Efficient Generation of Geographically Accurate Transit Maps

We present LOOM (Line-Ordering Optimized Maps), a fully automatic generator of geographically accurate transit maps. The input to LOOM is data about the lines of a given transit network, namely for each line, the sequence of stations it serves and the geographical course the vehicles of this line take. We parse this data from GTFS, the prevailing standard for public transit data. LOOM proceeds in three stages: (1) construct a so-called line graph, where edges correspond to segments of the network with the same set of lines following the same course; (2) construct an ILP that yields a line ordering for each edge which minimizes the total number of line crossings and line separations; (3) based on the line graph and the ILP solution, draw the map. As a naive ILP formulation is too demanding, we derive a new custom-tailored formulation which requires significantly fewer constraints. Furthermore, we present engineering techniques which use structural properties of the line graph to further reduce the ILP size. For the subway network of New York, we can reduce the number of constraints from 229,000 in the naive ILP formulation to about 4,500 with our techniques, enabling solution times of less than a second. Since our maps respect the geography of the transit network, they can be used for tiles and overlays in typical map services. Previous research work either did not take the geographical course of the lines into account, or was concerned with schematic maps without optimizing line crossings or line separations.Comment: 7 page

CelticGraph: Drawing Graphs as Celtic Knots and Links

Celtic knots are an ancient art form often attributed to Celtic cultures, used to decorate monuments and manuscripts, and to symbolise eternity and interconnectedness. This paper describes the framework CelticGraph to draw graphs as Celtic knots and links. The drawing process raises interesting combinatorial concepts in the theory of circuits in planar graphs. Further, CelticGraph uses a novel algorithm to represent edges as B\'ezier curves, aiming to show each link as a smooth curve with limited curvature.Comment: Appears in the Proceedings of the 31st International Symposium on Graph Drawing and Network Visualization (GD 2023

What?s your theory of effective schematic map design?

Amongst designers, researchers, and the general public, there exists a diverse array of opinion about good practice in schematic map design, and a lack of awareness that such opinions are not necessarily universally held nor supported by evidence. This paper gives an overview of the range of opinion that can be encountered, the consequences that this has for published designs, and a framework for organising the various views

Coordinated Schematization for Visualizing Mobility Patterns on Networks

GPS trajectories of vehicles moving on a road network are a valuable source of traffic information. However, the sheer volume of available data makes it challenging to identify and visualize salient patterns. Meaningful visual summaries of trajectory collections require that both the trajectories and the underlying network are aggregated and simplified in a coherent manner. In this paper we propose a coordinated fully-automated pipeline for computing a schematic overview of mobility patterns from a collection of trajectories on a street network. Our pipeline utilizes well-known building blocks from GIS, automated cartography, and trajectory analysis: map matching, road selection, schematization, movement patterns, and metro-map style rendering. We showcase the results of our pipeline on two real-world trajectory collections around The Hague and Beijing

A Survey on Transit Map Layout – from Design, Machine, and Human Perspectives

Transit maps are designed to present information for using public transportation systems, such as urban railways. Creating a transit map is a time‐consuming process, which requires iterative information selection, layout design, and usability validation, and thus maps cannot easily be customised or updated frequently. To improve this, scientists investigate fully‐ or semi‐automatic techniques in order to produce high quality transit maps using computers and further examine their corresponding usability. Nonetheless, the quality gap between manually‐drawn maps and machine‐generated maps is still large. To elaborate the current research status, this state‐of‐the‐art report provides an overview of the transit map generation process, primarily from Design, Machine, and Human perspectives. A systematic categorisation is introduced to describe the design pipeline, and an extensive analysis of perspectives is conducted to support the proposed taxonomy. We conclude this survey with a discussion on the current research status, open challenges, and future directions

Efficient Algorithms for Ortho-Radial Graph Drawing

Orthogonal drawings, i.e., embeddings of graphs into grids, are a classic topic in Graph Drawing. Often the goal is to find a drawing that minimizes the number of bends on the edges. A key ingredient for bend minimization algorithms is the existence of an orthogonal representation that allows to describe such drawings purely combinatorially by only listing the angles between the edges around each vertex and the directions of bends on the edges, but neglecting any kind of geometric information such as vertex coordinates or edge lengths. Barth et al. [2017] have established the existence of an analogous ortho-radial representation for ortho-radial drawings, which are embeddings into an ortho-radial grid, whose gridlines are concentric circles around the origin and straight-line spokes emanating from the origin but excluding the origin itself. While any orthogonal representation admits an orthogonal drawing, it is the circularity of the ortho-radial grid that makes the problem of characterizing valid ortho-radial representations all the more complex and interesting. Barth et al. prove such a characterization. However, the proof is existential and does not provide an efficient algorithm for testing whether a given ortho-radial representation is valid, let alone actually obtaining a drawing from an ortho-radial representation. In this paper we give quadratic-time algorithms for both of these tasks. They are based on a suitably constrained left-first DFS in planar graphs and several new insights on ortho-radial representations. Our validity check requires quadratic time, and a naive application of it would yield a quartic algorithm for constructing a drawing from a valid ortho-radial representation. Using further structural insights we speed up the drawing algorithm to quadratic running time

AutoGraff: towards a computational understanding of graffiti writing and related art forms.

The aim of this thesis is to develop a system that generates letters and pictures with a style that is immediately recognizable as graffiti art or calligraphy. The proposed system can be used similarly to, and in tight integration with, conventional computer-aided geometric design tools and can be used to generate synthetic graffiti content for urban environments in games and in movies, and to guide robotic or fabrication systems that can materialise the output of the system with physical drawing media. The thesis is divided into two main parts. The first part describes a set of stroke primitives, building blocks that can be combined to generate different designs that resemble graffiti or calligraphy. These primitives mimic the process typically used to design graffiti letters and exploit well known principles of motor control to model the way in which an artist moves when incrementally tracing stylised letter forms. The second part demonstrates how these stroke primitives can be automatically recovered from input geometry defined in vector form, such as the digitised traces of writing made by a user, or the glyph outlines in a font. This procedure converts the input geometry into a seed that can be transformed into a variety of calligraphic and graffiti stylisations, which depend on parametric variations of the strokes

Schematic maps in the laboratory

Empirical research into the usability of schematic maps is currently in its infancy. This paper justifies the necessity for research, reviews the most relevant recently-published studies, gives an overview of potential pitfalls of this topic, and suggests future directions

Radi(c)al departures Comparing conventional octolinear versus concentric circles schematic maps for the Berlin U-Bahn/S-Bahn networks using objective and subjective measures of effectiveness

An experiment is reported in which two designs of Berlin U-/S-Bahn network maps were compared for usability. One was conventional, based on standard schematic design rules used worldwide: Straight lines with tightly radiused corners, and only horizontal, vertical, or 45° diagonal angles permitted. The other was a novel concept, based on concentric circles and spokes radiating from a central point. The former has the benefit of simple line trajectories, the latter potentially has the benefit of a coherent overall appearance. The experiment investigated both an objective performance measure (time required to plan complex journeys) and a variety of subjective measures (choice between maps, ratings of statements associated with usability, direct ratings of usability). All subjects planned journeys using both designs. Overall, performance was worse for the concentric circles map, and it received poor ratings. However, in line with previous research, objective and subjective measures were dissociated. For example, many subjects expressed a preference for the design that was not the best for them in terms of objective performance