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Path simplification for metro map layout
 Proc. 14th Internat. Sympos. Graph Drawing (GD’06), volume 4372 of Lecture
, 2006
"... Abstract. We investigate the problem of creating simplified representations of polygonal paths. Specifically, we look at a path simplification problem in which line segments of a simplification are required to conform with a restricted set of directions C. An algorithm is given to compute such simpl ..."
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Abstract. We investigate the problem of creating simplified representations of polygonal paths. Specifically, we look at a path simplification problem in which line segments of a simplification are required to conform with a restricted set of directions C. An algorithm is given to compute such simplified paths in O(C  3 n 2) time, where n is the number of vertices in the original path. This result is extended to produce an algorithm for graphs induced by multiple intersecting paths. The algorithm is applied to construct schematised representations of real world railway networks, in the style of metro maps. 1
Increasing the readability of graph drawings with centralitybased scaling
 in Asia Pacific Symposium on Information Visualisation (APVIS2006), ser. CRPIT
"... A common problem in visualising some networks is the presence of localised high density areas in an otherwise sparse graph. Applying common graph drawing algorithms on such networks can result in drawings that are not highly readable in the dense areas. Additionally, networks whose layouts are defin ..."
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Cited by 4 (2 self)
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A common problem in visualising some networks is the presence of localised high density areas in an otherwise sparse graph. Applying common graph drawing algorithms on such networks can result in drawings that are not highly readable in the dense areas. Additionally, networks whose layouts are defined geographically often have dense areas that are located within small geographical regions relative to the size of the entire network. In cases where relationships within these dense areas are of interest, it is desirable to be able to distort the graph layout such that the denser areas are enlarged from their original sizes. In this paper, we propose a technique for enlarging dense areas of a given graph layout, and shrinking sparse areas. This technique is applied to geographical layouts of railway networks and forcedirected layouts of nongeographical networks. The results show an increase in readability of dense parts of the networks. In addition, they provide improved starting layouts for schematisation methods which may be used to further increase readability.
COPERNICUS: ContextPreserving Engine for Route Navigation with Interactive Usermodifiable Scaling
"... In this paper, we present an automated system for generating contextpreserving route maps that depict navigation routes as a path between nodes and edges inside a topographic network. Our application identifies relevant context information to support navigation and orientation, and generates custom ..."
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Cited by 3 (0 self)
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In this paper, we present an automated system for generating contextpreserving route maps that depict navigation routes as a path between nodes and edges inside a topographic network. Our application identifies relevant context information to support navigation and orientation, and generates customizable route maps according to design principles that communicate all relevant context information clearly visible on one single page. Interactive scaling allows seamless transition between the original undistorted map and our new map design, and supports userspecified scaling of regions of interest to create personalized driving directions according to the drivers needs. Categories and Subject Descriptors (according to ACM CCS): I.3.2 C.2.1 [Computer Graphics]: Graphics Systems
AreaPreserving Subdivision Schematization
"... Abstract. We describe an areapreserving subdivision schematization algorithm: the area of each region in the input equals the area of the corresponding region in the output. Our schematization is axisaligned, the final output is a rectilinear subdivision. We first describe how to convert a given ..."
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Abstract. We describe an areapreserving subdivision schematization algorithm: the area of each region in the input equals the area of the corresponding region in the output. Our schematization is axisaligned, the final output is a rectilinear subdivision. We first describe how to convert a given subdivision into an areaequivalent rectilinear subdivision. Then we define two areapreserving contraction operations and prove that at least one of these operations can always be applied to any given simple rectilinear polygon. We extend this approach to subdivisions and showcase experimental results. Finally, we give examples for standard distance metrics (symmetric difference, Hausdorff and Fréchetdistance) that show that better schematizations might result in worse shapes.
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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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
Homotopic rectilinear routing with few links and thick edges
 Proc. LATIN 2010, volume 6034 of Lecture Notes Comput. Sci
, 2010
"... We study the problem of finding noncrossing thick minimumlink rectilinear paths homotopic to a set of input paths in an environment with rectangular obstacles. This problem occurs in the context of map schematization under geometric embedding restrictions, for example, when schematizing a highwa ..."
