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21
Confluent drawings: Visualizing NonPlanar Diagrams in a Planar Way
 GRAPH DRAWING (PROC. GD ’03), VOLUME 2912 OF LECTURE NOTES COMPUT. SCI
, 2003
"... We introduce a new approach for drawing diagrams. Our approach is to use a technique we call confluent drawing for visualizing nonplanar graphs in a planar way. This approach allows us to draw, in a crossingfree manner, graphs—such as software interaction diagrams—that would normally have many cro ..."
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Cited by 28 (7 self)
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We introduce a new approach for drawing diagrams. Our approach is to use a technique we call confluent drawing for visualizing nonplanar graphs in a planar way. This approach allows us to draw, in a crossingfree manner, graphs—such as software interaction diagrams—that would normally have many crossings. The main idea of this approach is quite simple: we allow groups of edges to be merged together and drawn as “tracks” (similar to train tracks). Producing such confluent drawings automatically from a graph with many crossings is quite challenging, however, we offer a heuristic algorithm (one version for undirected graphs and one version for directed ones) to test if a nonplanar graph can be drawn efficiently in a confluent way. In addition, we identify several large classes of graphs that can be completely categorized as being either confluently drawable or confluently nondrawable.
Curvilinar graph drawing using the forcedirected method
 Proc. 12th Int. Symposium on Graph Drawing, 2004, Springer LNCS 3383
"... Abstract. We present a method for modifying a forcedirected graph drawing algorithm into an algorithm for drawing graphs with curved lines. Our method is based on embedding control points as dummy vertices so that edges can be drawn as splines. Our experiments show that our method yields aesthetica ..."
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Cited by 16 (0 self)
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Abstract. We present a method for modifying a forcedirected graph drawing algorithm into an algorithm for drawing graphs with curved lines. Our method is based on embedding control points as dummy vertices so that edges can be drawn as splines. Our experiments show that our method yields aesthetically pleasing curvilinear drawing with improved angular resolution. Applying our method to the GEM algorithm on the test suite of the “Rome Graphs ” resulted in an average improvement of 46 % in angular resolution and of almost 6 % in edge crossings. 1
Improving Angular Resolution in Visualizations of Geographic Networks
, 2000
"... In visualizations of largescale transportation and communications networks, node coordinates are usually fixed to preserve the underlying geography, while links are represented as geodesics for simplicity. This often leads ..."
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Cited by 13 (3 self)
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In visualizations of largescale transportation and communications networks, node coordinates are usually fixed to preserve the underlying geography, while links are represented as geodesics for simplicity. This often leads
Lombardi Drawings of Graphs
"... We introduce the notion of Lombardi graph drawings, named after the American abstract artist Mark Lombardi. In these drawings, edges are represented as circular arcs rather than as line segments or polylines, and the vertices have perfect angular resolution: the edges are equally spaced around each ..."
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Cited by 9 (6 self)
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We introduce the notion of Lombardi graph drawings, named after the American abstract artist Mark Lombardi. In these drawings, edges are represented as circular arcs rather than as line segments or polylines, and the vertices have perfect angular resolution: the edges are equally spaced around each vertex. We describe algorithms for finding Lombardi drawings of regular graphs, graphs of bounded degeneracy, and certain families of planar graphs.
Metabolic network visualization using constraint planar graph drawing algorithm
 iv
, 2006
"... ● Metabolic pathway: small subset of biochemical reactions that occur in a cell Glycolysis and Gluconeogenesis pathways ..."
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Cited by 6 (1 self)
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● Metabolic pathway: small subset of biochemical reactions that occur in a cell Glycolysis and Gluconeogenesis pathways
A new forcedirected graph drawing method based on edgeedge repulsion
 IN PROCEEDINGS OF THE NINTH INTERNATIONAL CONFERENCE ON INFORMATION VIZUALISATION (IV
, 2005
"... The conventional forcedirected methods for drawing undirected graphs are based on either vertexvertex repulsion or vertexedge repulsion. In this paper, we propose a new forcedirected method based on edgeedge repulsion to draw graphs. In our framework, edges are modelled as charged springs, and ..."
