Timeslices are often used to draw and visualize dynamic graphs. While timeslices are a natural way to think about dynamic graphs, they are routinely imposed on continuous data. Often, it is unclear how many timeslices to select: too few timeslices can miss temporal features such as causality or even graph structure while too many timeslices slows the drawing computation. We present a model for dynamic graphs which is not based on timeslices, and a dynamic graph drawing algorithm, DynNoSlice, to draw graphs in this model. In our evaluation, we demonstrate the advantages of this approach over timeslicing on continuous data sets.
3D Graph Drawing. Several 2D algorithms have been extended to 3D. Bru and Frick @cite_30 proposed Gem3D , which extends Gem @cite_36 to 3D. Cruz and Twarog @cite_17 extended the simulated annealing approach of Davidson and Harel @cite_0 to 3D. Other algorithms work in both 2D and 3D, such as GRIP by Gajer and Kobourov @cite_21 . Munzner @cite_35 proposed an algorithm to draw directed graphs in a 3D hyperbolic space. Several other algorithms deal with particular constraints, such as orthogonal @cite_25 , or nested @cite_33 drawings. Cordeil 16Cordeil investigate the visualization of graphs in 3D using immersive environments.
@cite_30 @cite_35 @cite_33 @cite_36 @cite_21 @cite_0 @cite_25 @cite_17
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We present a 3-D version of Gem [6], a randomized adaptive layout algorithm for nicely drawing undirected graphs, based on the spring-embedder paradigm [4]. The new version, Gem-3D, contains several improvements besides the adaptation to 3-D geometry. We present the H3 layout technique for drawing large directed graphs as node-link diagrams in 3D hyperbolic space. We can lay out much larger structures than can be handled using traditional techniques for drawing general graphs because we assume a hierarchical nature of the data. We impose a hierarchy on the graph by using domain-specific knowledge to find an appropriate spanning tree. Links which are not part of the spanning tree do not influence the layout but can be selectively drawn by user request. The volume of hyperbolic 3-space increases exponentially, as opposed to the familiar geometric increase of euclidean 3-space. We exploit this exponential amount of room by computing the layout according to the hyperbolic metric. We optimize the cone tree layout algorithm for 3D hyperbolic space by placing children on a hemisphere around the cone mouth instead of on its perimeter. Hyperbolic navigation affords a Focus+Context view of the structure with minimal visual clutter. We have successfully laid out hierarchies of over 20,000 nodes. Our implementation accommodates navigation through graphs too large to be rendered interactively by allowing the user to explicitly prune or expand subtrees. Abstract Most systems for visualizing large information structures use 2D graphics to view networks of nodes and arcs that represent data. To understand large structures it is often necessary to show both small-scale and large-scale structures. This has been called the problem of focus and context. Distortion, rapid zooming, elision and multiple windows are all techniques that have been developed to provide both focus and context within single representations. We review these techniques and argue that 3D visualization has a number of advantages. A system called NestedVision3D (NV3D) will be presented that has been developed to investigate the use of 3D visualization for understanding the structure of large computer programs. NV3D is a system for visualizing large nested graphs using interactive 3D graphics. It has been tested with graphs containing more than 35,000 nodes and 100,000 relationships. We describe NV3D and its design philosophy. Basic navigation is facilitated by a set of 3D widgets, rapid scaling and interactive elision. More experimental features include animations called snakes, which are used to trace dynamic software behavior. This paper describes a system for Graph dRawing with Intelligent Placement, GRIP. The system is designed for drawing large graphs and uses a novel multi-dimensional force-directed method together with fast energy function minimization. The system allows for drawing graphs with tens of thousands of vertices in under a minute on a mid-range PC. To the best of the authors' knowledge GRIP surpasses the fastest previous algorithms. However, speed is not achieved at the expense of quality as the resulting drawings are quite aesthetically pleasing. The paradigm of simulated annealing is applied to the problem of drawing graphs “nicely.” Our algorithm deals with general undirected graphs with straight-line edges, and employs several simple criteria for the aesthetic quality of the result. The algorithm is flexible, in that the relative weights of the criteria can be changed. For graphs of modest size it produces good results, competitive with those produced by other methods, notably, the “spring method” and its variants. There is a large number of effective methodologies and algorithms for the creation of aesthetically pleasing graph drawings in two dimensions. However, representing graphs in three dimensions offers various benefits. The extra dimension gives greater flexibility for placing the vertices and edges of a graph and crossings can be always avoided. On the other hand new challenges arise: current output media have a two-dimensional nature and can only provide a limited resolution and display area. Thus, the resulting drawings become complex and difficult to survey. These disadvantages can be weakened by the use of navigational operations such as rotation, shifting and zooming. These operations enable an effective use of screen space and allow users to resolve ambiguities in large graphs while maintaining their overall mental map. The possibility of changing the viewpoint in 3D will also diminish the relevance of edge crossing in the (two-dimensional) screen representation of the graph. A recent trend in graph drawing is directed to the visualization of graphs in 3D [1, 5, 6]. A promising research direction concerns the extension of proven 2D techniques to 3D. We present a system extending the simulated annealing algorithm of Davidson and Harel [2] for straight-line two-dimensional drawings of general undirected graphs to three dimensions. This system features an advanced 3D user interface that assists the user in choosing and modifying the cost function and the optimization components on-line.