Reconstruction of 3D interacting solids of revolution from 2D orthographic views

3D CAD is replacing 2D CAD to improve efficiency of product design and manufacturing. Therefore, converting legacy 2D drawings into 3D solid models is required. CSG based approaches reconstruct solid models from orthographic views more efficiently than traditional B-rep based approaches. A major limitation of CSG based approaches has been the limited domain of objects that can be handled. This paper aims at extending the capabilities of CSG based approaches by proposing a hint-based recognition of interacting solids of revolution. This approach can handle interacting solids of revolution as well as isolated solids of revolution.     

Handling sectional views in volume-based approach to automatically construct 3D solid from 2D views

This paper presents an algorithm for solid model reconstruction from 2D sectional views based on volume-ba`sed approach. None of the existing work in automatic reconstruction from 2D orthographic views have addressed sectional views in detail. It is believed that the volume-based approach is better suited to handle different types of sectional views. The volume-based approach constructs the 3D solid by a boolean combination of elementary solids. The elementary solids are formed by sweep operation on loops identified in the input views. The only adjustment to be made for the presence of sectional views is in the identification of loops that would form the elemental solids. In the algorithm, the conventions of engineering drawing for sectional views, are used to identify the loops correctly. The algorithm is simple and intuitive in nature. Results have been obtained for full sections, offset sections and half sections. Future work will address other types of sectional views such as removed and revolved sections and broken-out sections.     

Reconstruction of curved solids from engineering drawings

This paper presents a new approach for reconstructing solids with planar, quadric and toroidal surfaces from three-view engineering drawings. By applying geometric theory to 3-D reconstruction, our method is able to remove restrictions placed on the axes of curved surfaces by existing methods. The main feature of our algorithm is that it combines the geometric properties of conics with affine properties to recover a wider range of 3-D edges. First, the algorithm determines the type of each 3-D candidate conic edge based on its projections in three orthographic views, and then generates that candidate edge using the conjugate diameter method. This step produces a wire-frame model that contains all candidate vertices and candidate edges. Next, a maximum turning angle method is developed to find all the candidate faces in the wire-frame model. Finally, a general and efficient searching technique is proposed for finding valid solids from the candidate faces; the technique greatly reduces the searching space and the backtracking incidents. Several examples are given to demonstrate the efficiency and capability of the proposed algorithm.     

Solid reconstruction using recognition of quadric surfaces from orthographic views

The reconstruction of 3D objects from 2D orthographic views is crucial for maintaining and further developing existing product designs. A B-rep oriented method for reconstructing curved objects from three orthographic views is presented by employing a hybrid wire-frame in place of an intermediate wire-frame. The Link-Relation Graph (LRG) is introduced as a multi-graph representation of orthographic views, and quadric surface features (QSFs) are defined by special basic patterns of LRG as well as aggregation rules. By hint-based pattern matching in the LRGs of three orthographic views in an order of priority, the corresponding QSFs are recognized, and the geometry and topology of quadric surfaces are recovered simultaneously. This method can handle objects with interacting quadric surfaces and avoids the combinatorial search for tracing all the quadric surfaces in an intermediate wire-frame by the existing methods. Several examples are provided.     

基于独立环路组合的多面体视图三维重建

提出了一种基于平面独立环路组合的多面体视图三维重建完整算法，即先把三视图中的每个视图分解成一个个独立的不可再分的平面独立环路，然后从三面视图的三个环路组中逐个取出可能的环路组合按构造实心体几何方法（CSG）构成局部实心体模型，最后将局部实心体模型组合成整体实心体模型。已按上述算法编制出了能在Auto CAD图形系统中使用的实用软件。     

3D geometry reconstruction from orthographic views: A method based on 3D image processing and data fitting

Industrial esthetic designers typically produce hand-drawn sketches in the form of orthographic projections. A subsequent translation from 2D-drawings to 3D-models is usually necessary. This involves a considerably time consuming process, so that some automation is advisable.     

从二维视图到三维几何模型转换中视图的包围盒分离法

提出一种从二维视图到三维几何模型转换中视图的包围盒分离方法,通过考察图纸中图元的包围盒之间的相交情况进行视圈分离。与现有的视图分离方法相比,充分利用了转换中所需要的数据结构,与视图的边界曲线状况无关。利用基本视图之间的投影关系进行视图识别。给出一种面向二维视图到三维几何模型转换的数据结构和3个视图分离识别的例子。     

Constructing a wire-frame from views on arbitrary view planes for objects with conic sections inclined to all view planes

A new and efficient approach to construct a 3D wire-frame of an object from its orthographic projections is described. The input projections can be two or more and can include regular and complete auxiliary views. Each view may contain linear, circular and other conic sections. The output is a 3D wire-frame that is consistent with the input views.The approach can handle auxiliary views containing curved edges. This generality derives from a new technique to construct 3D vertices from the input 2D vertices (as opposed to matching coordinates that is prevalent in current art). 3D vertices are constructed by projecting the 2D vertices in a pair of views on the common line of the two views. The construction of 3D edges also does not require the addition of silhouette and tangential vertices and subsequently splitting edges in the views. The concepts of complete edges and n-tuples are introduced to obviate this need. Entities corresponding to the 3D edge in each view are first identified and the 3D edges are then constructed from the information available with the matching 2D edges. This allows the algorithm to handle conic sections that are not parallel to any of the viewing directions. The localization of effort in constructing 3D edges is the source of efficiency of the construction algorithm as it does not process all potential 3D edges.Working of the algorithm on typical drawings is illustrated.     

