改进的血管三维建模算法

针对现有基于细分曲面的血管建模算法不能处理任意拓扑结构的血管数据,以及保证血管分叉处的光滑过渡等问题,对该算法进行了改进.首先采用有向图表示血管段之间的关系,然后对血管中心线模型进行双向自适应采样,最后采用Loop细分模式生成血管曲面.实验结果表明,采用文中算法能够有效地处理任意拓扑复杂的血管数据,并且能生成高质量的三维血管模型.     

基于任意骨架的隐式曲面造型技术

给出了一个新的基于任意多面体网格骨架的构造性自由曲面造型算法.算法首先由每个给定骨架构造出一个距离场,然后利用隐函数光滑过渡技术和CSG(constructive solid geometry)表示技术将所构造的隐式曲面自由地两两粘合成一张光滑曲面.隐式曲面的多边形化算法则用来生成最终曲面网格.以任意骨架作为基本体素,突破了传统隐式曲面以点为基本骨架的限制.而且,距离曲面很好地逼近了原骨架形状,使用户可直观地对复杂曲面进行交互设计.而形变函数的引入,则极大地丰富了此方法的造型能力.实验结果表明,基于该算法的原型系统能够方便、直观地构造复杂的自由曲面.     

基于弹簧-质点模型的不规则曲面纹理映射

针对三角网格表示的不规则曲面的纹理映射问题,提出一种基于弹簧-质点模型的简单、高效、失真小的纹理映射算法。结合调和映射的参数化方法以及弹簧-质点模型的复杂平面展开方法,保持拓扑关系地将三维曲面投影于平面内;通过建立三角网格表示的投影面的弹簧-质点模型,将不规则曲面参数化于给定大小的矩形域;利用参数化的结果计算不规则曲面各顶点的纹理坐标,进行纹理贴图。实验结果表明,该算法能够实现纹理高效、均匀、变形小地映射于任意不规则曲面上。     

自由曲线曲面的任意次非均匀细分

提出一种有效的建模自由曲线曲面的非均匀细分算法。首先在节点插入技术基础上推导出任意次自由曲线的非均匀细分规则,然后把它推广到张量积曲面得到任意次自由曲面的非均匀细分规则,最后对奇异点附近曲面采用类Doo-Sabin和Catmull-Clark的细分规则,从而使该算法可以实现建模任意次具有任意拓扑基网格的非均匀细分曲面。此外,该方法也实现了对传统细分格式的统一,例如,当次数为2并采用均匀节点矢量便转化为Doo-Sabin细分,当次数为3并采用均匀节点矢量便转化为Catmull-Clark细分。     

在任意拓扑三角形网格上的光滑样条曲面

介绍了一种在控制三角形网格上创建光滑样条曲面的算法,该控制网格能够刻画具有或没有边界的任意自由曲面.生成的曲面有一个4次参数多项式表示并且被表示成一个切平面连续的三角形Bézier片网.曲面对网格的逼近程度受到一个混合比控制,当混合比为0时,产生的曲面插值网格.该算法是一种局部方法,简单且效率高,适合于外形设计.     

多裁剪自由曲面的修补缝合功能的实现

将初始的多个裁剪曲面粘合在一起,是从初始CAD模型转化生成为“不漏水”的网格化模型的子算法之一．首先叙述了初始多裁剪曲面的结构,然后阐述了该算法的数据结构,并给出了算法的具体实现．该算法可缝合多裁剪自由曲面,并对初始CAD模型中出现的裂缝、重叠等现象,以及不良的参数化边界曲线(如退化、折叠等现象)进行了相应的修补．程序测试表明,该算法稳定、快速．最后给出两个实例及相关数据．     

Catmull-Clark细分曲面的形状调整

提出一种调整细分曲面形状的算法．该算法用cosα(Ck)取代C-B样条的形状因子α，并将Ck的定义区间从[-1，1]扩大到[-1，∞)；然后用这种扩展了的GB样条来构造catmull—clark细分曲面；使得生成细分曲面的形状不仅能够在C-B样条的范围内可调，而且还能在标准的catmull-clark细分曲面和初始的控制网格之间任意调整．该算法保留了C-B样条和catmull-clark细分曲面的主要特点，如精确表示圆柱体、处理任意拓扑结构的控制网格等。     

