Drawing Algorithms Research Articles

Research on the Die Steel Cutting Simulation System Based on Intelligent Layout Algorithm

This paper chooses equal-rectangles dynamic-layout algorithm as die-steel intelligent-layout algorithm, combines with drawing algorithm and .NET visual component to convert three-dimensional entity into two-dimensional model by coordinate rotational projection. We realized intelligent-layout and simulated the process of die-steel cutting in three-dimensional perspective effect. This system offered autonomous-layout mode and intelligent-layout mode. The former simulated the cutting according to producer’s experience. The latter simulated the cutting on the basis of producer’s requirement by intelligent layout algorithm. The application of this system enhances the market competitiveness by increasing the die steel utilization rate and decreasing the enterprise production cost.

EVERY OUTER-1-PLANE GRAPH HAS A RIGHT ANGLE CROSSING DRAWING

There is strong empirical evidence that human perception of a graph drawing is negatively correlated with the number of edge crossings. However, recent experiments show that one can reduce the negative effect by ensuring that the edges that cross do so at large angles. These experiments have motivated a number of mathematical and algorithmic studies of “right angle crossing (RAC)” drawings of graphs, where the edges cross each other perpendicularly. In this paper we give an algorithm for constructing RAC drawings of “outer-1-plane” graphs, that is, topological graphs in which each vertex appears on the outer face, and each edge crosses at most one other edge. The drawing algorithm preserves the embedding of the input graph. This is one of the few algorithms available to construct RAC drawings.

Key Technologies Research on Color Contour Map of 3D Injection Molding Simulation Results

According to the color contour map of the 3D injection molding simulation results, the commonly used color contour map drawing algorithm was researched, and a three-dimensional color image rendering algorithm which based on the "physical field values and color range mapping" was given too. And the key technologies of the algorithm which was used to draw 3D color contour map were introduced in detail. In the end, an example was given.

A survey of two-dimensional graph layout techniques for information visualisation

Many algorithms for graph layout have been devised over the last 30 years spanning both the graph drawing and information visualisation communities. This article first reviews the advances made in the field of graph drawing that have then often been applied by the information visualisation community. There then follows a discussion of a range of techniques developed specifically for graph visualisations. Graph drawing algorithms are categorised into the following approaches: force-directed layouts, the use of dimension reduction in graph layout and computational improvements including multi-level techniques. Methods developed specifically for graph visualisation often make use of node-attributes and are categorised based on whether the attributes are used to introduce constraints to the layout, provide a clustered view or define an explicit representation in two-dimensional space. The similarities and distinctions between these techniques are examined and the aim is to provide a detailed assessment of currently available graph layout techniques, specifically how they can be used by visualisation practitioners, and to motivate further research in the area.

Multidimensional Projections for Visual Analysis of Social Networks

Visual analysis of social networks is usually based on graph drawing algorithms and tools. However, social networks are a special kind of graph in the sense that interpretation of displayed relationships is heavily dependent on context. Context, in its turn, is given by attributes associated with graph elements, such as individual nodes, edges, and groups of edges, as well as by the nature of the connections between individuals. In most systems, attributes of individuals and communities are not taken into consideration during graph layout, except to derive weights for force-based placement strategies. This paper proposes a set of novel tools for displaying and exploring social networks based on attribute and connectivity mappings. These properties are employed to layout nodes on the plane via multidimensional projection techniques. For the attribute mapping, we show that node proximity in the layout corresponds to similarity in attribute, leading to easiness in locating similar groups of nodes. The projection based on connectivity yields an initial placement that forgoes force-based or graph analysis algorithm, reaching a meaningful layout in one pass. When a force algorithm is then applied to this initial mapping, the final layout presents better properties than conventional force-based approaches. Numerical evaluations show a number of advantages of pre-mapping points via projections. User evaluation demonstrates that these tools promote ease of manipulation as well as fast identification of concepts and associations which cannot be easily expressed by conventional graph visualization alone. In order to allow better space usage for complex networks, a graph mapping on the surface of a sphere is also implemented.

