Geography Reference
In-Depth Information
Fig. 12.1
Conceptual space-time path and prism
segment whose slope is a function of velocity (i.e., a lower velocity corresponds with
a steeper angle and a higher velocity corresponds with a flatter incline).
Figure
12.1
b illustrates a
space-time prism
: this is the envelope of all possible
space-time paths between two fixed activity locations (e.g., home and work), a
time
budget
for travel and activity participation (e.g., the time interval between earliest
time a person can leave work and the latest time s/he must arrive at home), and the
maximum velocity (speed) for travel.
1
If known, activity participation time can be
netted from this prism (e.g., time spent for shopping groceries); this is the
stationary
activity time
in Fig.
12.1
b. The prism boundary delimits all locations in space-time
that the mobile object can occupy; the spatial footprint or
potential path area
(PPA)
delimits all accessible locations in geographical space.
Despite its simple geometry, it is difficult to describe a space-time prism
analytically over the entire time interval of its existence. However, we can easily
describe the spatial extent of a prism at an instantaneous time within the time
budget (Fig.
12.2
).Givenanoriginlocation(
x
i
,
y
i
), a destination location (
x
j
,
y
j
)., a
maximum travel velocity
V
m
, and a minimum stationary activity time
t
s
, the spatial
extent of the prism at any instant time
t
within the time budget can be defined
analytically (Miller
2005a
):
n
.x; y/
ˇ
ˇ
ˇ
f
i
.t /
\
p
j
.t /
\
g
ij
o
Z
ij
.t /
D
(12.1)
1
Strictly speaking from a physical perspective, the classic space-time prism is determined in part
by a maximum “speed” (a scalar value) not a “velocity” (a vector with direction and magnitude).
However, we will use the term “velocity” for consistency with the time geography literature.
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