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@INPROCEEDINGS{Chraibi:888115,
      author       = {Chraibi, Mohcine and Steffen, Bernhard and Tordeux,
                      Antoine},
      title        = {{A}nalysis of {P}edestrian {M}otion {U}sing {V}oronoi
                      {D}iagrams in {C}omplex {G}eometries},
      volume       = {252},
      address      = {Cham},
      publisher    = {Springer International Publishing},
      reportid     = {FZJ-2020-04690},
      series       = {Springer Proceedings in Physics},
      pages        = {39-44},
      year         = {2019},
      abstract     = {Voronoi diagrams are an established method in the analysis
                      of pedestrian motion for constructing a density from
                      two-dimensional positions. It is in turn used to give
                      pointwise values for speed, movement direction, flow etc.
                      The method was first described for high-density situations
                      inside a crowd moving in a simple geometry without
                      considering the influence of walls. However, more
                      complicated distance calculations are needed for more
                      complicated geometries where there are several obstacles or
                      corners. In addition, partially empty spaces also require
                      special treatment to avoid excessively big cells. These
                      problems can lead to estimation errors when not handled
                      correctly in subsequent use. In this work, we give details
                      on how to adapt the calculations of Voronoi diagrams to make
                      them fit for the presence of walls and obstacles in complex
                      geometries. Furthermore, we show how that for persons at the
                      edge of a group the personal space can be reasonably
                      restricted. Based on these modifications, having pointwise
                      values for quantities of interest allows to give average
                      values for arbitrary geometries, not just for lines or
                      rectangles of measurements. However, in order to obtain
                      reasonable measurement values, different quantities may need
                      different kind of averages—arithmetic or harmonic, or
                      weighted with density.},
      month         = {Jul},
      date          = {2019-07-02},
      organization  = {Traffic and Granular Flow 2019,
                       Pamplona (Spain), 2 Jul 2019 - 5 Jul
                       2019},
      cin          = {IAS-7},
      cid          = {I:(DE-Juel1)IAS-7-20180321},
      pnm          = {511 - Computational Science and Mathematical Methods
                      (POF3-511) / SISAME - SImulations for SAfety at Major Events
                      (HGF-DB001687)},
      pid          = {G:(DE-HGF)POF3-511 / G:(DE-Juel-1)HGF-DB001687},
      typ          = {PUB:(DE-HGF)8 / PUB:(DE-HGF)7},
      doi          = {10.1007/978-3-030-55973-1_5},
      url          = {https://juser.fz-juelich.de/record/888115},
}