History of cloth simulation

The study of cloth and its simulation began in the 1930’s in the textile industry, when a  paper  entitled  “On  the  geometry  of  cloth  structure”  was  published  .    The computer graphics community took an interest in the 1980’s with the publication of several papers on different methods of simulating cloth using computer graphics . Today, both industries approach the same subject, but from different angles.   The textile community are concerned with the physical properties of cloth, and the computer graphics community are concerned with creating visibly believable simulations with “realistic” computation times.

The computer graphics approach to cloth modelling has mainly focused on the issue of simulating the complex shapes and deformations of fabric and clothing in 3D.  The techniques that have been formulated and studied can be broken up into town main sections; Geometric Techniques and Physically Based Approaches.

1   Geometric Techniques

In 1986, a geometric method for modelling cloth hanging from a fixed number of points was introduced by Weil.  For this method the cloth is modelled as a 2D grid of 3D points and calculated using a two step process:

a.   The points are connected recursively with Catenary curves, and are dealt with depending on whether they hang inside or outside a convex hull.  The points that do not hang inside the hull are removed.

b.   The second step is a relaxation pass.   This pass is to ensure the distance constraints set between the particles are adhered to.  This will give a smooth cloth with a realistic cloth-like drape.

Later, other geometric approaches to modelling cloth–like surfaces began to emerge. In the 1990’s a number of papers were published on the topic .

One such technique was a mixture of geometric and physically based methods.   It involved a computational geometry technique to roughly estimate the shape a piece of cloth would have, when hanging from specific constrained points.

A wrinkle model was also introduced, again using a mixture of geometric and physically based methods.  This technique involved performing dynamic analysis on  a  small  deformable  sheet  of  material  and  using  this  analysis  to  identify characteristic deformations for wrinkling cloth.   This information was then used to define a model for cloth.  The method proved useful for providing cloth–like wrinkles for use in animations; however it did not prove to be accurate enough for modelling wrinkling cloth.

2  Physically Based Approaches

There are three main types of physically based models that have been developed for cloth simulation:

1.   Elasticity Based Methods

2.   Particle Based Methods

3.   Mass – Spring Damper Model

3 Elasticity Based Methods

In 1986, along with Weil’s geometric approach, another technique for modelling cloth simulation was introduced.  This was an Elasticity Based Model, which defined a set of energy functions over a 2D grid of 3D points.   The energy contained in this model  included  the  cloth’s  tensile  strain,  bending  and  gravity  information.    The method is based on the idea of treating cloth as a continuous material, with these energy functions being derived from Elastic Theory .  The distance between points and a simple measure of the curvature of this distance are used to calculate the elastic forces in the cloth.

4  Particle Based Methods

In 1992, Particle Based Methods were introduced by Breen & House .  They had developed a model for cloth drape simulation using an interacting particle system that represented the underlying mechanical structure of cloth.   The particles interacted with their adjacent particles and the surrounding environment, by using equations that described  associated  mechanical  connections,  represented  by  energy  functions. Further to this, a stochastic gradient descent technique  was used as a relaxation method to bring the cloth particles to a stable rest state.

This theory for modelling cloth using Particle Based Methods was built on further, by Eberhardt and Weber .  They reformulated the basic energy equations resulting in a set of Ordinary Differential Equations, which were then used to calculate the cloths dynamic behaviour.

5  Mass Spring Damber Model

This technique was first introduced in 1988 by Hamann and Parent  and was developed further in 1995 by Provot. It consists of cloth being modelled as a grid of particles that are connected by spring dampers.

This technique was used as the basis for the cloth simulation discussed in this report and is developed further in the following section.