Game Development Reference
Damping can always be used to enforce stability on spring systems, even if the
forces are not constructed to be stable with the used integration scheme [Bhasin
and Liu 06].
Every system loses energy over time. In a physical sense, the energy is not lost
but goes into motion that is not visible to perception, such as heating the materials
or the surrounding system. Here, a simple damping model is used that will cause
the system to come to rest by just scaling the velocity by a certain factor at every
Damping forces can be constructed to drain energy from the system in a more
sophisticated way so global damping can be reduced. But in the end, a form of
global damping should still be implemented.
14.3 Neighborhood Interaction
For the following forces, the neighborhood (nbr( i ))ofvertex x i needs to be de-
fined. The neighborhood can be quite a general set of vertices; we just need an
applicable definition of it. If we do not have any connectivity information, we can
define it to be every vertex that is within a certain radius of another. For vertices
that form a lattice, the neighborhood can be the nearest-neighbor lattice sites. A
triangle mesh has connectivity information supplied by definition, for example, in
the form of a stream of vertices and a stream of triangles that group three vertices
into one surface fragment and store additional information that is needed on a
Here, we define the vertex's ring-0 neighbors as its neighborhood. (This
equals the vertices that are grouped into one triangle with the vertex!) We also de-
fine each vertex as a neighbor of itself, which makes the formalism later simpler.
Figure 14.2. Avertex x i and its local neighborhood.