Game Development Reference
In-Depth Information
struct ContactPoint
{ Vector point; // world space contact point
Vector normal; // from object B to object A
float penetration; // negative for separated objects
}
Listing 4.1. A contact point.
affect the torques or angular impulses acting on the contacting bodies. Physical
simulation is discrete and must accommodate small errors. The rigid bodies may
penetrate (or not exactly touch, but be very close) at the point of contact.
Coordinates of the point of contact, the normal, and the penetration are the
main components of a contact point.
Collision response (the reaction, or how the objects bounce off of each other)
depends on relative velocities or accelerations at the point of contact (the action,
or how the objects push each other). This response is computed in the solver (see
Section 4.3), where it's better not to access the geometric shape data (vertices,
edges, faces) for performance reasons. Computing penetration at a point is non-
trivial and requires the knowledge of the geometric shape [Ganjugunte 07]. This
is why penetration is part of the ContactPoint structure in Listing 4.1.
Relative velocity and acceleration aren't in the ContactPoint structure,
although they could be. They are easy to compute in the solver, thus trading CPU
for memory bandwidth. And a discrete collision-detection routine doesn't need
access to velocity or accelerations.
A contact manifold is a set of contact points between a pair of objects. It's
not necessary to generate all contact points, only the corners of the contact shape
is enough. More specifically, for any set of contact points with the same friction
cone, it's enough to only generate the points forming a convex hull enclosing all
the other points; for example, all of the shapes in Figure 4.1 should ideally have
just four contact points generated, which are shown by their normal vectors. The
shape in Figure 4.1(d) is very irregular, and the contact area's convex hull is a
slightly rounded rectangle, but for a game simulation, it's still best approximated
by a rectangle. Some useless contacts from the interior of the convex hull are
marked with the
symbol. They don't contribute to the contact area/volume
convex hull (the wavy shapes), assuming their friction cones are the same. They
eat up time during the dynamic solver stage, and although an iterative solver may
be more stable with them, they generally need to be culled.
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