28 4. MASS-SPRING MODELS
Typically, cloth will stretch a small amount without too much resistance. However,
stretching beyond this point will result in very strong forces that will resist this deformation. For
example, cloth usually doesn’t stretch much under its own weight. is can be modeled using
advanced techniques which are briefly mentioned in the discussion of this chapter. A different
way to handle this is to implement tearable cloth.
Some materials rip when stretched too far. As it turns out, this is actually very easy to
model in our simulations and results in interesting dynamic motion. When the springs are
stretched a certain fraction too far from their rest length, we can assume the cloth breaks and
tears. In our model, we can simply remove this spring from the mass-spring network. is will
disconnect the particles in question, creating a tear. is is the most simple approach to the
tearing phenomenon. A more advanced method can be found in the work of Metaaphanon et
al. [2009].
4.6 OTHER MASS-SPRING APPLICATIONS
Beyond the Basics
In this chapter, we explained how mass-spring systems can be used to model the dynamics of
cloth. We wanted to quickly inform you of the fact that mass-spring systems have multiple
additional applications in physics-based animation. e focus of this book is cloth simulation
so we won’t go into too much detail here but we will point you to further reading.
4.6.1 HAIR SIMULATION
Mass-spring systems have been successfully used for the simulation of hair dynamics. e model
presented by Selle et al. [2008] incorporates collisions, friction, and torsion and is capable of
producing clumping and sticking behavior. Mass-spring systems have also been used by Iben
et al. [2013] to generate highly art directed curly hair. e method has proven to be incredibly
successful in production.
A simple mass-spring system for hair is shown in Figure 4.5. Note that in addition to
the geometric particles there are ghost particles that are necessary to model the hair dynamics.
ese ghost particle won’t be used to render the hair geometry, hence the name.
4.6.2 SOFT BODY DYNAMICS
An extension to three dimensional deformable objects can easily be made. Just like we modeled
cloth using triangles where the particles are connected by springs along the edge, we can model
deformable volumes using tetrahedra. e geometry is discretized using tetrahedra, representing
the full volume. is is also known as a tetrahedralization. A single tetrahedron is visualized in
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