Three-Dimensional Orthogonal Graph Drawing with Optimal Volume

An orthogonal drawing of a graph is an embedding of the graph in the rectangular grid, with vertices represented by axis-aligned boxes, and edges represented by paths in the grid that only possibly intersect at common endpoints. In this paper we study three-dimensional orthogonal drawings and provide lower bounds for three scenarios: (1) drawings where the vertices have a bounded aspect ratio, (2) drawings where the surfaces of vertices are proportional to their degrees, and (3) drawings without any such restrictions. Then we show that these lower bounds are asymptotically optimal, by providing constructions that in all scenarios match the lower bounds within a constant factor.     

Constraints in Graph Drawing Algorithms

Graphs are widely used for information visualization purposes, since they provide a natural and intuitive representation of complex abstract structures. The automatic generation of drawings of graphs has applications a variety of fields such as software engineering, database systems, and graphical user interfaces. In this paper, we survey algorithmic techniques for graph drawing that support the expression and satisfaction of user-defined constraints.     

Graph Regularized Sparse Autoencoders with Nonnegativity Constraints

Unsupervised feature learning with deep networks has been widely studied in recent years. Among these networks, deep autoencoders have shown a decent performance in discovering hidden geometric structure of the original data. Both nonnegativity and graph constraints show the effectiveness in representing intrinsic structures in the high dimensional ambient space. This paper combines the nonnegativity and graph constraints to find the original geometrical information intrinsic to high dimensional data, keeping it in a dimensionality reduced space. In the experiments, we test the proposed networks on several standard image data sets. The results demonstrate that they outperform existing methods.     

Metrics for Graph Drawing Aesthetics

Graph layout algorithms typically conform to one or more aesthetic criteria (e.g. minimizing the number of bends, maximizing orthogonality). Determining the extent to which a graph drawing conforms to an aesthetic criterion tends to be done informally, and varies between different algorithms. This paper presents formal metrics for measuring the aesthetic presence in a graph drawing for seven common aesthetic criteria, applicable to any graph drawing of any size. The metrics are useful for determining the aesthetic quality of a given graph drawing, or for defining a cost function for genetic algorithms or simulated annealing programs. The metrics are continuous, so that aesthetic quality is not stated as a binary conformance decision (i.e. the drawing either conforms to the aesthetic or not), but can be stated as the extent of aesthetic conformance using a number between 0 and 1. The paper presents the seven metric formulae. The application of these metrics is demonstrated through the aesthetic analysis of example graph drawings produced by common layout algorithms.     

Non-negative Matrix Factorization with Pairwise Constraints and Graph Laplacian

Neural Processing Letters - Non-negative matrix factorization (NMF) is a very effective method for high dimensional data analysis, which has been widely used in information retrieval, computer...     

Semi-Supervised Classification of Graph Convolutional Networks with Laplacian Rank Constraints

Neural Processing Letters - Graph convolutional networks (GCNs), as an extension of classic convolutional neural networks (CNNs) in graph processing, have achieved good results in completing...     

一个无向平面图的画图算法

提出了一种基于D*M*P平面性判定算法的新的平面图画图算法,与其它的算法相比,算法具有方法简单易于实现的优点.     

在动态演示系统中的图可视化

以图这一典型的数据结构为例,讨论图的圆形布局方案、应用力导引算法的布局方案、应用二维弹性模型算法的布局方案等,讨论这三种布局在图的布局中的应用,对过实验分析它们的优缺点,并总结这三种布局方案在动态演示系统中的可行性.     

Special Feature: An Easy-to-Use Graph Drawing Package

With suitable software, some graphics applications can be brought within reach of general computer users who have specific graphical requirements. One such package is SIMPLEPLOT.     

On the Parameterized Complexity of Layered Graph Drawing

We consider graph drawings in which vertices are assigned to layers and edges are drawn as straight line-segments between vertices on adjacent layers. We prove that graphs admitting crossing-free h-layer drawings (for fixed h) have bounded pathwidth. We then use a path decomposition as the basis for a linear-time algorithm to decide if a graph has a crossing-free h-layer drawing (for fixed h). This algorithm is extended to solve related problems, including allowing at most k crossings, or removing at most r edges to leave a crossing-free drawing (for fixed k or r). If the number of crossings or deleted edges is a non-fixed parameter then these problems are NP-complete. For each setting, we can also permit downward drawings of directed graphs and drawings in which edges may span multiple layers, in which case either the total span or the maximum span of edges can be minimized. In contrast to the Sugiyama method for layered graph drawing, our algorithms do not assume a preassignment of the vertices to layers. Research initiated at the International Workshop on Fixed Parameter Tractability in Graph Drawing, Bellairs Research Institute of McGill University, Holetown, Barbados, Feb. 9–16, 2001, organized by S. Whitesides. Research of Canada-based authors is supported by NSERC; research of Quebec-based authors is also supported by a grant from FCAR. Research of D.R. Wood completed while visiting McGill University. Research of G. Liotta supported by CNR and MURST.     

