The k-nearest neighbour (kNN) problem appears in many different fields of computer science, such as computer animation and robotics. In crowd simulation, kNN queries are typically used by a collision-avoidance method to prevent unnecessary computations. Many different methods for finding these neighbours exist, but it is unclear which will work best in crowd simulations, an application which is characterised by low dimensionality and frequent change of the data points. We therefore compare several data structures for performing kNN queries. We find that the nanoflann implementation of a k-d tree offers the best performance by far on many different scenarios, processing 100,000 agents in about 35 ms on a fast consumer PC.
A multi-layered environment is a representation of the walkable space in a 3D virtual environment that comprises a set of twodimensional layers together with the locations where the different layers touch, which are called connections. This representation can be used for crowd simulations, e.g. to determine evacuation times in complex buildings. Since the execution times of many algorithms depend on the number of connections, we will study multi-layered environments with a minimal number of connections. We show how finding a minimally connected multi-layered environment can be formulated as an instance of the multicut problem. We will prove that finding a minimally connected multi-layered environment is an NP-Hard problem. Lastly, we will present techniques which shrink the size of the underlying graph by removing redundant information. These techniques decrease the input size for algorithms that use this representation for finding multi-layered environments.
a) Polygonal Environment (b) Walkable Environment (c) Multi-Layered Environment (d) Navigation Mesh Figure 1: (a): A polygonal environment or model. (b): The walkable environment for this model. (c): Its multi-layered environment. Polygons with the same colour are in the same layer. (d): By using the multi-layered environment we can create, for example, a navigation mesh.
The quantification of pedestrian safety is an important research topic. If reliable quantification is possible, it can be used to predict and prevent dangerous situations, such as the crowd crush at the 2010 Love Parade. To quantify safety, we can use several metrics like density, velocity, flow and pressure. Unfortunately, there are several methods to evaluate these metrics, which may give different results. This can lead to different interpretations of similar situations. Researchers compare these metrics visually or search for trends in fundamental diagrams. This is inherently subjective. We propose an objective methodology to compare these methods, where we emphasize the different quantifications of peak “dangerousness”. Furthermore, we refine existing methods to include the obstacles in environments by replacing the Euclidean distance with the geodesic distance. In our experimental analysis, we observe large differences between different methods for the same scenarios. We conclude that switching to a different method of analysing crowd safety can lead to different conclusions, which asks for standardisation in this research field. Since we are concerned with human safety, we prefer to err on the side of caution. Therefore, we advocate the use of our refined Gaussian-based method, which consistently reports higher levels of danger.
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