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Similar to the project mentioned above, we would design an algorithm to search a space of possible designs guided by feedback solicited from the user. However, in this project, it is not building designs we want to explore, but schematizations of public transportation networks, in order to find a most appealing design for a schematized map. | Similar to the project mentioned above, we would design an algorithm to search a space of possible designs guided by feedback solicited from the user. However, in this project, it is not building designs we want to explore, but schematizations of public transportation networks, in order to find a most appealing design for a schematized map. | ||
- | ====Nearest-neighbour-preserving sets of space-filling curves (BM)==== | ||
- | A space-filling curve is essentially a continuous, surjective function //f// from the unit interval to some two- or higher-dimensional volume. As //t// goes from 0 to 1, the image // | ||
- | That guarantee is not as good as we would like it to be, and this may have something to do with the following fact: at many points of the space-filling curves used by Liao et al., 2< | ||
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- | ====Quantifying the roughness of space-filling curves (M)==== | ||
- | A space-filling curve is essentially a continuous, surjective function //f// from the unit interval to some two- or higher-dimensional volume. As //t// goes from 0 to 1, the image // | ||
====Sonifying algorithms (BM)==== | ====Sonifying algorithms (BM)==== | ||
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Recently I have been co-supervising projects on environment perception for automated driving. These projects were executed in the research laboratories of Audi in Ingolstadt. If you are interested in this topic, feel free to contact me and we can see if we can set up a similar project for you. Note: this may take several months to set up, and includes an application procedure. So if you are interested, it is best to contact me in the beginning of the semester that precedes the semester in which you want to start your graduation project. | Recently I have been co-supervising projects on environment perception for automated driving. These projects were executed in the research laboratories of Audi in Ingolstadt. If you are interested in this topic, feel free to contact me and we can see if we can set up a similar project for you. Note: this may take several months to set up, and includes an application procedure. So if you are interested, it is best to contact me in the beginning of the semester that precedes the semester in which you want to start your graduation project. | ||
- | ====Cost cues for maps of transportation networks (BM)==== | ||
- | Schematic maps of transportation networks are designed to show the connections between different train or metro lines clearly. However, from such maps it may be hard to get an impression which routes are costly (in terms of travel time, or otherwise) and which routes are preferable. To remedy this shortcoming, | ||
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- | ==Shortest-path preserving rounding of weights in a graph (M)== | ||
- | The goal of this project is to decide which edges of the transportation network should cross zone boundaries, such that map users who choose their routes so as to minimize the number of zone boundary crossings, end up choosing the routes that indeed have the lowest total cost. The problem lends itself to theoretical research (is it NP-hard or not?) and/or practical research (what heuristic solution gives satisfactory results on realistic networks?). | ||
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- | ==Separating groups of points by disjoint disks (M)== | ||
- | Given which edges cross zone boundaries, and thus, which groups of stations must lie in the same zone, we need to draw the zones. To minimize clutter on the map, the zones should have simple shapes---ideally, | ||
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- | ==Inferring a cost map from costs of line segments (BM)== | ||
- | We are given a network drawn in the plane, with a cost associated with each edge. The goal is to assign a weight to each point in the plane, such that the integral of the weight function over the set of points covered by each edge matches that edge's specified cost. A technically correct solution would be nearly trivial to obtain, but to obtain a readable map, we should satisfy additional criteria that make the problem considerably more challenging. For example, the weight function should be as smooth as possible, and it should not have steep gradients where they would be obscured by the network drawing. In a Master project, we could also try to investigate how the computed background affects users' perception of the network and how it affects what routes they would choose to travel. | ||
====Labels-first schematic cartography (M)==== | ====Labels-first schematic cartography (M)==== |