点云表面曲线的手绘构造方法

为了勾勒点云的骨架或在点云上标记符号，提出一种基于手绘的点云表面曲线构造方法．首先将手绘的二维草图识别成二次曲线；然后将其均匀离散化并分别投影到点云表面；最后判断投影点是否接近于同一平面，如果是，则将二次曲线重新投影到该拟合平面；否则，将投影点连接成B样条曲线并对其平滑去噪．实验结果表明，利用该方法可以快速勾勒出点云轮廓，并在点云表面高效地绘制出二次曲线或者平滑的B样条曲线．     

基于单元划分的复杂岩层面三维建模方法研究

针对现有岩层面三维建模方法未系统考虑含断层、陷落柱等地质条件的复杂岩层面三维模型构建的问题,通过定义投影度和投影单元,给出了不同地质条件下岩层面水平投影单元特征,同时提出一种基于单元划分的复杂岩层面三维建模方法。先划分岩层面水平投影单元和空间插值单元,将水平投影单元边界、空间插值单元边界、岩层面控制点和控制线作为约束条件,对实投影单元进行约束Delaunay三角剖分;然后分别求解各个空间插值单元内三角网顶点对应的岩层面空间插值点,并应用计算机三维图形技术绘制岩层面三维图形。实例分析结果表明,通过划分水平投影单元和空间插值单元,可将复杂岩层面分解为多个一般岩层面,从而降低其三维建模难度;合理进行约束Delaunay三角剖分和空间插值,可有效构建复杂岩层面的三维模型。     

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。     

圆柱面上G1插值曲线

用向量吸收投影的方法解决了由圆柱面上给定的点及该点处切平面上的单位矢量,来构造圆柱面上的一条光滑插值曲线问题.首先,由圆柱面上给定的点及该点处切平面上的单位矢量构造一条插值给定点及给定单位向量的空间3次Bézier样条插值曲线,然后再将空间3次Bézier曲线吸收投影到圆柱面上,就得到所求的限制在圆柱面上满足插值条件G1连续的插值曲线.     

光滑曲面上的G1插值曲线

在计算机图形学和计算机辅助几何设计中,限制在光滑曲面上保持几何连续的曲线插值技术显现出越来越重要的作用.文中用直纹面投影的思想研究了这一问题,给出了一种在光滑曲面上保持G1连续的样条曲线插值技术.首先构造一条插值曲面上已知点列的空间3次Bézier样条曲线,然后通过一张直纹面将这条空间插值曲线投影到已知曲面上,即可得到限制在已知光滑曲面上的G1插值曲线.理论推导和实例显示表明,该技术具有推广应用的广阔前景.     

一种基于旋转体的摄像机定位方法

基于旋转体的摄像机定位是单目合作目标定位领域中的涉及较少并且较为困难的一个问题,传统的基于点基元、直线基元及曲线基元的定位方法在用于旋转体定位过程中都存在相应的问题.文中设计了一种由4个相切椭圆构成的几何模型,该模型环绕于圆柱体表面,利用二次曲线的投影仍然是二次曲线的特性和椭圆的相应性质能够得到唯一确定模型位置的3个坐标点,从而将旋转体定位问题转化为P3P问题.在对P3P的解模式区域进行分析后,推导了根据模型上可视曲线的弯曲情况来确定P3P问题解模式的判别方法,并给出证明过程.仿真实验表明了这种模型定位方法的有效性.最后利用这个模型引导机械手完成目标定位的实验.     

空间二次曲线射影重建计算方法研究

利用二次曲线上点和直线的对应以及利用二次曲线光流对二次曲线进行解释,需要寻求多元方程组的最优解,计算过程较为复杂。将空间二次曲线表示为一个空间二次曲面和一个平面的交线,提出了一对对应二次曲线存在两个独立的多项式条件;利用两个二次曲面的基曲线推导出二次曲线重建的两个对应条件,在此基础上,给出了空间二次曲线射影重建的计算方法和计算步骤。实验验证表明该算法实用和可靠。     

一种构造任意类三次三角曲线的方法

在自由曲线曲面造型中,一般多以多项式为基函数构造参数曲线曲面,而在三角函数空间中也能构造参数曲线曲面.给出了一种构造任意类三次三角参数曲线的方法,该法以三次多项式曲线的基本性质为基础,从而构造出的曲线与对应的三次多项式曲线具有几乎完全相似的性质,而且所构造的曲线能精确表示圆弧、椭圆弧、抛物线弧等二次曲线,为曲线曲面造型提供了一种新方法.     

正多边形剖分球面投影及其应用

提出了利用正多面体顶点分布来剖分球面，得到球面上物体的投影点，利用这些投影点得到物体的二维投影。这种二维投影的获取方式具有投影点分布均匀的特点，并且根据三维物体的特点对特定区域的投影点进行加密，以获取更多的二维投影信息。该方法已经应用到三维模型及三维动作的识别中，取得了良好的效果。     

主成分分析方法(PCA)在车辆牌照识别中的应用

将主成分分析方法（PCA）应用于车牌识别。首先根据采集到样本分类构造各类样本对应特征子空间，然后对待识别字符图片进行预处理，再分别向各类特征空间投影，根据重构误差判断类别识别字符。     

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.     

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.     