A multilevel layout algorithm for visualizing physical and genetic interaction networks, with emphasis on their modular organization

BackgroundGraph drawing is an integral part of many systems biology studies, enabling visual exploration and mining of large-scale biological networks. While a number of layout algorithms are available in popular network analysis platforms, such as Cytoscape, it remains poorly understood how well their solutions reflect the underlying biological processes that give rise to the network connectivity structure. Moreover, visualizations obtained using conventional layout algorithms, such as those based on the force-directed drawing approach, may become uninformative when applied to larger networks with dense or clustered connectivity structure.MethodsWe implemented a modified layout plug-in, named Multilevel Layout, which applies the conventional layout algorithms within a multilevel optimization framework to better capture the hierarchical modularity of many biological networks. Using a wide variety of real life biological networks, we carried out a systematic evaluation of the method in comparison with other layout algorithms in Cytoscape.ResultsThe multilevel approach provided both biologically relevant and visually pleasant layout solutions in most network types, hence complementing the layout options available in Cytoscape. In particular, it could improve drawing of large-scale networks of yeast genetic interactions and human physical interactions. In more general terms, the biological evaluation framework developed here enables one to assess the layout solutions from any existing or future graph drawing algorithm as well as to optimize their performance for a given network type or structure.ConclusionsBy making use of the multilevel modular organization when visualizing biological networks, together with the biological evaluation of the layout solutions, one can generate convenient visualizations for many network biology applications.

Integral Algorithm for Generating Anti-Aliasing Circle Based on Bresenham Algorithm

For generating anti-aliasing circle with a high speed and a simple manner, an algorithm which uses only integral operation to convert gray levels of pixels based on modified Bresenham Algorithm is presented. According to the decision parameter established in Bresenham algorithm, the algorithm generated the accurate distances between candidate points and true curve, abandoned the higher-order epsilon with litter effect, and used look-up table or range binary search to calculate the gray levels of the nearest pixels. The new algorithm only modified the local structure of the original algorithm and can generate smooth circle rapidly because of simple structure and only integer operation employed in it. Besides, the new algorithm makes the basic generating algorithm and anti-aliased drawing algorithm can be easily generated under the same framework.

Drawing trees in a streaming model

We pose a new visualization challenge, asking Graph Drawing algorithms to cope with the requirements of Streaming applications. In this model a source produces a graph one edge at a time. When an edge is produced, it is immediately drawn and its placement cannot be altered. The drawing has an image persistence, that controls the lifetime of edges. If the persistence is k, an edge remains in the drawing for the time spent by the source to generate k edges, and then it fades away. In this model we study the area requirement of planar straight-line grid drawings of trees and we assess the output quality of the presented algorithms by computing the competitive ratio with respect to the best known offline algorithms.

EDPF: A REAL-TIME PARAMETER-FREE EDGE SEGMENT DETECTOR WITH A FALSE DETECTION CONTROL

We propose a real-time, parameter-free edge/edge segment detection algorithm based on our novel edge/edge segment detector, the edge drawing (ED) algorithm; hence the name edge drawing parameter free (EDPF). EDPF works by running ED with ED's parameters set at their extremes. This produces all edge segments in a given image with numerous false detections. The detected edge segments are then validated by an "a contrario" validation step due to the Helmholtz principle, which eliminates invalid detections leaving only "meaningful" edge segments.

Improving multiple aesthetics produces better graph drawings

Many automatic graph drawing algorithms implement only one or two aesthetic criteria since most aesthetics conflict with each other. Empirical research has shown that although those algorithms are based on different aesthetics, drawings produced by them have comparable effectiveness.The comparable effectiveness raises a question about the necessity of choosing one algorithm against another for drawing graphs when human performance is a main concern. In this paper, we argue that effectiveness can be improved when algorithms are designed by making compromises between aesthetics, rather than trying to satisfy one or two of them to the fullest. We therefore introduce a new algorithm: BIGANGLE. This algorithm produces drawings with multiple aesthetics being improved at the same time, compared to a classical spring algorithm. A user study comparing these two algorithms indicates that BIGANGLE induces a significantly better task performance and a lower cognitive load, therefore resulting in better graph drawings in terms of human cognitive efficiency.Our study indicates that aesthetics should not be considered separately. Improving multiple aesthetics at the same time, even to small extents, will have a better chance to make resultant drawings more effective. Although this finding is based on a study of algorithms, it also applies in general graph visualization and evaluation.

