Graphics Reference
In-Depth Information
11 Motion
11.1 Introduction
As vectors have always been associated with dynamics, this text concludes with a short chapter
on the motion of objects within an animation context. To begin with, we compute the shortest
distance between a stationary observer (which we refer to as “you”) and a moving object,
followed by that between a moving observer (still “you”) and a moving object.
11.2 Close encounters of the first kind
Imagine watching an object fly past you at a speed s
O
in a direction
v
O
. The nearest the object
approaches you is when a line connecting you to the object is perpendicular to
ˆ
ˆ
v
O
, as shown in
Fig. 11.1.
Y
Y
ou
v
o
object
X
Z
Figure 11.1.
If the object is positioned at Q at time t
=
0, its future position is given by
p
=
q
+
t
P
s
O
ˆ
v
O
where t
P
is the time taken to move from Q to P, as shown in Fig. 11.2.
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