Graphics Reference
In-Depth Information
users in the tasks for which they are used. The real world does not consist of isolated
objects however. Objects interact due to a variety of forces. We need to broaden our
outlook. Another goal should be to facilitate the modeling of the real world with its
interactions. Geometric modeling, the modeling of isolated static objects, is an impor-
tant step toward modeling real world scenes, but it is only a first step. The next step
is to make it easier for users to include the interactions of the objects.
For example, if we wanted to model a ball in a scene with a cloth draped over it,
we could do it with the standard modeling system, but it would take quite some effort.
We would have to figure out the creases in the cloth on our own. These creases are
determined by gravity and other physical forces associated to the particular material
from which the cloth is made. We could use the relevant equations of physics to define
the set of spline surface patches, or whatever, that would generate the correct picture.
How much easier it would be if we only had to tell the CAD program the position and
radius of the ball, the material properties of the flat cloth, the starting position of the
cloth parallel to the floor at the top of the ball, and then let the program compute the
final shape of the cloth after it has reached equilibrium with respect to the forces
acting on it. Obviously, a program that could do this would have to have the relevant
equations and algorithms programmed within it, but this would only have to be done
once.
As another example, suppose that we wanted to show a ball bouncing on a floor.
Again, we could do this animation ourselves with a traditional CAD system by deter-
mining by hand the series of positions of the ball along with the time intervals between
those positions that made up the animation. Why can the CAD program not do this
for us, so that all we had to input was an initial height from which the ball is dropped?
Obviously, the CAD system could be programmed to do this. This would take some
hard work, but again, it would only have to be done once, and then it could help many
users in this and similar types of problems.
Modeling that also considers the dynamics of physical objects in addition to their
static properties is called
physically based modeling
. The objects may be simple parti-
cles or rigid objects, but could also be much more complex, like cloth. As indicated
earlier, we are not really dealing with a new representation scheme but rather an
extension of “traditional” representation schemes. This is a relatively new branch of
computer graphics, with the name “physically based modeling” being introduced for
the first time in an ACM SIGGRAPH 87 course by A.H. Barr ([BarrA87]). To carry out
its program involves a great deal of knowledge about physics and other sciences.
Physically based modeling can be interpreted quite generally to encompass the
three main areas in computer graphics, modeling, rendering, and animation, but at
its core, it deals with classical dynamics of rigid or flexible bodies, interaction of
bodies, and constraint-based control. An active area of research is how a user can best
control the models. There is a trade-off between realism and control. If the models
perform realistically, they are typically controlled by differential equations and the
only control a user has in initial conditions. On the other hand, giving the user more
control might mean that objects will perform less realistically. Constraint-based tech-
niques are a common way to deal with this problem. This includes constraints defined
by equations in physics but also refers to situations where we would like the user to
be able to say things like “move object A so that it touches both objects B and C,” “let
a ball roll down a hill following a given path,” or “show a moving robot, figure, or
object in a domain with obstacles.” Unfortunately, if constraints are not chosen care-
