Graphics Reference
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(a)
(b)
(c)
Figure 2.5 (a) Top: If both objects move simultaneously, there is no collision. Bottom: If the
circle object moves before the triangle, the objects collide. In (b), again there is no collision
for simultaneous movement, but for sequential movement the objects collide. (c) The objects
collide under simultaneous movement, but not under sequential movement.
one object at a time and any collisions are detected and resolved before the process
continues with the next object.
Clearly, sequential movement is not a physically accurate movement model. Some
objects may collide with objects that have not yet moved in this frame but that would
have moved out of the way were the two objects moving simultaneously (Figure 2.5a).
Other objects may collide with objects that moved before they did and are now in
their path (Figure 2.5b). In some cases, where two simultaneously moving objects
would have collided halfway through their motion, collisions will now be missed as
one object is moved past the other (Figure 2.5c). For games, for example, the problems
introduced by a sequential movement model can often be ignored. The high frame
rate of games often makes the movement step so small that the overlap is also small
and not really noticeable.
One of the benefits of the sequential movement model is that an object nonpen-
etration invariant is very easy to uphold. If there is a collision during the movement
of an object, the movement can simply be undone (for example). Only having to
undo the movement of a single object should be contrasted with the simultaneous
movement model using a fixed time step, where the movement of all simultaneously
moved objects would have to be undone.
2.4.3 Discrete Versus Continuous Motion
Something that can greatly affect both the computational effort needed to deter-
mine a collision result and the accuracy of the result itself is if the two objects
involved in a pairwise test are moving at the time of testing. Static collision detection
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