Fluids: Liquids and Gases - Computer Animation: Algorithms and Techniques - page 254

FIGURE 8.5
Normal vector displacement versus height displacement.

Normal

s

Tangent

s
L

t
T

⎛ ⎛ ⎞ 2 ⎞

h P ( s , t ) A cos π

⎝ ⎝ ⎠ ⎠

d h p ( s , t )

A 2 L

s
L

t
T

⎛ ⎛ ⎛ ⎞ 2 π ⎞ ⎞

------ sin

⎝ ⎝ ⎝ ⎠ ⎠ ⎠

d s

d
d

⎛ ⎛ ⎞ ⎞

h p ( s , t ), 0 Tangent 1 ,

s

d h p ( s , t )

⎛ ⎞

⎛ ⎞

⎛ ⎛ ⎞ ⎞

Normal 1 ,0

d

FIGURE 8.6
Normal vector for two-dimensional wave function.

The anatomy of waves
A more sophisticated model must be used to model waves with greater realism, one that incorporates
more of the physical effects that produce their appearance and behavior. Waves come in various
frequencies, from tidal waves to capillary waves, which are created by wind passing over the surface
of the water. The waves collectively called wind waves are those of most interest for visual effects.
The sinusoidal form of a simple wave has already been described and is reviewed here in a more appro-
priate form for the equations that follow. In Equation 8.1 , the function f ( s , t ) describes the amplitude
of the wave in which s is the distance from the source point, t is a point in time, A is the maximum
amplitude, C is the propagation speed, and L is the wavelength. The period of the wave, T , is the time