基于点线关系从透视画隐线图重构三维平面立体

提出了一种基于点与直线关系从透视投影画隐线图建立平面立体线框模型的新方法。给出了基于点线关系的基本约束,根据透视投影画隐线图中隐含的点与直线位置关系建立约束方程,建立一个线性系统,通过求解该线性系统得到平面立体的三维信息。用算例进行验证,得到了平面立体的三维信息。     

基于约束关系的平面立体三维重建

提出一种基于约束的平面立体三维重建算法。该算法采用参数化方式来表示空间直线及其投影,这种参数化方式能满足数字图像中直线提取所需的唯一性、有界性及均匀性条件。依据平面立体投影线图的拓扑结构隐含的三维信息,建立平面立体上棱线、表面空间位置参数之间的约束方程,联立约束方程组求其最小二乘解,恢复出平面立体的三维结构。研究成果可用于计算机视觉和智能CAD系统。     

基于迭代技术的有误差单幅线图的计算机解释

提出一种利用迭代技术从单幅有误差线图恢复平面立体定量结构的新算法.根据线图中隐含的平面立体上棱线和平面之间的从属关系,建立平面立体参数满足的一些基本约束和迭代中止的目标函数,联立基本约束得到一个线性方程组.最小二乘解作为迭代初始值,将棱线再投影到投影平面上,与原线图对应线段加权平均并求最优解,重复执行,直到目标函数小于设定阈值.算法可以从准确线图和有误差线图正确恢复平面立体三维结构,对有误差线段和节点进行校正.实验验证了算法的有效性.     

三维直线的表示及其约束

三维直线的表示是计算机图形学和计算机视觉中最基本的问题之一。在介绍了直线的表示原则以及分析了二维和三维直线的各种表示方法的基础上,选择并提出了适合三维重建的二维和三维直线表示方法:用法线式表示法表示二维直线;基于法线式表示法用垂直相交两平面表示法表示三维直线。提出了二维和三维直线的坐标概念,给出了正轴测投影和透视投影下三维直线之间的一些基本约束关系及其证明。     

曲面立体线图的补线技术研究

文中根据已有的曲面立体自然线图的标记原理，得到了曲面立体画隐线图的标记原理和方法。曲面立体的不完整线图中的L型节点是曲面立体完整线图中W型节点的退化。基于曲面立体画出隐藏线的完整线图标记原理和方法，详细分析并建立了曲面立体不完整线图中L型节点与曲面立体完整线图中W型节点的对应关系。提出了曲面立体不完整线图的标记和补线方法，结合算例详细论述了曲面立体不完整线图的标记和补线过程，从曲面立体不完整线图获得了合理的曲面立体完整线图。     

正轴测投影反求建模研究

论文应用投影变换方法建立正轴测投影数学求解模型,提出一般伸缩系 数方法,实现了反求正轴测投影图的真实尺寸,再进行三维实体建模,达到原始设计不受 计算机约束,充分发挥人脑的想象力之目的。根据有立体感的正轴测投影图反求真实尺寸 后进行实体建模,生成二维加工图,这些过程由计算机完成,使之更符合设计从三维开始 的本质。     

基于几何约束识别简单平面立体

已有的识别方法对于简单平面立体的识别均不能凑效。依据投影几何中的距离约束和角度约束,给出了三边形和平行四边形的识别方法;提出用属性关系图（ARG）表示平面立体和线图,该描述方法是一种结合表面特征和几何特征的方法。提出一种从单幅线图识别简单平面立体的新方法,该方法在匹配待识别线图与模型结点之前,先用拓扑信息进行候选模型的筛选,大大提高了识别的效率。结合几何特征和拓扑特征表示ARG中的每个结点,不仅能识别不同形状的目标,而且能把拓扑结构相同,但各部分大小、比例不相同的目标区分开。实验结果表明该识别方法是有效的,能够用于识别形状为简单平面立体的工业部件等。     

光栅投影式3维照相系统中光栅投影仪的标定

提出了一种光栅投影式立体照相系统中光栅投影平面的标定方法。将光栅投影到已知目标平面,通过数字摄影得到光栅平面与目标平面相交的光栅图像。根据光栅图像记录的信息,在每条交线上提取两点,作为对应光栅平面拟合用的两点。按一定规律移动目标平面,即可得到每个光栅平面上若干对点。利用最小二乘法分别拟合出每个光栅平面的空间平面方程。     

基于类似形原理从单幅透视图识别平面立体

根据透视不变性提出了5个描述多边形形状的拓扑特征和几何特征,以这些特征作为约束条件给出透视投影下类似形的定义。根据类似形的定义提出了识别多边形是类似形的新方法。据此提出了基于类似形原理从单幅透视投影线图识别平面立体的新方法。新定义的类似形能将平面立体中的表面分类。匹配过程限制在类似形内进行,大大减少了搜索范围。用拓扑结构对类似形进行定性分析,对噪音不敏感,用几何特征进行定量分析,则能反应平面立体形状的细微差别。该识别方法不仅能识别不同形状的平面立体目标,而且还可以区分形状相同但大小、比例不同的平面立体目标。实验结果表明该方法是有效的。     

关于赤平投影计算机求解法的研究

赤平极射投影可表示空间上的点、直线、平面等几何要素,根据它们的空间方向和产状可以作出赤平极射投影图,同时,可以根据赤平极射投影图,测读它们的空间方向和产状,因此在岩体工程地质学中得到广泛应用。本文利用苏联学者吴尔福1902年发表的一个赤平极射投影网,称为吴氏投影网,根据吴氏网的作图原理,推导出求两结构面交线倾伏角和倾伏向及位于同一平面两条相交直线的夹角的数学公式,可以方便的使用计算机绘制投影图,使用计算器,甚至可用智能手机求直线、平面空间的方向和产状。     

