Graphics Reference
In-Depth Information
Figure 2.4 The broad phase identifies disjoint groups of possibly intersecting objects.
the broad-phase system generally must work harder (or be more sophisticated) to
identify groups than it would for a set of homogeneously sized objects. How object
size affects broad-phase methods is discussed further in Chapter 7.
2.4.2 Sequential Versus Simultaneous Motion
In real life, objects are moving simultaneously during a given movement time step,
with any eventual collisions resolved within the time step. For an accurate computer
simulation of the real-life event, the earliest time of contact between any two of the
moving objects would somehow have to be determined. The simulation can then
be advanced to this point in time, moving all objects to the position they would
be in when the first collision occurs. The collision is then resolved, and the process
continues determining the next collision, repeating until the entire movement time
step has been used up.
Executing a simulation by repeatedly advancing it to the next earliest time of contact
becomes quite expensive. For example, as one or more objects come to rest against a
surface, the next time of collision follows almost immediately after the current time
of collision. The simulation is therefore only advanced by a small fraction, and it can
take virtually “forever” to resolve the full movement time step. One solution to this
problem is to use the broad phase to identify groups of objects that may interact
within the group, but not with objects of other groups during the time step. The
simulation of each group can therefore proceed at different rates, helping to alleviate
the problem in general.
An alternative option is to move objects simultaneously, but setting a fixed (small)
time step for the movement. Simultaneous movement can result in objects interpen-
etrating, which typically must be dealt with somehow, for example, by backing up the
simulation to an earlier state. In both cases, simultaneous updates remain expensive
and are therefore often reserved for accurate rigid-body simulations. However, many
games, as well as other applications, are not rigid-body simulations and it would be
overkill and wasted effort to try to simulate motion with high accuracy. For these,
an alternative option is to resolve motion sequentially . That is, objects are moved
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