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iterative collaboration with the application scientists, tailored towards their specific
needs.
That study indicated that the seemingly straightforward derivation of movement
properties (such as speed, azimuth, turning angle, or sinuosity) allows for substantial
methodological diversity. There is not just one way of computing speed, azimuth,
or sinuosity for movement data. Instead, from the various possible combinations of
(i) data capture procedures, (ii) conceptual movement models, (iii) different notions
of movement properties found in different application fields, and finally, (iv) vari-
able analysis scales (see Sect. 2.3.2 ) , results a surprising diversity of approaches to
compute movement descriptors.
In many ways the work in Laube et al. ( P3 . 2007 ) was a predecessor to later work,
especially Laube and Purves ( P13 . 2011 ). The outlook section of the 2007 study
suggested that the notion of interval operators, there conceptualized as a smoothing
operator for imperfect trajectory data, would allow for systematically varying the
analysis scale, aiming at investigating movement data at variable temporal granular-
ities. The study reported on in Laube and Purves ( P13 . 2011 ) followed that idea and
presented experiments systematically varying the temporal granularity of deriving
movement descriptors from trajectories.
2.3.2 Scale
Scale is a quintessential geographic concept. All three meanings of scale—
cartographic scale, analysis scale, and phenomenon scale (Montello 2001 )—are rel-
evant to CMA.
Cartographic scale expresses the relationship between the earth's surface and
its necessarily much smaller depiction on a map (Montello 2001 ). This is clearly
relevant as the visual display of movement traces is an entry point to CMA. How-
ever, GIScience and related application sciences have so far given little attention to
methodological challenges around cartographic scale of mapping movement, which
is surprising given typically large and heterogeneous raw data volumes and the disci-
pline's rich history in aggregation and generalization. Trajectories are either mapped
in their entirety as polylines ( P10 . Dennis et al. 2010 ) or aggregated to density maps
for giving a quick overview (see, for example, Fig. 8 in P3 . Laube et al. 2007 ).
Aggregation and generalization of trajectories remains an important topic for further
research.
Analysis scale refers to the granularity at which phenomena are measured or
aggregated (Montello 2001 ). Whenever movement is modeled as trajectories, analy-
sis scale refers to the spacing of the fixes, that is the spatial and/or temporal separation
of location measurements along the movement trace. Laube and Purves ( P13 . 2011 )
made the point that the granularity of data capture (the inbuilt or user-set sampling
rate of the tracking system) does not necessarily prejudice the subsequent analysis
scale. By contrast, the experimental piece investigated the implications of varying
the temporal analysis scale at which the movement descriptors speed, turning angle
 
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