曲面三角网格模型顶点法矢计算与交互式分割

本文给出一种三角网格模型顶点法矢计算公式,该公式采用网格模型中三角片面积与顶角角度综合加权,其计算精度高于现有的面积加权计算方法．另外,本文还提出了一种简便灵活的任意拓扑曲面三角网格模型交互式分割方法．利用该方法,可有效地将任意拓扑三角网格模型分割为几个与盘形拓扑同胚的区域,为后续处理提供方便。     

基于拓扑信息的多张裁剪曲面缝合算法

曲面缝合是曲面造型过程中常用到的处理技术,即把由多张裁剪曲面表示的模型转换成一个“不漏水”的模型。曲面缝合主要采用先离散后缝合的方法,但离散精度难以控制．提出一种多张裁剪曲面缝合算法,根据被缝合曲面的几何信息建立与其相缝合的邻接曲面信息,利用邻接曲面信息寻找其邻接边界;然后由邻接边界计算边界曲线的匹配参数,建立曲面的拓扑信息;最后根据曲面之间的拓扑信息对曲面进行缝合处理．通过实例对文中算法进行验证,结果显示该算法缝合效果良好。     

Doo-Sabin细分模式的尖锐特征造型

通过推广准均匀二次B样条的节点插入算法,对边界面、折痕面、角点面等特征面给出新的细分规则,从而使Doo-Sabin细分模式可以表示边界、折痕、角点、刺点等尖锐特征,且特征处不受拓扑结构的限制.在特征附近进行了连续性分析,所得到的极限曲面具有分片G1连续性.该算法既可以设计有特征的、任意拓扑的复杂曲面,又可以精确地表示球面、柱面、锥面等工程技术中常用的二次曲面,在CAD/CAM领域具有广泛的应用前景.     

基于拓扑相似性的等距参数曲面求交算法

等距曲面求交算法通常采用曲面求交算法反复迭代计算交线,没有考虑不同Offset距离等距曲面交线的相似性进行求交简化.提出了一种基于拓扑相似性的等距曲面求交优化算法.算法首先求取曲面的拓扑特征点,根据拓扑特征点分布图,确定交线环拓扑结构,在交线拓扑结构信息的指导下,确定初始点的搜索策略.采用提出的方法可以有效解决等距曲面的子环、奇点遗漏、分支跳跃、乱序跟踪和初始点求取问题,精确、鲁棒地计算出交线.     

基于Geodatabase模型的配电网拓扑算法

针对配电网管理平台的网络拓扑问题,提出一种基于Geodatabase模型的配电网拓扑分析算法.引入Geodatabase数据模型和网络拓扑模型,定义配电网数学模型,采用XML描述配电网设备,构建配电网拓扑模型,设计拓扑算法流程.应用于配电网拓扑关系生成和电源分析过程的算例表明,该算法具有结构简单、流程清晰等特点,能满足...     

Automatic extraction of free-form surface features (FFSFs)

This paper presents a new algorithm for extracting Free-Form Surface Features (FFSFs) from a surface model. The extraction algorithm is based on a modified taxonomy of FFSFs from that proposed in the literature. A new classification scheme has been proposed for FFSFs to enable their representation and extraction. The paper proposes a separating curve as a signature of FFSFs in a surface model. FFSFs are classified based on the characteristics of the separating curve (number and type) and the influence region (the region enclosed by the separating curve). A method to extract these entities is presented. The algorithm has been implemented and tested for various free-form surface features on different types of free-form surfaces (base surfaces) and is found to correctly identify and represent the features irrespective of the type of underlying surface. The representation and extraction algorithm are both based on topology and geometry. The algorithm is data-driven and does not use any pre-defined templates. The definition presented for a feature is unambiguous and application independent. The proposed classification of FFSFs can be used to develop an ontology to determine semantic equivalences for the feature to be exchanged, mapped and used across PLM applications.     

