined, it can be used to reconstruct the target’s shape. In the first two steps, an evolutionary approach is taken to maximizing the similarity between the feature and the target shape. Finally, the target shape is reconstructed to incorporate the recognized feature. An extensive application example is given and the method is validated by applying it to a large number of artificially created test cases.     

基于多特征的模型检索技术

本文提出了三维模型表面特征点分布与质心向量夹角分布相结合的检索技术,将模型预处理之后,统计模型表面特征点的分布规律,再统计模型质心到特征点向量所构成夹角的分布规律,将两者的相似度乘以适当的权值得出最终三维模型的相似度。实验表明,该检索技术性能较单用一种特征的检索技术性能有所提高。     

Volumetric feature recognition for machining components with freeform surfaces

This paper describes a procedure for the extraction of features of a part containing a combination of 2.5D features and freeform surfaces. This work invokes a previous algorithm that was designed to recognize machining features from 2.5D parts destined to be machined on a 3-axis milling machine. The essence of that algorithm was a volume decomposition based on a recursive descent into the part, yielding a feature graph that captured both the geometry and the spatial relationships of the features. This work augments the previous algorithm with the ability to handle a limited class of components having freeform surfaces. Freeform features are defined similar to the 2.5D features as comprising a planar contour, but substituting a bottom freeform surface for the depth. Covering faces, defined as projection of the freeform surface on the faces of the bounding box of the surface, are used as equivalent planar faces for performing the recursive descent. Inter-feature open edges are used to signal the relationship between the freeform feature and other neighboring features. Examples of molds and components that were machined using the proposed algorithms are also presented.     

流线型结构特征造型方法及其在高速列车设计中的应用

提出了一种基于自由曲面的流线型结构特征造型方法,并将其应用于200km／h电动车组“先锋号”的流线型结构设计之中,流线型结构特征所描述的实体模型对自由曲面外形的变化具有自适应性,该方法便于流线型结构数据存取和修改,可在自由曲面外形和流线型结构各种参数多次修改的情况下自动生成流线型结构实体;大幅度地减少了人机交互时间,解决了高速列车流线型结构实体造型过程中设计周期过长的问题。     

Deformable Surface Techniques for Field Visualization

Surface extraction from data fields is often used in scientific visualization, as surfaces can represent meaningful information and they are well suited for display. This paper describes a general method for localized surface extraction from scalar and vector fields. An initial polygonal surface is placed within the field, and the shape of the surface is adapted to the field by iterative displacement of surface nodes according to a displacement criterion. To achieve a good approximation of a smooth surface, the polygon mesh can be locally refined during iteration. The type of surface extracted depends on the displacement criterion, which can be any function of the available field variables. Techniques for displacement and mesh refinement are discussed in detail. The results we show are generation of a local isosurface and extraction of a vortex tube. Finally, we will draw conclusions and discuss some issues for further development.