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M.T.: Focus+context metro maps
 IEEE Transactions on Visualization and Computer Graphics
"... National Chiao Tung University1 National Chengchi University2 Abstract — We introduce a focus+context method to visualize a complicated metro map of a modern city on a small displaying area. The context of our work is with regard the popularity of mobile devices. The best route to the destination, w ..."
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Cited by 4 (0 self)
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National Chiao Tung University1 National Chengchi University2 Abstract — We introduce a focus+context method to visualize a complicated metro map of a modern city on a small displaying area. The context of our work is with regard the popularity of mobile devices. The best route to the destination, which can be obtained from the arrival time of trains, is highlighted. The stations on the route enjoy larger spaces, whereas the other stations are rendered smaller and closer to fit the whole map into a screen. To simplify the navigation and route planning for visitors, we formulate various map characteristics such as octilinear transportation lines and regular station distances into energy terms. We then solve for the optimal layout in a least squares sense. In addition, we label the names of stations that are on the route of a passenger according to human preferences, occlusions, and consistencies of label positions using the graph cuts method. Our system achieves realtime performance by being able to report instant information because of the carefully designed energy terms. We apply our method to layout a number of metro maps and show the results and timing statistics to demonstrate the feasibility of our technique. 1
On the Hardness of OrthogonalOrder Preserving Graph Drawing
, 2009
"... There are several scenarios in which a given drawing of a graph is to be modified subject to preservation constraints. Examples include shape simplification, sketchbased, and dynamic graph layout. While the orthogonal ordering of vertices is a natural and frequently called for preservation constrai ..."
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There are several scenarios in which a given drawing of a graph is to be modified subject to preservation constraints. Examples include shape simplification, sketchbased, and dynamic graph layout. While the orthogonal ordering of vertices is a natural and frequently called for preservation constraint, we show that, unfortunately, it results in severe algorithmic difficulties even for the simplest graphs. More precisely, we show that orthogonalorder preserving rectilinear and uniform edge length drawing is NPhard even for paths.
Schematisation of Tree Drawings
, 2006
"... Abstract. Given a tree T spanning a set of points S in the plane, we study the problem of drawing T using only line segments aligned with a fixed set of directions C. The vertices in the drawing must lie within a given distance r of each original point p ∈ S, and an objective function counting the n ..."
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Cited by 1 (1 self)
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Abstract. Given a tree T spanning a set of points S in the plane, we study the problem of drawing T using only line segments aligned with a fixed set of directions C. The vertices in the drawing must lie within a given distance r of each original point p ∈ S, and an objective function counting the number of bends must be minimised. We propose five versions of this problem using different objective functions, and algorithms to solve them. This work has potential applications in geographic map schematisation and metro map layout. 1
On MetroLine Crossing Minimization
, 2010
"... We consider the problem of drawing a set of simple paths along the edges of an embedded underlying graph G = (V, E) so that the total number of crossings among pairs of paths is minimized. This problem arises when drawing metro maps, where the embedding of G depicts the structure of the underlying n ..."
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We consider the problem of drawing a set of simple paths along the edges of an embedded underlying graph G = (V, E) so that the total number of crossings among pairs of paths is minimized. This problem arises when drawing metro maps, where the embedding of G depicts the structure of the underlying network, the nodes of G correspond to train stations, an edge connecting two nodes implies that there exists a railway track connecting them, whereas the paths illustrate the metro lines connecting terminal stations. We call this the metroline crossing minimization problem (MLCM). We examine several variations of the problem for which we develop algorithms that yield optimal solutions.
OrthogonalOrdering Constraints make Graph Drawing Hard
, 2010
"... There are several scenarios in which a given drawing of a graph is to be modified subject to preservation constraints. Examples include shape simplification, sketchbased, and dynamic graph layout. While the orthogonal ordering of vertices is a natural and frequently called for preservation constrai ..."
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There are several scenarios in which a given drawing of a graph is to be modified subject to preservation constraints. Examples include shape simplification, sketchbased, and dynamic graph layout. While the orthogonal ordering of vertices is a natural and frequently called for preservation constraint, we show that, unfortunately, it results in severe algorithmic difficulties even for the simplest graphs. More precisely, we show that orthogonalorder preserving rectilinear, octilinear and uniform edge length drawing is N Phard even for paths. Submitted:
Communicated by:
, 2012
"... We show that rectilinear graph drawing, the core problem of bendminimum orthogonal graph drawing, and uniform edgelength drawing, the core problem of forcedirected placement, are N Phard even for embedded paths if subjected to orthogonalordering constraints. Submitted: ..."
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We show that rectilinear graph drawing, the core problem of bendminimum orthogonal graph drawing, and uniform edgelength drawing, the core problem of forcedirected placement, are N Phard even for embedded paths if subjected to orthogonalordering constraints. Submitted:
TravelRouteCentered Metro Map Layout and Annotation
"... When providing travel guides for a specific route in a metro network, we often place the route around the center of the map and annotate stations on the route with thumbnail photographs. Nonetheless, existing methods do not offer an effective means of customizing the network layout in order to accom ..."
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When providing travel guides for a specific route in a metro network, we often place the route around the center of the map and annotate stations on the route with thumbnail photographs. Nonetheless, existing methods do not offer an effective means of customizing the network layout in order to accommodate such large annotation labels while preserving its planar embedding. This paper presents a new approach for designing the metro map layout in order to annotate stations on a specific travel route with large annotation labels. Our idea is to elongate the travel route to be straight along the centerline of the map so that we can systematically annotate such stations with external labels. This is accomplished by extending the conventional mixedinteger programming technique for computing octilinear layouts where orientations inherent to the metro line segments are plausibly rearranged. The stations are then connected with external labels through leaders while minimizing intersections with metro lines for enhancing visual clarity. We present several design examples of metro maps and user studies to demonstrate that the proposed aesthetic criteria successfully direct viewers ’ attention to specific travel routes. 1.
engineering faculty,
"... Metrovis is an extensible graph drawing package with Silverlight technology. This package is a web base tool to present the octilinear layout of a graph. It provides an application programming interface (API) on top of which Webbased applications that need to visualize any entities in terms of grap ..."
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Metrovis is an extensible graph drawing package with Silverlight technology. This package is a web base tool to present the octilinear layout of a graph. It provides an application programming interface (API) on top of which Webbased applications that need to visualize any entities in terms of graphs. This layout has got many application such as representation of thesis map, designing the web pages. Metrovis, could be enhanced in any platform, and it’s compatible by any algorithm. To illustrate its application, it has been performed with the real metro maps. Key words automatic visualization, metro map, octilinear layout, graph. 1.