基于AutoCAD2000平台的平面立体三维重建的算法与实现

介绍了在AutoCAD2000平台上用VisualLISP语言编程实现平面立体的三给重建的一些算法和技巧,通过对几个主要步骤的探讨,成功地编写了平面立体三维重建的实用化程序。     

基于形体逼近的三维重建算法

该文提出一种新的由三视图重建三维实体的算法,能扩展自顶向下的三维重建算法的形体覆盖域,并在Auto-CAD平台上验证了算法的有效性。算法的主要步骤是首先用平扫-旋转-求交的实体运算法则构造出与所求实体形状相近的实体———第1参照体,再模拟人脑的识图过程:把第1参照体的三视图与初始三视图对比,根据两者之间的差别构造出差异体,再从第1参照体中逐一减去差异体,得到第2参照体、第3参照体......最后得到所求的实体。     

从2D视图重建3D实体中的假元删除算法

从2D视图重建3D实体的过程中,2D视图中的虚线会在3D重建中引起假边和假面的生成.针对此,提出一些规则在重建早先的阶段识别并删除这些假元.对于一个完全可见面,一旦搜索到它的外环和内环的边界,那么在该面内投影为虚线的边均将被删除.     

A new method for identifying and validating features from 2D sectional views

Feature identification is one of the key steps for 3D solids reconstruction from 2D vector engineering drawings using the volume-based method. In this paper, we propose a novel method to identify and validate features from sectional views. First, features are classified as explicit features (EPFs) and implicit features (IPFs), which are then identified in an order of priority using heuristic hints. We show that the problem of constructing EPFs can be formulated as a 0-1 integer linear program (ILP), and the IPFs are generated based on the understanding of semantic information of omitted projections in sectional views. Then, the Loop-Relation Graph (LRG) is introduced as a multi-connected-subgraph representation for describing the relations between loops and features. According to the LRG, a reasoning technique based on confidence is implemented to interactively validate features. This method can recover features without complete projections, and the level of understanding sectional views is improved. Full sections, partial sections, offset sections as well as revolved sections can be handled by our method. Several examples are provided to demonstrate the practicability of our approach.     

三维实体重建时投影图数据的预处理

介绍三维实体重建过程中投影图数据的处理算法,绘制同一图层的图形时,视图分割算法添加平行于两坐标轴的辅助直线,移动辅助线使其将三视图分割开来;对基于同一坐标系的投影三视图数据,推出从设备坐标系到各视图坐标系的转换公式并为其设计了转换算法,该算法求出三视图坐标系共有的原点,再根据视图分割的结果将每一图形元素转换到新的坐标系统中;隐含点的求取算法先判断同一视图中图元间的位置关系,再求出它们之间的公共点,这些点将用于线框搜索过程中,以上算法处理的投影图点线数据分别存入点线链表中。     

二维视图到三维几何模型转换中的BOX显示法

提出一种从二维视图到三维几何模型转换中视图的BOX显示方法,该方法可以将分离识别后的视图自动按照视图投影的方向放置,即将单一的二维视图平面向多投影面转换,建立视图之间的投影对应关系,从而直观地表达实体的投影视图,帮助用户进行形体想象。给出了两个视图BOX显示的例子。     

Projective Reconstruction from Multiple Views with Minimization of 2D Reprojection Error

The problem of projective reconstruction by minimization of the 2D reprojection error in multiple images is considered. Although bundle adjustment techniques can be used to minimize the 2D reprojection error, these methods being based on nonlinear optimization algorithms require a good starting point. Quasi-linear algorithms with better global convergence properties can be used to generate an initial solution before submitting it to bundle adjustment for refinement. In this paper, we propose a factorization-based method to integrate the initial search as well as the bundle adjustment into a single algorithm consisting of a sequence of weighted least-squares problems, in which a control parameter is initially set to a relaxed state to allow the search of a good initial solution, and subsequently tightened up to force the final solution to approach a minimum point of the 2D reprojection error. The proposed algorithm is guaranteed to converge. Our method readily handles images with missing points.     

从二维投影视图构造三维实体算法的效率提高途径

从二维视图构造三维实体在计算机图形学中具有重要意义。该文在通常的自底向上法进行三维重建过程中,增加了一个新的判别过程,使整个算法的时间复杂度大为降低,提高了效率。     

二维概念格图形的三维重构研究

介绍了二维概念格图形向三维空间转化和延伸的必要性和现状。通过对传统概念格图形分层定位布局方法的研究与分析,提出并实现了一种新的以具有大量的平行四边形和有向线段为基本特征的概念格在三维空间的自动布局算法,描述了一种基于该算法的二维概念格图形的三维重构机制,有效地解决了节点横向过度扩张的问题并减少了线段交叉,较好地实现了复杂概念格图形的三维可视化,为知识发现和知识处理提供了良好的基础。     

Identification of sections from engineering drawings based on evidence theory

View identification is the basic process for solid reconstruction from engineering drawings. A new method is presented to label various views from a section-involved drawing and identify geometric planes through the object at which the sections are to be located. In the approach, a graph representation is developed for describing multiple relationships among various views in the 2D drawing space, and a reasoning technique based on evidence theory is implemented to validate view relations that are used to fold views and sections in the 3D object space. This is the first automated approach which can handle multiple sections in diverse arrangements, especially accommodating the aligned section for the first time. Experimental results are given to show that the proposed solution makes a breakthrough in the field and builds a promising basis for further expansibility, although it is not a complete one.     

工业CT断层序列图像三维重建的实现

文中对ICT序列断层图像进行三维结构的重建和显示。先对图像进行预处理，去掉空气环，然后再利用Matlab功能强大的函数用体绘制方法进行断层序列图像的三维重建，对某一工业CT机提供的实测数据进行了三维重建，实验结果比较理想。     

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.