Labeling Line Drawings with Hidden-Part-Drawn of Planar Object with Trihedral Vertices

Although line drawings consist of only line segments on a plane, they convey much information about the three-dimensional object structures. For a computer interpreting line drawings, some intelligent mechanism is required to extract three-dimensional information from the two-dimensional line drawings. In this paper, a new labeling theory and method are proposed for the two-dimensional line drawing with hidden-part-draw of a three-dimensional planar object with trihedral vertices. Some rules for labeling line drawing are established. There are 24 kinds of possible junctions for line drawing with hidden-part-draw, in which there are 8 possible Y and 16 W junctions. The three problems are solved that Sugihara's line drawing labeling technique exists. By analyzing the projections of the holes in manifold planar object, we have put forward a labeling method for the line drawing. Our labeling theory and method can discriminate between correct and incorrect hidden-part-draw natural line drawings. The hidden-part-draw natural line drawings can be labeled correctly by our labeling theory and method, whereas the labeling theory of Sugihara can only label the hidden-part-draw unnatural line drawings in which some visible lines must be drawn as hidden lines, and some invisible lines must be drawn as continuous lines.     

具有相切面的曲面立体线画图标记研究

为了更好地理解三维景物，介绍了前人对线画图标记的研究成果，同时建立了一种标记具有相切面的曲面立体线画图的方法，并给出了具有相切面的曲面立体线画图的标记规则。由于线画图中的节点是由三面角构成的顶点的投影，因此对于画出隐藏线的具有相切面的曲面立体线画图，其合法的节点标记形式有38种，其中Y型节点有6种，W型节点有18种，V型节点有14种。新的标记方法适用于由平面立体和曲面立体组合而成的复杂立体线画图。     

轴测投影的若干问题

重新审视了轴测投影定义的表述。轴测投影法是用平行投影的方法,沿投射方向 将空间坐标系投射到投影面上得到轴测坐标系并进而在这个坐标系下表述空间形体,用这种方 法得到的图纸叫轴测图。三视图用3 个视图分别表示形体的3 个方向(面),轴测图用一个视图 同时表示三直三面角,其本质都是要表达出形体的3 个方向(面),在平面上表述空间形体。讨 论了轴测投影中的一些根本问题,包括平行投影体系、轴测三角形、轴测投影体系、轴测投影 的基本要素和基本公式,剖析了正轴测投影和斜轴测投影之共性和不同,给出了其原理图。     

Plane-based optimization for 3D object reconstruction from single line drawings

In previous optimization-based methods of 3D planar-faced object reconstruction from single 2D line drawings, the missing depths of the vertices of a line drawing (and other parameters in some methods) are used as the variables of the objective functions. A 3D object with planar faces is derived by finding values for these variables that minimize the objective functions. These methods work well for simple objects with a small number N of variables. As N grows, however, it is very difficult for them to find expected objects. This is because with the nonlinear objective functions in a space of large dimension N, the search for optimal solutions can easily get trapped into local minima. In this paper, we use the parameters of the planes that pass through the planar faces of an object as the variables of the objective function. This leads to a set of linear constraints on the planes of the object, resulting in a much lower dimensional nullspace where optimization is easier to achieve. We prove that the dimension of this nullspace is exactly equal to the minimum number of vertex depths which define the 3D object. Since a practical line drawing is usually not an exact projection of a 3D object, we expand the nullspace to a larger space based on the singular value decomposition of the projection matrix of the line drawing. In this space, robust 3D reconstruction can be achieved. Compared with two most related methods, our method not only can reconstruct more complex 3D objects from 2D line drawings, but also is computationally more efficient.     

Identification of faces in a 2D line drawing projection of awireframe object

An important key to reconstructing a three-dimensional object depicted by a two-dimensional line drawing projection is face identification. Identification of edge circuits in a 2D projection corresponding to actual faces of a 3D object becomes complex when the projected object is in wireframe representation. This representation is commonly encountered in drawings made during the conceptual design stage of mechanical parts. When nonmanifold objects are considered, the situation becomes even more complex. This paper discusses the principles underlying face identification and presents an algorithm capable of performing this identification. Face-edge-vertex relationships applicable to nonmanifold objects are also proposed. Examples from a working implementation are given     

正轴测投影图直观效果优化条件的研究

正轴测投影图具有直观性好、形象逼真等优点,其立体感效果与物体相对 于投影面的位置有关系,选择合适的视角可以增强图形的立体感、提高图形的可读性。通过 对正轴测投影图中显示物体的可见面数、面积大小和面积变化率等参数的定量研究和数据分 析,获得影响物体立体感效果的变化规律,使用CAD 内嵌的VisualLISP 语言和VB 软件编 辑人机交互系统,为用正轴测投影图更有效地表达物体提供了依据。     

Wireframe Projections: Physical Realisability of Curved Objects and Unambiguous Reconstruction of Simple Polyhedra

The reconstruction of an object from a single 2D projection of a 3D wireframe model is a vision problem with applications in CAD/CAM and computer graphics.We propose an algorithm for the interpretation of wireframe projections based on assigning semantic and numerical depth labels to lines. This method allows us to state necessary and sufficient conditions for the physical realisability of a wireframe projection of a curved object. The presence of linear features provides further constraints on the positions of object vertices. For example, each straight line gives rise to a coplanarity constraint between a set of object vertices.We show that extra information, such as vanishing points, parallel lines or user-entered depth-parity information, is sufficient to uniquely determine the face-circuits in wireframe projections of polyhedra with simple trihedral vertices. In fact, a polyhedron with simple trihedral vertices can be unambiguously reconstructed from its 3D wireframe model.