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Cited by 6 (0 self)
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The conventional forcedirected methods for drawing undirected graphs are based on either vertexvertex repulsion or vertexedge repulsion. In this paper, we propose a new forcedirected method based on edgeedge repulsion to draw graphs. In our framework, edges are modelled as charged springs, and a final drawing can be generated by adjusting positions of vertices according to spring forces and the repulsive forces, derived from potential fields, among edges. Different from the previous methods, our new framework has the advantage of overcoming the problem of zero angular resolution, guaranteeing the absence of any overlapping of edges incident to the common vertex. Given graph layouts probably generated by classical algorithms as the inputs to our algorithm, experimental results reveal that our approach produces promising drawings (especially for trees and hypercubes) not only preserving the original properties of a high degree of symmetry and uniform edge length, but also preventing zero angular resolution. By allowing vertexvertex overlapping, our algorithm also results in more symmetrical drawings. Furthermore, we apply the model to producing dynamical balloon view drawings of rooted trees, usually used in information visualization.
Planar and PolyArc Lombardi Drawings
"... Abstract. In Lombardi drawings of graphs, edges are represented as circular arcs, and the edges incident on vertices have perfect angular resolution. However, not every graph has a Lombardi drawing, and not every planar graph has a planar Lombardi drawing. We introduce kLombardi drawings, in which ..."
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Cited by 4 (4 self)
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Abstract. In Lombardi drawings of graphs, edges are represented as circular arcs, and the edges incident on vertices have perfect angular resolution. However, not every graph has a Lombardi drawing, and not every planar graph has a planar Lombardi drawing. We introduce kLombardi drawings, in which each edge may be drawn with k circular arcs, noting that every graph has a smooth 2Lombardi drawing. We show that every planar graph has a smooth planar 3Lombardi drawing and further investigate topics connecting planarity and Lombardi drawings. 1
L.: Forcedirected Lombardistyle graph drawing
 In: Proc. 19th Int. Symp. on Graph Drawing
, 2011
"... Abstract. A Lombardi drawing of a graph is defined as one in which vertices are represented as points, edges are represented as circular arcs between their endpoints, and every vertex has perfect angular resolution (angles between consecutive edges, as measured by the tangents to the circular arcs a ..."
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Cited by 4 (2 self)
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Abstract. A Lombardi drawing of a graph is defined as one in which vertices are represented as points, edges are represented as circular arcs between their endpoints, and every vertex has perfect angular resolution (angles between consecutive edges, as measured by the tangents to the circular arcs at the vertex, all have the same degree). We describe two algorithms that create “Lombardistyle” drawings (which we also call nearLombardi drawings), in which all edges are still circular arcs, but some vertices may not have perfect angular resolution. Both of these algorithms take a forcedirected, springembedding approach, with one using forces at edge tangents to produce curved edges and the other using dummy vertices on edges for this purpose. As we show, these approaches both produce nearLombardi drawings, with one being slightly better at achieving nearperfect angular resolution and the other being slightly better at balancing vertex placements. 1
Fast Layout Methods for Timetable Graphs
 Proceedings of Graph Drawing 2000, Lecture Notes in Computer Science
, 2000
"... Timetable graphs are used to analyze transportation networks. In their visualization, vertex coordinates are xed to preserve the underlying geography, but due to small angles and overlaps, not all edges should be represented by geodesics (straight lines or great circles). A previously introduced ..."
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Cited by 3 (1 self)
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Timetable graphs are used to analyze transportation networks. In their visualization, vertex coordinates are xed to preserve the underlying geography, but due to small angles and overlaps, not all edges should be represented by geodesics (straight lines or great circles). A previously introduced algorithm represents a subset of the edges by Bezier curves, and places control points of these curves using a forcedirected approach [5]. While the results are of very good quality, the running times make the approach impractical for interactive systems. In this paper, we present a fast layout algorithm using an entirely different approach to edge routing, based on directions of control segments rather than positions of control points. We reveal an interesting theoretical connection with Tutte's barycentric layout method [18], and our computational studies show that this new approach yields satisfactory layouts even for huge timetable graphs within seconds. 1
Graph Drawing Algorithm Engineering with AGD
, 2000
"... We discuss the algorithm engineering aspects of AGD, a software library of algorithms for graph drawing. AGD represents algorithms as classes that provide one or more methods for calling the algorithm. There is a common base class, also called the type of an algorithm, for algorithms providing basic ..."
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Cited by 3 (2 self)
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We discuss the algorithm engineering aspects of AGD, a software library of algorithms for graph drawing. AGD represents algorithms as classes that provide one or more methods for calling the algorithm. There is a common base class, also called the type of an algorithm, for algorithms providing basically the same functionality. This enables us to exchange components and experiment with various algorithms and implementations of the same type. We give examples for algorithm engineering with AGD for drawing general nonhierarchical graphs and hierarchical graphs.