Cloth modeling is the term used for simulating

cloth Textile is an umbrella term that includes various fiber-based materials, including fibers, yarns, filaments, threads, different fabric types, etc. At first, the word "textiles" only referred to woven fabrics. However, weaving is not the ...

within a computer program, usually in the context of

3D computer graphics 3D computer graphics, or “3D graphics,” sometimes called CGI, 3D-CGI or three-dimensional computer graphics are graphics that use a three-dimensional representation of geometric data (often Cartesian) that is stored in the computer for t ...

. The main approaches used for this may be classified into three basic types: geometric, physical, and particle/energy.

Background

Most models of cloth are based on "particles" of mass connected in some manner of mesh.

Newtonian Physics Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classical mec ...

is used to model each particle through the use of a "black box" called a

physics engine A physics engine is computer software that provides an approximate simulation of certain physical systems, such as rigid body dynamics (including collision detection), soft body dynamics, and fluid dynamics, of use in the domains of computer gr ...

. This involves using the basic law of motion (Newton's Second Law): :

\vec = m \vec

In all of these models, the goal is to find the position and shape of a piece of fabric using this basic equation and several other methods.

Geometric methods

André Weil
pioneered the first of these, the geometric technique, in 1986.
/ref> His work was focused on approximating the look of cloth by treating cloth like a collection of cables and using

Hyperbolic cosine In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points form a circle with a unit radius, the points form the right half of the u ...

(catenary) curves. Because of this, it is not suitable for dynamic models but works very well for stationary or single-frame renders. This technique creates an underlying shape out of single points; then, it parses through each set of three of these points and maps a catenary curve to the set. It then takes the lowest out of each overlapping set and uses it for the render.

Physical methods

The second technique treats cloth like a grid work of particles connected to each other by springs. Whereas the geometric approach accounted for none of the inherent stretch of a woven material, this physical model accounts for stretch (tension), stiffness, and weight: :

E(Particle_) = k_E_ + k_E_ + k_E_

* s terms are elasticity (by

Hooke's Law In physics, Hooke's law is an empirical law which states that the force () needed to extend or compress a spring by some distance () scales linearly with respect to that distance—that is, where is a constant factor characteristic of ...

) * b terms are bending * g terms are gravity (see Acceleration due to gravity) Now we apply the basic principle of

mechanical equilibrium In classical mechanics, a particle is in mechanical equilibrium if the net force on that particle is zero. By extension, a physical system made up of many parts is in mechanical equilibrium if the net force on each of its individual parts is zero ...

in which all bodies seek lowest energy by differentiating this equation to find the minimum energy.

Particle/energy methods

The last method is more complex than the first two. The particle technique takes the physical methods a step further and supposes that we have a network of particles interacting directly. Rather than springs, the energy interactions of the particles are used to determine the cloth's shape. An energy equation that adds onto the following is used: :

U_ = U_ + U_ + U_ + U_ + U_{Gravity}

* The energy of repelling is an artificial element we add to prevent cloth from intersecting itself. * The energy of stretching is governed by

Hooke's law In physics, Hooke's law is an empirical law which states that the force () needed to extend or compress a spring by some distance () scales linearly with respect to that distance—that is, where is a constant factor characteristic of ...

as with the Physical Method. * The energy of bending describes the stiffness of the fabric * The energy of trellising describes the shearing of the fabric (distortion within the plane of the fabric) * The energy of gravity is based on acceleration due to gravity Terms for energy added by any source can be added to this equation, then derive and find minima, which generalizes our model. This allows for modeling cloth behavior under any circumstance, and since the cloth is treated as a collection of particles its behavior can be described with the dynamics provided in our physics engine.

External links

Cloth Modeling
by Kristopher Babic

Notes