Game Engine Architecture

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can have friction as well. For example, a rusted hinge or axle might resist be-
ing turned by introducing a friction torque.
Let’s look at an example to understand the essence of how friction works.
Linear sliding friction is proportional to the component of an object’s weight
that is acting normal to the surface on which it is sliding. The weight of an
object is just the force due to gravity , G = mg, which is always directed down-
ward. The component of this force normal to an inclined surface that makes an
angle θ with the horizontal is just GN = mg cos θ. The friction force f is then

f=μmg^ cos ,θ

where the constant of proportionality μ is called the coeffi cient of friction. This
force acts tangentially to the surface, in a direction opposite to the att empted
or actual motion of the object. This is illustrated in Figure 12.28.
Figure 12.28 also shows the component of the gravitational force acting
tangent to the surface, GT = mg sin θ. This force tends to make the object accel-
erate down the plane, but in the presence of sliding friction, it is counteracted
by f. Hence, the net force tangent to the surface is

Fnet=GT− =f mg s( in θ− μcos ).θ

If the angle of inclination is such that the expression in parentheses is zero,
the object will slide at a constant speed (if already moving) or be at rest. If the
expression is greater than zero, the object will accelerate down the surface. If it
is less than zero, the object will decelerate and eventually come to rest.

12.4.7.6. Welding

An additional problem arises when an object is sliding across a polygon soup.
Recall that a polygon soup is just what its name implies—a soup of essentially
unrelated polygons (usually triangles). As an object slides from one triangle
of this soup to the next, the collision detection system will generate additional

G=mg

|GN|=

mg cosθ

|GT|=

mg sinθ

|f|=

μmg cosθ

Figure 12.28. The force of friction f is proportional to the normal component of the object’s
weight. The proportionality constant μ is called the coeffi cient of friction.

12.4. Rigid Body Dynamics