Graphics Reference
In-Depth Information
The user may also work directly with the distance-time curve. For some users, this is the most intu-
itive approach. Assuming that a point starts at the beginning of the curve at t ¼
0 and traverses the curve
to arrive at the end of the curve at t ¼
1, then the distance-time curve is constrained to start at (0, 0) and
end at (1, 1). If the objective is to start and stop with zero velocity, then the slope at the start and end
should be 0. The restriction that a point traveling along the curve may not back up any time during
the traversal means that the distance-time curve must be monotonically increasing (i.e., always have
a non-negative slope). If the point may not stop along the curve during the time interval, then there can
be no horizontal sections in the distance-time curve (no internal zero slopes) (see Figure 3.20 ) .
s
s
t
t
Backs up
Starts and ends abruptly
s
s
t
t
Stalls
Smoothly starts and stops
s
s
t
t
Starts partway along the curve
and gets to the end before t = 1.0
Waits a while before starting
and does not reach the end
FIGURE 3.20
Sample distance-time functions.
 
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