Practical Algorithms for 3D Computer Graphics, 2nd Edition

6.6. Animating cloth and hair 247

(d)

(b)

(a)

(c)

(e)

(f)

p´

p´

Fixed

point

∆x

F = k∆x

p

p

1

F

4

F´

3

F´

2

F´

1

F´

4

F

3

F

2

F

1

p

p

p

2

p´

2

Figure 6.36: A spring mass particle system model for elastic deformation. (See the

discussion in the text.)

sented by particles at points such as p. In (b), pulling p away from its original

position establishes restoring forces in the springs that would tend to return th e

mesh to its original shape when we releas e the vertex at point p

′

. In a simple

one-dimensional spring (c), the restoring force is proportional to the extension

in the length of the spring. (d) When two or more springs are connected, all

the non-fixed points such as p

1

may move. ...