结合Delaunay 三角面分离法与搜索球策略的三维曲面重建算法

基于曲面重建在计算机图形学、三维GIS、逆向工程等领域有重要应用,结合区 域生长法与Delaunay 三角剖分的优势,提出了一种新的散乱点云曲面重建算法。首先根据曲面 中轴性质提出了分离角定义并推导了相关结论,利用局部Delaunay 三角形分离角性质抽取大量 位于模型表面三角形,从而构建种子三角网增加初始区域的生长面积其次运用自适应搜索球法 加快邻域三角形搜索并识别曲面边界。对比传统的基于Delaunay 法和传统区域生长法,该方法 只需要一次三角剖分,无需极点与法向量计算,重建速度快,具有Delaunay 三角网格的优良结 构特性,孔洞数量少,重建出的三维模型几何信息与拓扑关系准确。实验表明,结合Delaunay 三角剖分与区域生长法重构有向的流形三角网格模型,能够提高三维模型的重建效果与速度, 有效地自动识别曲面边界。     

Isogeometric topology optimization using trimmed spline surfaces

In the present work, a new spline based topology optimization using trimmed spline surfaces and the isogeometric analysis is proposed. In the proposed approach, the trimmed surface analysis which can treat topologically complex spline surfaces using trimming information provided by CAD systems is employed for structural response analysis and sensitivity calculation in the topology optimization. The outer and inner boundaries of design models are represented by a spline surface and trimming curves. Design variables used in this approach are the coordinates of control points of a spline surface and those of trimming curves. New sensitivity formulations for the control points in the trimmed surface analysis are proposed and their efficiency and accuracy are verified. The creation of new inner fronts during optimization is allowed for the topological flexibility. An inner front merging algorithm is also presented. The proposed spline based topology optimization is used to solve some benchmarking problems. Design space dependency which is one of serious shortcomings in conventional topology optimization approaches is naturally eliminated by the proposed spline based optimization. Design dependent load problems which are difficult to treat with conventional grid based topology optimization methods are easily dealt with by the proposed one. It is also shown that post-processing effort for converting to CAD model is eliminated by using the same spline information in numerical analysis and design optimization.     

Topology design of three-dimensional continuum structures using isosurfaces

Isolines Topology Design (ITD) is an iterative algorithm for the topological design of two-dimensional continuum structures using isolines. This paper presents an extension to this algorithm for topology design of three-dimensional continuum structures. The topology and the shape of the design depend on an iterative algorithm, which continually adds and removes material depending on the shape and distribution of the contour isosurfaces for the required structural behaviour. In this study the von Mises stress was investigated. Several examples are presented to show the effectiveness of the algorithm, which produces final designs with very detailed surfaces without the need for interpretation. The results demonstrate how the ITD algorithm can produce realistic designs by using the design criteria contour isosurface.     

由三视图重建包含圆环面的形体

机械零件中的管道和曲面过渡通常都由圆环面构成.分析了圆环面在三视图中的投影性质,将圆环面不同方向投影中的具有独特性的二次曲线特征定义为它的主特征和次特征,以工程图标注的语义信息为辅,提出基于曲面特征识别的圆环面重建算法.该算法首先在三视图中识别圆环面特征,然后由特征计算曲面参数,最后构造拓扑结构.用该算法对带有管道和曲面过渡的实例进行了验证.     

Recursively generated B-spline surfaces on arbitrary topological meshes

This paper describes a method for recursively generating surfaces that approximate points lying-on a mesh of arbitrary topology. The method is presented as a generalization of a recursive bicubic B-spline patch subdivision algorithm. For rectangular control-point meshes, the method generates a standard B-spline surface. For non-rectangular meshes, it generates surfaces that are shown to reduce to a standard B-spline surface except at a small number of points, called extraordinary points. Therefore, everywhere except at these points the surface is continuous in tangent and curvature. At the extraordinary points, the pictures of the surface indicate that the surface is at least continuous in tangent, but no proof of continuity is given. A similar algorithm for biquadratic B-splines is also presented.     

运动曲面求交优化算法

运动曲面求交通常采用曲面求交算法，通过反复迭代求取曲面交线，没有考虑运动曲面自身的特性进行求交简化．由于运动曲面不同运动瞬间的曲面交线之间存在必然联系，因此通过对曲面内在属性分析，提出了运用运动曲面不同运动瞬间曲面交线相似性进行运动曲面求交的优化算法．首先对两个运动曲面的基曲面进行预处理。获取表征曲面交线拓扑的特征点；根据特征点分布图确定不同运动瞬间曲面交线起始点搜索策略，采用跟踪法动态调整步长和跟踪方向求解整个交线环．采用文中方法可以有效地解决运动曲面的子环、奇点遗漏、分支跳跃、乱序跟踪和初始点求取问题，精确、鲁棒、快速地计算出交线．