Movement Spaces and Movement Traces - Computational Movement Analysis - page 11

(a) (b) (c)

(d) (e) (f)

Fig. 2.1 Six basic space models accommodating the movement of point objects. a Euclidean homo-
geneous space, b constrained Euclidean space, c space-time aquarium, d heterogeneous field space,
e irregular tessellation, f network space ( P9 . Laube 2009 ) (Reprinted from Behaviour Monitor-
ing and Interpretation, BMI, Smart Environments , Gottfried, B. and Aghajan, H. (eds.), Laube, P.,
Progress in Movement Pattern Analysis, p. 49, Copyright (2009), with permission from IOS Press)

furthermore made apparent three dimensions discriminating conceptual movement
spaces. These dimensions capture how movement is perceived from a physics per-
spective (Sect. 2.2.1 ) , varying degrees of freedom of the moving objects in the move-
ment spaces (Sect. 2.2.2 ) , and the distinction between continuous and discrete spaces
(Sect. 2.2.3 ) .

2.2.1 Lagrangian Versus Eulerian Movement

Movement can be perceived from two different perspectives (see Fig. 2.2 ). The
Lagrangian view considers changes in a moving object's location ( P19 .Bothetal.
2013 ). This results in a stream of location fixes, typically in the form of

-
tuples, describing movement as a two-dimensional, time-stamped polyline. The
nodes represent the fixes, the straight-line edges between the nodes a simple approx-
imation about the path taken in between. GPS tracking results in trajectories akin to
the Lagrangian view. The Eulerian perspective describes movement as changes in
location of moving objects relative to known, fixed points in space ( P19 .Bothetal.
2013 ). Movement is perceived as a flux of objects passing by beacons, RFID tag

( x , y , t )