Cloths

This very simple model of a cloth seems to be resonably accurate. I have managed to get a very realistic cloth, draping over tables and wrinkling up at the edges (see picture below). You can lay a cloth over a torus, then drop a sphere onto it so that they both fall through the hole and the cloth ends up in a crumpled heap on the floor. I have tested this cloth routine against a real sheet and it compares very well. I have rendered some nice animation files of cloth which I will put here if I have space.

Actually, the picture above is rather misleading. It implies that you compare each point with its 4 nearest neighbours. Infact, if you do this, you will find that the cloth behaves much more like a fisherman's net. It is best if the points are connected to at least their 8 nearest neighbours. This will produce a very flexable cloth. If you go one step wider, and join to the 24 nearest neighbours, you will get a more realistic, stiffer cloth, though it's much slower to compute.

Here's some pseudo code do describe a massless cloth routine:

cloth1 (0 to 31, 0 to 31)
cloth2 (0 to 31, 0 to 31)

Variables:

VECTOR: MovementVector
VECTOR: SpringVector
VECTOR: ForceVector
VECTOR: Gravity  (initialised to (0, 0, g) where g is gravity, 0.02 is a good number)
NUMBER: Length
NUMBER: ForceScaler
NUMBER: NormalLength

For every point (p,q) on the cloth:

    MovementVector = Gravity

    For each of the 24 neighbouring points (NB obviously less at edges)
	SpringVector = (position in space of neighbour) - (position in space of point (p,q))
	Length       = length of SpringVector
	NormalLength = The length SpringVector would be if the cloth were unstretched
	ForceScaler  = (Length - NormalLength) / NormalLength
	SpringVector = SpringVector * (1/Length)
	ForceVector  = SpringVector * ForceScaler
	ForceVector  = ForceVector * SmallAmount
	add ForceVector to MovementVector
    end of loop

    Add MovementVector to cloth1(p,q) and store it in cloth2(p,q)
	
    make sure this point does not move inside an object
end of loop

Copy all the values in cloth2 to cloth1

keep doing all this forever

You will need some objects for the cloth to interact with. The simplest is a floor. Check each point on the cloth to see if it is below the floor, and if it is, then move it to the surface.
It is quite easy to make a sphere for the cloth to fall over. Check each point to see if it is inside the sphere. If it is, then move it to the nearest point on the surface of the sphere.

NUMBER: Distance
Distance = distance from the point(p,q) to the center of the sphere

if Distance < (radius of sphere) then:
    ForceVector = (position of point in space) - (center of sphere)
    ForceVector = Forcevector / Distance * radius
    point(p,q) = (center of sphere) + ForceVector
end if

First the cloth must be broken down into triangles. This is easy to do, since the cloth is already described as an array of points. The effect of the wind on the cloth is calculated on each of these triangles individually. At each point of the cloth, the sum of the effect of the wind on the surrounding triangles is calculated.

VECTOR: force
VECTOR: normal
VECTOR: wind
	
set force vector to (0,0,0) on all points on cloth
	
loop through all triangles	
    force = unitvector(normal) * dotproduct(normal, wind)
    add force to all points making up this triangle
end of loop

loop through all points on cloth
    add gravity to force
    add force to velocity
end of loop

	-- rest of cloth routine --