Geography Reference
In-Depth Information
Fig. 12.2
Analytical space-time prism
where
.x; y/
ˇ
ˇ
ˇ
.t
t
i
/
V
m
q
.x
x
i
/
2
C
.y
y
i
/
2
f
i
.t /
D
(12.2)
.x; y/
ˇ
ˇ
ˇ
t
V
m
q
x
x
j
2
C
y
y
j
2
t
j
p
j
.t /
D
(12.3)
.x; y/
ˇ
ˇ
ˇ
q
.x
x
i
/
2
q
x
x
j
2
C
y
y
j
2
C
.y
y
i
/
2
g
ij
D
C
t
s
V
m
t
j
t
i
(12.4)
This definition indicates that the spatial extend of the prism at time
t
is generally
determined by two discs and the PPA (Fig.
12.2
b): (1) the
future disc
(Eq.
12.2
)
delimiting all locations that can be reached from the first anchor by that moment;
(2) the
past disc
(Eq.
12.3
) delimiting all locations that can reach the second anchor
given the remaining time; and (3) the PPA (Eq.
12.4
) that constraints the prism
locations to account for any stationary activity time.
We can also describe the prism from a locational perspective. Given any location
(
x
,
y
) within the PPA (Eq.
12.4
), the time interval [
t
min
,
t
max
] available for activity
participation at that location can be calculated (Fig.
12.3
):
q
.x
x
i
/
2
C
.y
y
i
/
2
V
m
t
min
D
t
i
C
(12.5)
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