Confluent Layered Drawings

Eppstein, David; Goodrich, Michael T.; Meng, Jeremy Yu

doi:10.1007/s00453-006-0159-8

Cited by 32 publications

(20 citation statements)

References 26 publications

(24 reference statements)

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“…There is also significant work on confluent drawings [10,15], where curvilinear edges are used to bundle similar edges together and avoid edge crossings. In confluent drawings, edges are drawn like train-tracks using locally-monotone curves which do not self-intersect and which do not have sharp turns.…”

Section: Related Workmentioning

confidence: 99%

Smooth Orthogonal Layouts

Bekos¹,

Kaufmann²,

Kobourov³

et al. 2013

JGAA

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Abstract. We study the problem of creating smooth orthogonal layouts for planar graphs. While in traditional orthogonal layouts every edge is made of a sequence of axis-aligned line segments, in smooth orthogonal layouts every edge is made of axis-aligned segments and circular arcs with common tangents. Our goal is to create such layouts with low edge complexity, measured by the number of line and circular arc segments. We show that every biconnected 4-planar graph has a smooth orthogonal layout with edge complexity 3. If the input graph has a complexity-2 traditional orthogonal layout we can transform it into a smooth complexity-2 layout. Using the Kandinsky model for removing the degree restriction, we show that any planar graph has a smooth complexity-2 layout.

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Section: Related Workmentioning

confidence: 99%

Smooth Orthogonal Layouts

Bekos¹,

Kaufmann²,

Kobourov³

et al. 2013

JGAA

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show abstract

“…For example, Goodrich and Wagner [21] give algorithms for drawing planar graphs using Bézier splines for edges, and Cheng et al [6] describe a scheme for drawing graphs using circular arc poly-edges. Several groups of researchers have also studied confluent drawings [9,14,15,23], which bundle edges together in smooth curves so as to reduce crossings.…”

Section: Related Workmentioning

confidence: 99%

Force-Directed Lombardi-Style Graph Drawing

et al. 2012

Self Cite

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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 "Lombardi-style" drawings (which we also call near-Lombardi drawings), in which all edges are still circular arcs, but some vertices may not have perfect angular resolution. Both of these algorithms take a force-directed, spring-embedding 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 near-Lombardi drawings, with one being slightly better at achieving near-perfect angular resolution and the other being slightly better at balancing vertex placements.

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“…Confluent drawing is a technique for drawing non-planar diagrams without crossings [7,8,9,15,16] by merging together groups of edges and drawing them as tracks that, like train tracks, meet smoothly at junction points but do not cross. A confluent drawing consists of a set of labeled points (vertices and junctions) and curves (track segments) in the Euclidean plane, such that the two endpoints of each track segment are vertices or junctions, such that no two track segments intersect except at a shared endpoint, and such that all track segments that meet at a junction share a common tangent line at that point.…”

Section: Confluent Drawingmentioning

confidence: 99%

“…Thus given two different ways to present information, we should choose the more succinct and crossing-free presentation. Confluent drawing [7,8,9,15,16] is a style of graph drawing in which multiple edges are combined into shared tracks, and two vertices are considered to be adjacent if a smooth path connects them in these tracks ( Figure 1). This style was introduced to reduce crossings, and in many cases it will also improve the ink requirement by representing dense subgraphs concisely.…”

Section: Introductionmentioning

confidence: 99%

Confluent Hasse Diagrams

Eppstein

Simons

2012

Graph Drawing

Self Cite

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Abstract. We show that a transitively reduced digraph has a confluent upward drawing if and only if its reachability relation has order dimension at most two. In this case, we construct a confluent upward drawingFor the digraphs representing series-parallel partial orders we show how to construct a drawing with O(n) features in an O(n) × O(n) grid in O(n) time from a series-parallel decomposition of the partial order. Our drawings are optimal in the number of confluent junctions they use.

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Confluent Layered Drawings

Cited by 32 publications

References 26 publications

Smooth Orthogonal Layouts

Smooth Orthogonal Layouts

Force-Directed Lombardi-Style Graph Drawing

Confluent Hasse Diagrams

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