Geography Reference
In-Depth Information
It can be used for visual exploration of continuous spatial and temporal
movement patterns. Several analytical models and measurements have been
developed by Miller (2005) such as space-time prism, composite path-prisms,
stations, bundling and intersections to further analyze the complex spatio-
temporal relationships among human activities and interactions under special
space-time constraints. But when numerous of trajectories were collected in
the datasets, it was hard to visualize and interpret.
Different approaches for generalization and aggregation of massive move-
ment data have been introduced such as
traffic-oriented view
and
trajectory-
oriented view
(Andrienko and Andrienko, 2008)
.
In the urban context, the aggregation of massive human movement
trajectories by origins and destinations (OD) can be utilized to understand the
dynamic OD-flow patterns among traffic analysis zones (TAZs) or other poly-
gonal divisions of region in different temporal scales. Traditional flow
mapping is used for representing the amount and the direction (with arrow
symbol) of
from-to
movements of human or things among regions in a 2D
space, such as migration and goods trade (Tobler, 1987).
Some graph layout optimization algorithms and aggregation strategies
have been suggested to minimize the edge crossings between flow symbols
(Phan et al., 2005; Andrienko and Andrienko, 2011). Here we introduce
another approach of using vertical Bézier curves in 3D-GIS environment for
interactive visual exploration of information or movement flows between
places. The main advantages of such an approach lie in the integration of 3D
visualization techniques which support interactions between 3D geometry
objects and OD-flow values in multiple time snapshots or in a continuous
animation.
A Bézier curve is defined by a set of control points
P
0
through
P
n
, where n
represents called its order (n = 1 for linear, n = 2 for quadratic which is used in
our work, etc.). Bézier curves have been widely used in computer graphics and
geometry designs (Farin, 1996). We develop an algorithm to approximate the
quadratic Bézier curves.
As shown in Figure 3, the first point
P
0
and the last point
P
2
are used to
represent the centroids of two regions (i.e., the origin and the destination of
each flow) and the intermediate control points are interpolated by the standard
Bézier functions. We then project a flow between regions in the 3D-GIS
environment. We write a Python script to generate all Bézier curve controlling
points based on the OD-flow matrix table and link them in Esri's ArcScene
software for further interactive exploration of information flow or physical
movement flow patterns.