Pinning balloons with perfect angles and optimal area

We study the problem of arranging a set of n disks with prescribed radii on n rays emanating from the origin such that two neighboring rays are separated by an angle of 2π/n. The center of the disks have to lie on the rays, and no two disk centers are allowed to lie on the same ray. We require that the disks have disjoint interiors, and that for every ray the segment between the origin and the boundary of its associated disk avoids the interior of the disks. Let $\widetilde r$ be the sum of the disk radii. We introduce a greedy strategy that constructs such a disk arrangement that can be covered with a disk centered at the origin whose radius is at most $2\widetilde r$ , which is best possible. The greedy strategy needs O(n) arithmetic operations. As an application of our result we present an algorithm for embedding unordered trees with straight lines and perfect angular resolution such that it can be covered with a disk of radius n3.0367, while having no edge of length smaller than 1. The tree drawing algorithm is an enhancement of a recent result by Duncan et al. [Symp. of Graph Drawing, 2010] that exploits the heavy-edge tree decomposition technique to construct a drawing of the tree that can be covered with a disk of radius 2 n4.

A fuzzy genetic algorithm for automatic orthogonal graph drawing

This paper reflects results of research related to developing a new methodology for automatic graph drawing based on applying genetic algorithms. The methodology has permitted the elaboration of a hybrid technique that combines the most popular, classical, topology-shape-metric approach to orthogonal drawings on the grid and a genetic algorithm that is directed, in its evolutionary process, at multicriteria decision making in a fuzzy environment. In the traditional use of the topology-shape-metric approach, a single fixed planar embedding is obtained in the planarization step. Thereafter this embedding is subjected to the orthogonalization and compaction steps. However, this sequence does not guarantee that the fixed planar embedding will generate a final drawing of a good quality. Moreover, every topology-shape-metric step is classified as a NP-hard problem, and choices as well as heuristics used in previous stages have a direct impact on subsequent ones. Taking this into account, the developed hybrid technique generates a greater number of planar embeddings by varying the order of edges’ insertion when forming the planar embeddings in planarization step. Thus, the problem is formulated as a permutation-based combinatorial optimization problem. The genetic algorithm is applied at the planarization step of the topology-shape-metric. This allows one to generate the population with the corresponding number of planar embeddings. Each planar embedding obtained in the planarization step is submitted to the orthogonalization and compaction. Their results serve for applying the procedures of multicriteria decision making in a fuzzy environment. Thus, in the evolutionary process, the genetic algorithm is able to select individuals, which provide more harmonious solutions (relatively of the solutions obtained with traditional applying the topology-shape-metric approach) from the point of view of the aesthetic criteria that are usually utilized at the three steps of automatic graph drawing. This is convincingly demonstrated by experimental results given in the paper.

The Shape of Orthogonal Cycles in Three Dimensions

Let σ be a directed cycle whose edges have each been assigned a desired direction in 3D (East, West, North, South, Up, or Down) but no length. We say that σ is a shape cycle. We consider the following problem. Does there exist an orthogonal representation Γ of σ in 3D space such that no two edges of Γ intersect except at common endpoints and such that each edge of Γ has the direction specified in σ? If the answer is positive, we say that σ is simple. This problem arises in the context of extending orthogonal graph drawing techniques from 2D to 3D. We give a combinatorial characterization of simple shape cycles that yields linear time recognition and drawing algorithms.

Semi-automatic drawing of metabolic networks

In the living cell, biochemical reactions catalyzed by enzymes are the drivers for metabolic processes like growth, energy production, and replication. Metabolic networks are the representation of these processes describing the complex interactions of biochemical compounds. The large amount of manifold data concerning metabolic networks continually arising from current research activities in biotechnology leads to the great challenge of information visualization. Visualizing information in networks first of all requires appropriate network diagrams. In the context of metabolic networks, historical conventions regarding the network layout have been established. These layouts are not realizable by prevailing algorithms for automatic graph drawing. Hence, manual graph drawing is the predominating way to set up metabolic network diagrams. This is very time-consuming without software support, especially considering large networks with more than 500 nodes. We present a semi-automatic approach to drawing networks which relies on manual editing supported by two concepts of the interactive and automatic arrangement of nodes and edges. The first concept, called the layout pattern, uses an arbitrarily shaped skeleton as a backbone for the arrangement of nodes and edges. The second concept allows us to wrap a set of repeating drawing steps onto a so-called motif stamp, which can be appended to other parts of a diagram during the drawing process. Finally, a case study demonstrates that both semi-automatic drawing techniques diminish the time to be devoted for the manual network drawing process.

