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。     

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。     

从单幅正轴测投影线图建立平面立体的模型

提出了一种从单幅二维正轴测投影线图建立平面立体线框模型的新方法。提出一种新的空间直线坐标表示法，根据正轴测投影线图中隐含的直线与平面之间的从属关系建立约束方程。考虑画出隐藏线的正轴测投影线图，根据线画图中隐含的约束条件，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。证明解释平面立体正轴测投影线图至少有4个自由度。     

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。     

The Interpretation of Line Drawings with Contrast Failure and Shadows

In line drawings derived from real images, lines may be missing due to contrast failure and objects with curved surfaces may cast shadows from multiple light sources.This paper shows that it is the presence of shadows, rather than contrast failure, that renders the line drawing labelling problem NP-complete. However, shadows are a valuable visual cue, since their presence is formally shown to reduce the average ambiguity of drawings. This is especially true when constraints concerning shadow formation are employed to differentiate shadow and non-shadow lines.The extended junction constraint, concerning straight lines colinear with junctions, compensates the loss of information caused by contrast failure. In fact, we observe the contrast failure paradox: a drawing is sometimes less ambiguous when lines are partly missing due to contrast failure.It is known that the coplanarity of sets of object vertices can be deduced from the presence of straight lines in the drawing. This paper shows that these coplanarity constraints are robust to the presence of contrast failure.     

Line drawing via saliency map and ETF

Line drawing is a means of superior visual communication which can effectively convey useful information to viewers. Artists usually draw what they see rather than what exists, which means the most attractive object is emphasized while the rest are inhibited. Moreover, artists draw the whole object with coherent lines instead of fractured lines, which also contribute to the outstanding visual effect. From these perspectives, generating line drawings with saliency and coherence remains a great challenge. Existing line drawing generation methods ignore these important properties and cannot generate coherent lines in some cases since they do not take into account how artists draw a picture. To this end, a novel saliency-aware line drawing method was proposed to better grasp the viewer’s attention on an image. First, a saliency enhanced line extraction method combining saliency map and edge tangent flow was proposed to ensure the saliency and coherence of lines, especially in salient but low contrast areas. Then, the salient information was highlighted while irrelevant details were eliminated by inhibiting lines in less salient areas to enhance the saliency of the line drawing. Finally, the transparency of lines was adjusted to further emphasize important information. Various results showed that our method can generate line drawings with better visual saliency and coherence than the state-of-the-art methods.     

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.     

3D Reconstruction from 2D Line Drawings only with Visible Vertices and Edges

The human vision system can reconstruct a 3D object easily from single 2D line drawings even if the hidden lines of the object are invisible. Now, there are many methods have emulated this ability, but when the hidden lines of the object are invisible, these methods cannot reconstruct a complete 3D object. Therefore, we put forward a new algorithm to settle this hard problem. Our approach consists of two steps： （1） infer the invisible vertices and edges to complete the line drawing, （2） propose a vertex-based optimization method to reconstruct a 3D object.     

含误差完整画隐线图的校正处理

经过删补处理的不完整画隐线图,往往具有边缘外部轮廓位置比较准确,内部轮廓位置误差相对较大的特点.针对这一特点,提出了一种基于线图内部元素之间约束关系来校正处理含误差完整画线图的方法.从隐含的平面立体信息之间的约束关系及平行、垂直等特殊关系,建立相应的约束方程,然后平面线图节点位置进行最优位置的迭代处理,直至满足设定的阈值.通过实验验证,证实此方法是有效的.     

手绘图风格的三维模型线条渲染

现有的三维模型线条渲染方法,由于模型是网格结构,渲染得到线条图由大量的小线段组成,导致图形中有许多明显的棱角和孤立线段.提出了一种新的手绘图风格的三维模型线条渲染方法,将观察到的三维模型转化成简洁、自然的线条图.算法首先采用Suggestive Contours方法得到模型的特征线段集,通过分析线段的空间信息,将小线段连接成若干长线条,并用三次B样条曲线插值这些线条,然后引入B样条小波对线条进行简化.实验结果表明,本文的方法可以很好地连接这些线段集,得到平滑、简洁的手绘风格模型线条图.     

基于形状演化的线条画风格转换与变形

根据线条画和线条画中笔画的形状特征，运用平面形状演化理论对线条画和笔画的形状进行平滑或增强，并对宽度进行相应的调整，最后得到不同风格的线条画．该风格转换水需要任何样本，而且能够控制转换的程度，提高了线条画风格转换的自由度．     

基于MAR 的工程制图助学系统研究

在工程制图课程中根据二维图纸来构思三维形状,对于初学者来说有相当大的难 度。针对传统基于PC 端工程制图的多媒体辅助教学方式在交互性和易用性上的不足,研究基 于移动增强现实的工程制图助学系统。采用无标记识别技术实现工程图样与三维数字化模型的 自然交互,并在此基础上开发了一个功能齐全的助学APP,使用者可以通过手机摄像头扫描识 别二维工程图,在屏幕上叠加显示三维模型以及其他相关教学资源,用户可实时完成模型缩放、 旋转等操作,并且可对复杂的工程装配体模型进行拆卸和组装。实验结果表明,该系统不仅便 于学生自主学习,而且在一定程度上改善了工程制图课程的教学环境。     

Frontal geometry from sketches of engineering objects: is line labelling necessary?