基于遗传算法的平面图画图算法

提出了一种基于遗传算法的新的平面图画图算法,算法将平面图画图问题转化为约束优化问题,用遗传算法求解目标函数的最优解的近似值,从而得到平面图的平面直线画法．新算法的优点是：方法简单,易于实现,画出的图形美观．实验结果表明：算法画出的图形要比文献[8]中的算法画出的图形美观,而其收敛性则要高于标准遗传算法．     

无向图在计算机绘图中的应用

本文把笔式绘图仪绘图过程时间最少的调度问题转换为在加权无向图中求解最优H-回路,并且利用最小生成树、欧拉回路、非二部图赋权匹配的算法给出了一种近似调度算法,旨在减少绘图仪移动空走时间和换笔时间,从而提高绘图效率。本算法经RP-MF160等绘图仪应用,效率提高约15%。     

绘制任意图形的两自由度机器人软件系统

在两自由度机器人原有软件系统的基础上，开发出了独立的绘图面板的服务程序。利用标准化的Windows操作系统环境。以动态链接库的方式提供独立的、可方便扩展的人机交互界面以及便捷的操作功能，不仅使原来仅能作简单示教的功能扩展成可以绘制具有复杂数学关系式的二维图形，而且使操作者通过鼠标操作就可以便捷完成任意的手画图形曲线的绘制。所开发的软件操作系统具有良好的可扩展性和通用性，利用同样的思想，还可以进一步为控制系统添加网络和视觉功能。     

数据库管理系统中直方图的绘制和显示

本文介绍的是利用ＵＣＤＯＳ３．１的特殊显示功能在ＦＯＸＰＲＯ环境中实现直方图的绘制和显示，并通过程序实例为类似图形如饼图，曲线图等的一切提供了一种思路。     

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。     

SetCoLa: High‐Level Constraints for Graph Layout

Constraints enable flexible graph layout by combining the ease of automatic layout with customizations for a particular domain. However, constraint‐based layout often requires many individual constraints defined over specific nodes and node pairs. In addition to the effort of writing and maintaining a large number of similar constraints, such constraints are specific to the particular graph and thus cannot generalize to other graphs in the same domain. To facilitate the specification of customized and generalizable constraint layouts, we contribute SetCoLa: a domain‐specific language for specifying high‐level constraints relative to properties of the backing data. Users identify node sets based on data or graph properties and apply high‐level constraints within each set. Applying constraints to node sets rather than individual nodes reduces specification effort and facilitates reapplication of customized layouts across distinct graphs. We demonstrate the conciseness, generalizability, and expressiveness of SetCoLa on a series of real‐world examples from ecological networks, biological systems, and social networks.     

一种包括隐含图形信息提取的工程图识别算法

工程图识别应该模仿人阅读工程图,把隐含图形信息提取出来,文中提出一种由稀疏的行程段直接提取整条图线,包括隐含图形信息提取的工程图识别算法,该算法首先提取整条图线的信息,再确定图线交点,通过分析线素,间隔等的规律确定线型,最后,基于工程图知识对图线拓扑关系进行校正。     

工程制图多媒体教学软件中图形处理方法

介绍了在工程制图多媒体教学软件研制中,采用AutoCAD与3DSMAX、MSPaint相结合,进行图形处理的方法。     

基于Visual C++平台的电法勘探中蒙太奇图的绘制系统

针对现有功能单一的商用绘图软件的不足，采用Visual C 可视化编程语言，运用面向对象的程序设计方法，建立了一个具有交互式编辑功能的蒙太奇图图形系统。通过把数据绘制成蒙太奇图，直观、快速地反映了地层中水平与垂直方向的电性特征。     

计算机地图制图软件中图形控制措施的探讨

对于人脑无法处理的浩瀚如海的各种科学数据,计算机地图制图软件提供了一种直观、实时、可控制的有效处理手段。而制图软件中涉及的图形的无级缩放,图形的平移,图形被破坏后的快速恢复技术在很大程度上决定了该软件的效率与性能。基于此,该文逐一给出了实现这几项技术的比较有效的措施。