Visualization of quasi-median networks

An algorithm for automatic drawing of quasi-median networks is proposed that uses Eulerian cycles in the non-strong-compatibility graph to lay out the network in the plane.

Line drawing algorithm based on pixel chain

In order to increase the efficiency of the line drawing algorithm when the slope of the line is greater than 0.5,a line drawing algorithm based on pixel chain was proposed.A straight line was treated as an aggregation of several horizontal pixel chains or diagonal pixel chains.An algorithm of line drawing in a reverse direction,which was similar to Bresenham algorithm,was introduced,by which the slope between 0.5 and 1 was converted to that between 0 and 0.5 while generating line.One pixel chain was generated by one judgment.The simulation results show the straight line generated by new algorithm is as same as that generated by Bresenham algorithm,but the calculation is greatly reduced.The new algorithm has generated two integer arithmetic: addition and multiplication,and it is suitable for hardware implementation.The generation speed of the new algorithm is 4 times of Bresenham algorithm with the same complexity of design.

EDLines: A real-time line segment detector with a false detection control

We propose a linear time line segment detector that gives accurate results, requires no parameter tuning, and runs up to 11 times faster than the fastest known line segment detector in the literature; namely, the line segment detector (LSD) by Grompone von Gioi et al. The proposed algorithm makes use of the clean, contiguous (connected) chain of edge pixels produced by our novel edge detector, the Edge Drawing ( ED) algorithm; hence the name EDLines. The detector includes a line validation step due to the Helmholtz principle, which lets it control the number of false detections. With its accurate results and blazing speed, EDLines will be very suitable for the next generation real-time computer vision and image processing applications.

Drawing a tree as a minimum spanning tree approximation

We introduce and study ( 1 + ε ) -EMST drawings, i.e., planar straight-line drawings of trees such that, for any fixed ε > 0 , the distance between any two vertices is at least 1 1 + ε the length of the longest edge in the path connecting them. ( 1 + ε ) -EMST drawings are good approximations of Euclidean minimum spanning trees. While it is known that only trees with bounded degree have a Euclidean minimum spanning tree realization, we show that every tree T has a ( 1 + ε ) -EMST drawing for any given ε > 0 . We also present drawing algorithms that compute ( 1 + ε ) -EMST drawings of trees with bounded degree in polynomial area. As a byproduct of one of our techniques, we improve the best known area upper bound for Euclidean minimum spanning tree realizations of complete binary trees.

Mental map preserving graph drawing using simulated annealing

Visualizing graphs has been studied extensively in the community of graph drawing and information visualization over the years. In some applications, the user is required to interact with a graph by making slight changes to the underlying graph structure. To visualize graphs in such an interactive environment, it is desirable that the differences between the displays of the original and the modified graphs be kept minimal, allowing the user to comprehend the changes in the graph structure faster. As the mental map concept refers to the presentation of a person’s mind while exploring visual information, the better the mental map is preserved, the easier the structure change of a graph is understood. It is somewhat surprising that preserving the user’s mental map has largely been ignored in the graph drawing community in the past. We propose an effective mental-map-preserving graph drawing algorithm for straight-line drawings of general undirected graphs based on the simulated-annealing technique. Our experimental results and questionnaire analysis suggest this new approach to be promising.

ImPrEd: An Improved Force‐Directed Algorithm that Prevents Nodes from Crossing Edges

AbstractPrEd [Ber00] is a force‐directed algorithm that improves the existing layout of a graph while preserving its edge crossing properties. The algorithm has a number of applications including: improving the layouts of planar graph drawing algorithms, interacting with a graph layout, and drawing Euler‐like diagrams. The algorithm ensures that nodes do not cross edges during its execution. However, PrEd can be computationally expensive and overly‐restrictive in terms of node movement.In this paper, we introduce ImPrEd: an improved version of PrEd that overcomes some of its limitations and widens its range of applicability. ImPrEd also adds features such as flexible or crossable edges, allowing for greater control over the output. Flexible edges, in particular, can improve the distribution of graph elements and the angular resolution of the input graph. They can also be used to generate Euler diagrams with smooth boundaries. As flexible edges increase data set size, we experience an execution/drawing quality trade off. However, when flexible edges are not used, ImPrEdproves to be consistently faster than PrEd.