Game Development Reference

In-Depth Information

3. The behavior of the object is symmetric in all directions at any point, i.e.,

we assume that the object is
isotropic
.

These assumptions lead to a simpler version of the elasticity matrix that only

depends on two independent values, Poisson's ratio
ν
and Young's modulus
Y
:

⎡

⎤

λ
+2
μλ λ
000

λ

⎣

⎦

+2
μλ
000

λ

λ

λ
+2
μ

000

E
=

,

0

0

0

μ

00

0

0

0

0

μ

0

0

0

0

0

0

μ

where

νY

(1 +
ν
)(1

λ
=

−

2
ν
)

and

Y

2(1 +
ν
)
.

μ
=

The symbols
λ
and
μ
are known as the Lame constants of the material. Pois-

son's ratio controls the conservation of the volume of the object, and its values are

normally between 0.0 for nonvolume preservation (in practice, it is usually 0.25)

and 0.5 for a perfect incompressible object. Young's module represents the resis-

tance to stretching, which can intuitively be stated as the stiffness of the material.

These values can be obtained from the mechanics literature. However, Young's

module values for soft bodies may be sometimes more difficult to find than values

for hard materials. This is not really a big issue since it is, in fact, the game artist

who chooses the right value for specific soft bodies. The programmer can help the

game artist by providing a manner in which to vary Young's modulus values (e.g.,

with sliders). In any case, a first coarse approximation can be found in books.

10.3

Linear FEM

The finite element method is an analytical tool for stress, thermal, and fluid anal-

yses of systems and structures. We use it here to describe the deformations of

objects due to external loads. The finite element method is probably the most

physically correct model among all the methods used in computer graphics to

simulate deformations, however, its use has not been spread out in the video game

community due to its complex and lengthy simulations. We show how to simulate

soft bodies in real-time using finite elements, keeping a high degree of realism.