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- David Eppstein, Marc J. van Kreveld, Bettina Speckmann, Frank Staals
- Int. J. Comput. Geometry Appl.
- 2013

Associating the regions of a geographic subdivision with the cells of a grid is a basic operation that is used in various types of maps, like spatially ordered treemaps and OD maps. In these cases the regular shapes of the grid cells allows easy representation of extra information about the regions. The main challenge is to find an association that allows a… (More)

- Boris Aronov, Anne Driemel, Marc J. van Kreveld, Maarten Löffler, Frank Staals
- ACM Trans. Algorithms
- 2013

In the trajectory segmentation problem, we are given a polygonal trajectory with <i>n</i> vertices that we have to subdivide into a minimum number of disjoint segments (subtrajectories) that all satisfy a given criterion. The problem is known to be solvable efficiently for <i>monotone</i> criteria: criteria with the property that if they hold on a certain… (More)

- Ferran Hurtado, Maarten Löffler, +4 authors Frank Staals
- ISAAC
- 2013

We study the problem of visibility in polyhedral terrains in the presence of multiple viewpoints. We consider three fundamental visibility structures: the visibility map, the colored visibility map, and the Voronoi visibility map. We study the complexity of each structure for both 1.5D and 2.5D terrains, and provide efficient algorithms to construct them.… (More)

- Joachim Gudmundsson, Marc J. van Kreveld, Frank Staals
- SIGSPATIAL/GIS
- 2013

We study one of the basic tasks in moving object analysis, namely the location of <i>hotspots</i>. A hotspot is a (small) region in which an entity spends a significant amount of time. Finding such regions is useful in many applications, for example in segmentation, clustering, and locating popular places. We may be interested in locating a minimum size… (More)

The collective motion of a set of moving entities like people, birds, or other animals, is characterized by groups arising, merging, splitting, and ending. Given the trajectories of these entities, we define and model a structure that captures all of such changes using the Reeb graph, a concept from topology. The trajectory grouping structure has three… (More)

- Irina Kostitsyna, Marc J. van Kreveld, Maarten Löffler, Bettina Speckmann, Frank Staals
- Symposium on Computational Geometry
- 2015

In recent years trajectory data has become one of the main types of geographic data, and hence algorithmic tools to handle large quantities of trajectories are essential. A single trajectory is typically represented as a sequence of time-stamped points in the plane. In a collection of trajectories one wants to detect maximal groups of moving entities and… (More)

- Arthur van Goethem, Marc J. van Kreveld, Maarten Löffler, Bettina Speckmann, Frank Staals
- Symposium on Computational Geometry
- 2016

We present algorithms and data structures that support the interactive analysis of the grouping structure of one-, two-, or higher-dimensional time-varying data while varying all defining parameters. Grouping structures characterise important patterns in the temporal evaluation of sets of time-varying data. We follow Buchin et al. [9] who define groups… (More)

We revisit the minimum-link path problem: Given a polyhedral domain and two points in it, connect the points by a polygonal path with minimum number of edges. We consider settings where the min-link path’s vertices or edges can be restricted to lie on the boundary of the domain, or can be in its interior. Our results include bit complexity bounds, a novel… (More)

- Maarten Löffler, Mira Kaiser, Tim van Kapel, Gerwin Klappe, Marc J. van Kreveld, Frank Staals
- ACM Trans. Graph.
- 2014

In this paper we introduce several innovative variants on the classic Connect-The-Dots puzzle. We study the underlying geometric principles and investigate methods for the automatic generation of high-quality puzzles from line drawings.
Specifically, we introduce three new variants of the classic Connect-The-Dots puzzle. These new variants use different… (More)

We study grouping of entities moving amidst obstacles, extending the recent work of Kostitsyna et al. [5]. We present an alternative algorithm that can compute the Reeb-graph, a graph which captures when and how the partition of the entities into groups changes, when the entities move amidst arbitrary polygonal obstacles. Our new algorithm is significantly… (More)