C.Feynman - "Modelling the Appearance of Cloth" (1986)

Why this paper?
This was the first paper pointed to by the Survey Paper that looks at physically modelling cloth. From 1986, it is also probably one of the first written on the topic.


How is cloth represented?
In this paper, Feynman represents cloth as a discrete, uniform grid of points. A "multi-grid method" is used, where multiple grids of varied densities are used to represent cloth; see below.
Cloth is modelled such that each point represents a piece of cloth sized h*h (where h is the distance between points) The behaviour of a point is governed only by its nearest neighbours, thus two points on opposite sides of the cloth have no impact on each other.


What are the "Driving Equations" behind the cloth?
Cloth is simulated by minimizing its energy state. This is also known as relaxation. The sum of the energies at each point equals the energy state of the entire cloth.

Each point is relaxed one-by-one. Each point in the grid is relaxed by evaluating a "force vector" that will move the point into a position of decreased energy. When this is done for all points, the overall energy state of the cloth is decreased.

Feynman derives and equation to evaluate the energy state of the cloth from the theory of elastic plates. This equation attempts to mimic the energy dynamics of cloth in "real-life". In his approximation, the total energy is a combination of gravitational effects, bend effects and strain effects. (Strain being distortion within the plane of the cloth, and bend being distortion outside the plane.)

The multi-grid method is an optimization based on the premise that creating large features (large folds ect) through relaxation on a fine grid is more costly than on a coarse grid. In fact there is an optimal grid size (point-spacing) for a feature of a certain size, so that it is small enough to represent to the feature but coarse enough that as few as possible points have to be relaxed.

The idea behind the multi-grid method then, is that multiple relaxation sweeps are done for grids of multiple resolutions -- finer grids for small features and coarser grids for larger features. Finally results from these relaxation sweeps are molded together, incorporating both the small and large features into one grid.


How are collisions with the cloth handled (if at all)?
Feynman included support for collisions with ellipsoids. Ellipsoids can be used to represent a wide range of solid objects, whilst can be algebraically defined easily (although Feynman admits the collision detection is still a slow process). He defines a collision as one or more points being inside the volume of the ellipsoid. A collision is handled by placing the point back at the nearest point outside of the ellipsoid.

Feynman comments that the results involving collisions are disappointing and highlights that when the cloth grid is too coarse it is possible for solid objects to completely pass through the cloth without a collision even being detected.


Any results or conclusions of interest?
Feynman simulated environments with hanging clothes and cloth draped over a sphere.
But no results regarding the time taken to run these simulations were given.
Note that this paper produced static results not animated ones. Feynman discusses the difficulty of using the energy minimization approach to a dynamic simulation. Since one of my "requirements" is that my simulation is dynamic, perhaps, as Feynman advises, the energy minimization technique would not be the best approach for me to take.

An interesting observation that Feynman highlights was the difference between stretching and compressing cloth, and the different way it responds to these actions. He explains how cloth is strong when it comes to resisting stretching but weak at resisting compression because of buckling. When you attempt to compress cloth, the fabric itself will most likely not give, but it will buckle instead (bend out of it's plane). Although mentioned, buckling is not a phenomenon taken care of in this work.

Another behavioural property of cloth highlighted is cloth's tendency to arrange itself in positions it has previously been in (particularly for long periods of time). This is due to prolonged arrangement of fibres in cloth and the friction between them. This phenomenon was also unaccounted for.