Two Accelerating Techniques for 3D Reconstruction

Automatic reconstruction of 3D objects from 2D orthographic views has been a major research issue in CAD/CAM.In this paper,two acceleratin techniques to improve the efficiency of reconstruction are presented.First,some peudo elements are removed by depth and topology information as soon as the wire-frame is constructed ,which reduces the searching space.Second.the proposed algorithm does not establish all possible surfaces in the process of generating 3D faces.The surfaces and edge loops are generated by using the relationship between the boundaries of 3D faces and their projections,This avoids the growth in combinational complexity of previous methods that have to check all possible pairs of 3D candidate edges.     

基于三视图的三维形体重建技术

基于工程图纸的三维形体的重建技术是根据形体的二维视图中的几何信息和拓扑信息,生成相应的三维形体,这是一个从爸维到高维的构造过程,文中提出了一个三维形体重建算法,该算法首先根据三视图生成形体的线框图,然后应用左邻边搜索策略求出线框图内的所有面及相应的极小环,最后利用Ｍｏｅｂｉｕｓ规则及工程图的性质,删除重建过程中生成的非法元素,该方法利用二几何基元和三维几何基元的几何性质及生成关系,减少了重建过程中     

Fitting conics to paracatadioptric projections of lines

The paracatadioptric camera is one of the most popular panoramic systems currently available in the market. It provides a wide field of view by combining a parabolic shaped mirror with a camera inducing an orthographic projection. Previous work proved that the paracatadioptric projection of a line is a conic curve, and that the sensor can be fully calibrated from the image of three or more lines. However, the estimation of the conic curves where the lines are projected is hard to accomplish because of the partial occlusion. In general only a small arc of the conic is visible in the image, and conventional conic fitting techniques are unable to accurately estimate the curve. The present work provides methods to overcome this problem. We show that in uncalibrated paracatadioptric views a set of conic curves is a set of line projections if and only if certain properties are verified. These properties are used to constrain the search space and correctly estimate the curves. The conic fitting is solved naturally by an eigensystem whenever the camera is skewless and the aspect ratio is known. For the general situation the line projections are estimated using non-linear optimization. The set of paracatadioptric lines is used in a geometric construction to determine the camera parameters and calibrate the system. We also propose an algorithm to estimate the conic locus corresponding to a line projection in a calibrated paracatadioptric image. It is proved that the set of all line projections is a hyperplane in the space of conic curves. Since the position of the hyperplane depends only on the sensor parameters, the accuracy of the estimation can be improved by constraining the search to conics lying in this subspace. We show that the fitting problem can be solved by an eigensystem, which leads to a robust and computationally efficient method for paracatadioptric line estimation.     

Geometric operations for visual reasoning of a solid from orthographic projections

The ability of an engineer to visualize and reason about geometric aspects of physical objects and processes is crucial to the success of engineering activities. The article describes the development of geometric operations for a visual reasoning instructional software system using so-called missing view problem. The missing view problem requires construction of a valid solid given two orthographic projections. Sweeping operations, which are the reverse procedure of orthographic projection, are used to solve missing view problems by forming the boundary faces of a solid from the loops of orthographic views. Specifically, this geometric operation which forms a primary user interface of the system is described in detail in the article.     

Reconstruction of intersecting curved solids from 2D orthographic views

This paper presents a new approach to reconstruct curved solids composed of elementary volumes intersecting with one another from three-view engineering drawings. Intersection curves arising from two intersecting curved surfaces are mostly higher order spatial curves, which cannot be described exactly by 2D orthographic projections and normally represented as smooth curves passing through several key points or even simplified as arcs or lines. Approximated sketches of higher order intersection curves in 2D views result in the invalidation of existing methods that need the exact projection information as input. Based on some heuristic hints, our method is able to recover the complete and correct half-profiles of the intersecting elementary volumes using the least traces left by them, which ensure the correctness of solution solids constructed finally. Several examples are provided to show the validation of the described method.     

Geometric assistance for visual reasoning and construction of solids with curved surfaces from 2D orthographic views

As the extensive use of solid models becomes widespread, it is important to have a mechanism by which existing engineering drawings can be converted into solid models. Therefore, a geometric assistance that can aid in visual reasoning and constructing of solid models is beneficial. In this paper, we present key operations for a system called the Assistant for Reasoning and Construction of Solids (ARCS), which provides this assistance given a set of two orthographic views. The geometric domain of ARCS encompasses curved solids with cylindrical and spherical surfaces, such as those found in typical mechanical parts. We have devised the Cylindrical and Spherical Warping operations to create cylindrical and spherical surfaces, which use interactive computer graphics that guide a human user to curved faces of a solid. These operations are then illustrated with examples using ARCS to create the solid models of typical mechanical parts from their orthographic projections.     

基于面域理解的多面体三维重建

已有的三维重建算法一般是从点线或体的角度来理解视图,实际上,视图中的环包含了 大量的形体面信息,可以直接从中间层次的面理解形体的投影。文中根据实体构成和平面投影的约束和规则重建显式表达的面,并进一步推导出隐式表达的面,从而得到完整的形体边界模型,本算法适用于平面多面体,通过面域作为中介,容易实现与模型引导方法的融合,从而拓展到二次曲面体的重建。