4.3. COMPUTING FORCES 23
In order to model resistance to deformations, we can simply construct a spring connecting
every pair of neighboring particles. A simple mass-spring system containing nine particles is
shown in Figure 4.2. e springs that we just constructed can be thought of as two different
types that serve a different purpose. e springs that are shown in green resist stretching of the
lattice and the purple springs counteract shearing forces.
A lot of the interesting visual information such as wrinkles and folds results from the cloth
bending. A way to incorporate this in our model is to connect 2-ring neighbor particles with a
spring, skipping the particle in between. ese are called bend springs and are shown in yellow.
It might be interesting to keep these types separated because the spring constant depends
on the type of spring. is will make it easier to set material parameters on the model so we have
dials to control stretch and shear resistance separately. Most materials have a lower resistance
to shearing. Varying the shear stiffness affects the visual behavior dramatically. As a guideline,
stretch springs will have very stiff constants whereas shear and bend springs will have small
values. Obviously, there is not a complete separation between stretching, shearing, and bending.
For example, shear springs will also have some effect on stretching.
Keep in mind that it is totally up to you which particles you connect with springs. Just
know that this will eventually have a profound effect on the way the cloth behaves. is will be
more clear later on.
Rendered Particles
Stretch Springs
Shear Springs
Bend Springs
Figure 4.2: A simple mass-spring system consisting of nine particles connected by stretch springs
and shear springs. Bend springs connect with every other particle.
4.3.1 ENERGY MINIMIZATION
Physical systems are always trying to reach a minimal energy state. Just think of a marble rolling
down a hill, decreasing its potential energy. We can model this is by defining energies and by
minimizing them. e forces are those that will try to bring the system in a state that has lower
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