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We study the problem of finding noncrossing thick minimumlink rectilinear paths homotopic to a set of input paths in an environment with rectangular obstacles. This problem occurs in the context of map schematization under geometric embedding restrictions, for example, when schematizing a highway network for use as a thematic layer. We present a 2approximation algorithm that runs in O(n3 + kin logn + kout) time, where n is the total number of input paths and obstacles and kin and kout are the total complexities of the input and output paths, respectively. Our algorithm not only approximates the minimum number of links, but also minimizes the total length of the paths. An approximation factor of 2 is optimal when using smallest paths as lower bound. 1
Drawing Subway Maps: A Survey
"... Abstract This paper deals with automating the drawing of subway maps. There are two features of schematic subway maps that make them different from drawings of other networks such as flow charts or organigrams. First, most schematic subway maps use not only horizontal and vertical lines, but also di ..."
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Abstract This paper deals with automating the drawing of subway maps. There are two features of schematic subway maps that make them different from drawings of other networks such as flow charts or organigrams. First, most schematic subway maps use not only horizontal and vertical lines, but also diagonals. This gives more flexibility in the layout process, but it also makes the problem provably hard. Second, a subway map represents a network whose components have geographic locations that are roughly known to the users of such a map. This knowledge must be respected during the search for a clear layout of the network. For the sake of visual clarity the underlying geography may be distorted, but it must not be given up, otherwise map users will be hopelessly confused. In this paper we first give a rather generally accepted list of rules that should be adhered to by a good subway map. Next we survey three recent methods for drawing subway maps, analyze their performance with respect to the above rules, and compare the resulting maps among each other and to official subway maps drawn by graphic designers. We then focus on one of the methods, which is based on mixedinteger linear programming, a widelyused global optimization technique. This method guarantees to find a drawing that fulfills a subset of the abovementioned rules (if such a drawing exists) and optimizes a weighted sum of costs that correspond to the remaining rules. The method can draw even large subway networks such as the London Underground in an aesthetically pleasing manner, similar to maps made by professional graphic designers. If station labels are included in the optimization process, so far only mediumsize networks can be drawn. Finally we give evidence why drawing good subway maps is difficult (even without labels).
A Software Framework for the Automated Production of Schematic Maps
"... Schematic Maps are mainly used for depicting transportation networks. They are generated through a schematization process where irrelevant details are eliminated and important details are emphasized. This process, being manually performed by teams of expert designers, is expensive and time consuming ..."
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Schematic Maps are mainly used for depicting transportation networks. They are generated through a schematization process where irrelevant details are eliminated and important details are emphasized. This process, being manually performed by teams of expert designers, is expensive and time consuming. Such manual execution is unsuitable for the production of schematic maps for locationbased services or on demand schematic maps, as near realtime and usercentered properties are needed. This work proposes GeneX, a framework that can support the automated generation of schematic maps. The framework and the new algorithms developed were able to completely eliminate erroneous map point placement, and to decrease by 33 % the contention for map point placement, producing schematic maps without human intervention in soft real time.
Autogeneration of Geographic Cognitive Maps for Browsing Personal Multimedia
"... Abstract. A geographic map is an important browsing tool for multimedia data that can include personal photos, but geographically correct maps are not always easy to use for that purpose due to the frequent zooming and panning, as well as the existence of extraneous information. This paper proposes ..."
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Abstract. A geographic map is an important browsing tool for multimedia data that can include personal photos, but geographically correct maps are not always easy to use for that purpose due to the frequent zooming and panning, as well as the existence of extraneous information. This paper proposes a new userinterface concept for geotagged personal multimedia browsing in the form of a cognitive map. In addition, design criteria are defined and an autogeneration method is presented for this map. The proposed method produces a map represented as a clustered graph with vertices and edges in real time. It is visually compact, preserves geographical relationships among locations and is designed for both PCs and mobile devices. An experiment was conducted to test the proposed method with reallife data sets. 1
Schematization in Cartography, Visualization, and Computational Geometry
"... The Dagstuhl Seminar 10461 “Schematization in Cartography, Visualization, and Computational Geometry ” was held November ..."
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The Dagstuhl Seminar 10461 “Schematization in Cartography, Visualization, and Computational Geometry ” was held November