A tool which can quickly interpret line drawings (with hidden lines removed) of engineering objects as boundary representation CAD models would be of significant benefit in the process of engineering design. Inflation of the drawing to produce a frontal geometry, a geometric realisation of that part of the object visible in the drawing, is an important stage of this process.Previous methods of producing frontal geometries have relied on the technique of line labelling (labelling edges as convex, concave or occluding). Although restricted subsets of the line-labelling problem have known solutions, reliable methods have not been found for the general line-labelling problem, and traditional methods, when adapted to drawings with non-trihedral junctions, are unacceptably slow.Many other papers assume that line labelling is an essential step. Here, we show this is not necessarily true, and that comparable results can be obtained by a novel alternative approach. Firstly, we consider what outputs from line labelling are essential to the production of frontal geometry. Secondly, we investigate by what other means these outputs can be produced.Our work indicates that the only essential output from line labelling for frontal geometry is the determination of which T-junctions in a drawing are occluding and which are non-occluding. This information is required for inflation, and also for detection of symmetry and for constructing hidden topology.Thus, we propose and analyse a new method which, in the absence of line labels, simultaneously inflates a drawing to produce the frontal geometry and attempts to determine whether each T-junction is occluding or not. For drawings of objects with holes or pockets, and for cases where line labelling is particularly unreliable, our new method can provide a better alternative.     

Interpretation of an axonometric projection of a polyhedron

This paper addresses some problems in interpretation of axonometric line drawings of polyhedrons, especially the problems of how much and what kind of further information is necessary to reconstruct uniquely the shape of objects from their axonometric line drawings. For line drawings which are precise, in the sense that vertices are drawn in correct position, the problems can be treated in terms of linear algebra, and a method for solving them is established. When line drawings are roughly drawn, on the other hand, the problems are much more difficult; a solution based on some combinatorial technique is given to a restricted object world in which each vertex lies on exactly three faces.     

Animated 3D Line Drawings with Temporal Coherence

Producing traditional animation is a laborious task where the key drawings are first drawn by artists and thereafter inbetween drawings are created, whether it is by hand or computer‐assisted. Auto‐inbetweening of these 2D key drawings by computer is a non‐trivial task as 3D depths are missing. An alternate approach is to generate all the drawings by extracting lines directly from animated 3D models frame by frame, concatenating and rendering them together into an animation. However, animation quality generated using this straightforward method bears two problems. Firstly, the animation contains unsatisfactory visual artifacts such as line flickering and popping. This is especially pronounced when the lines are extracted using high‐order derivatives, such as ridges and valleys, from 3D models represented in triangle meshes. Secondly, there is a lack of temporal continuity as each drawing is generated without taking its neighboring drawings into consideration. In this paper, we propose an improved approach over the straightforward method by transferring extracted 3D line drawings of each frame into individual 3D lines and processing them along the time domain. Our objective is to minimize the visual artifacts and incorporate temporal relationship of individual lines throughout the entire animation sequence. This is achieved by creating correspondent trajectory of each line from each frame and applying global optimization on each trajectory. To realize this target, we present a fully automatic novel approach, which consists of (1) a line matching algorithm, (2) an optimizing algorithm, taking into account both the variations of numbers and lengths of 3D lines in each frame, and (3) a robust tracing method for transferring collections of line segments extracted from the 3D models into individual lines. We evaluate our approach on several animated model sequences to demonstrate its effectiveness in producing line drawing animations with temporal coherence.     

Decomposition of complex line drawings with hidden lines for 3D planar-faced manifold object reconstruction

Three-dimensional object reconstruction from a single 2D line drawing is an important problem in computer vision. Many methods have been presented to solve this problem, but they usually fail when the geometric structure of a 3D object becomes complex. In this paper, a novel approach based on a divide-and-conquer strategy is proposed to handle the 3D reconstruction of a planar-faced complex manifold object from its 2D line drawing with hidden lines visible. The approach consists of four steps: 1) identifying the internal faces of the line drawing, 2) decomposing the line drawing into multiple simpler ones based on the internal faces, 3) reconstructing the 3D shapes from these simpler line drawings, and 4) merging the 3D shapes into one complete object represented by the original line drawing. A number of examples are provided to show that our approach can handle 3D reconstruction of more complex objects than previous methods.     

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     

A rich discrete labeling scheme for line drawings of curved objects

We present a discrete labeling scheme for line drawings of curved objects which can be seen as an information-rich extension of the classic line-labeling scheme in which lines are classified as convex, concave, occluding or extremal. New labels are introduced to distinguish between curved and planar surface-patches, to identify orthogonal edges and to indicate gradient directions of planar surface-patches.