Physically Based Animation - Computer Animation: Algorithms and Techniques - page 234

Computing accurate dynamics is a nontrivial thing to do. However, because of the developed liter-
ature from the robotics community and the interest from the computer animation community, understand-
able presentations of the techniques necessary are available to the mathematically inclined. For real-time
applications, approximate methods that produce visually reasonable results are very accessible.
7.5 Cloth
Cloth is a type of object that is commonly encountered in everyday living in a variety of forms—most
notably in the form of clothes, but also as curtains, tablecloths, flags, and bags. Because of its ubiquity,
it is a type of object worth devoting special attention to modeling and animating. Cloth is any man-
made fabric made out of fibers. It can be woven, knotted, or pressed (e.g, felt). The distinguishing attri-
butes of cloth are that it is thin, flexible, and has some limited ability to be stretched. In addition, there
are other cloth-like objects, such as paper and plastic bags, that have similar attributes that can be mod-
eled with similar techniques. However, for purposes of this discussion, woven cloth, a frequently
encountered type of cloth-like object, will be considered.
Woven cloth, as well as some knotted cloth, is formed by a rectilinear pattern of threads. The two
directions of the threads are typically referred to as warp , in the longitudinal direction, and weft , in the
side-to-side direction and orthogonal to the warp direction. The thread patterns of cloth vary by the
over-under structure of the threads. For example, in a simple weave, each thread of the warp goes over
one weft thread and then under the next. The over-under of adjacent warp rows are offset by one thread.
This same over-under pattern holds for the weft threads relative to the warp threads. Other patterns can
be used, such as over-over-under and over-over-under-under ( Figure 7.30 ). For more variety, different
over-under patterns can be used in the weft and warp directions. Such differences in the weave pattern
make the material more or less subject to shear and bend.
Because cloth is thin, it is usually modeled as a single sheet of geometric elements, that is, it is not
modeled as having an interior or having any depth. Because it is flexible and distorts easily, cloth of any
significant size is usually modeled by a large number of geometric elements typically on the order of
hundreds, thousands, or even tens of thousands of elements. The number of elements depends on the
desired quality of the resulting imagery and the amount of computation that can be tolerated. Because
of the large number of elements, it is difficult for the animator to realistically animate cloth using sim-
ple positioning tools, so more automatic, and computationally intensive, approaches are employed.
Major cloth features, such as simple draping, can be modeled directly or the underlying processes that
give rise to those features can be modeled using physically based methods.
The main visual feature of cloth is simple draping behavior. This draping behavior can be modeled
kinematically— just by modeling the fold that is generated between fixed points of the cloth (see the
following section). This is possible in simple static cases where the cloth is supported at a few specific
points. However, in environments where the cloth is subject to external forces, a more physically based
approach is more appropriate. Because cloth can be stretched to some limited degree, a common
approach to modeling cloth is the use a mass-spring-damper system. Modifying the mass-spring-
damper parameters provides for some degree of modeling various types of cloth material and various
types of cloth weave. The spring model, being physically based, also allows the cloth mesh to react to
external forces from the environment, such as gravity, wind, and collisions. Real-time systems, such as
computer games or interactive garment systems, place a heavy demand on computational efficiency not
required of off-line applications and techniques have to be selected with an appropriate quality-cost