Fluids: Liquids and Gases - Computer Animation: Algorithms and Techniques - page 264

The processes that form clouds consist of adding moisture to the air or cooling the air. In either case
the moisture content becomes higher than what can be handled transparently by the air. As a result,
water droplets form and cling to dust particles in the air. The cooling of an air mass is often due to
an air mass rising in altitude; air tends to cool as it rises and loses pressure. The cause for this rise
is usually due to something forcing the air mass upward: the traveling air mass encounters an incline
like a mountain slope; the air mass travels up and over a colder, denser air mass (a warm front); and a
cold, dense air mass forces its way underneath the warmer air mass and raises the warm air mass (a cold
front). The air mass temperature can also be cooled by the cooling of the earth's surface, often creating
fog or other low-level clouds. Adding moisture to the air mass is often accomplished by water evap-
orating at the earth's surface underneath the air mass.
Cloud models in CG
Although modeling clouds as a single, static background painting can be effective in some animations,
limited cloud animation can be done cost effectively. This can just be a texture mapped quadrilateral.
Simply moving (i.e., panning) the background provides some degree of animation. Most animation
effects can be introduced by using an animated texture map, essentially a movie, of clouds for the back-
ground. Additionally, using multiple, semitransparent background images, representing clouds at vary-
ing heights, and moving them relative to one another, simulating parallax, can produce the impression
of a deep three-dimensional space at minimal cost. In some situations, it is more appropriate to use a
spherical shell instead of a planar surface, although care must be taken at the horizon to avoid unre-
alistic transitions between sky and ground. To display a fog effect, a simple linear distance-based atten-
uation of object shading can be used. However, the animation of fog swirls requires an approach similar
to CFD discussed earlier in this chapter.
For more control and added visual realism, appropriately shaded geometric primitives can be used
as cloud building blocks. Two-dimensional primitives can be used for distant clouds while three-
dimensional primitives give a greater sense of distance and depth when viewed from various angles
and are appropriate for more immersive environments. The primitives can be moved relative to one
another and scaled up or down, providing easy control for an animator. While not physically based,
this approach can produce effective visuals if the primitives are carefully designed.
The use of such building blocks was pioneered in 1984 by Geoffrey Gardner [ 8 ][ 9 ] and the general
approach is still an attractive way to model clouds. Gardner's technique uses a sky plane that is parallel
to the ground plane and some distance above it. Ellipsoids are used as the cloud building blocks and are
positioned by the user relative to the sky plane. The ellipsoid surface is textured (as described in the
following paragraphs) and then mapped onto a sky plane. Gardner also uses these textured ellipsoids to
build full three-dimensional cloud models, which allows for a full three-dimensional effect as the view-
ing angle changes relative to the ellipsoids. Notice, however, that the texturing function is not defined
on the interior of the ellipsoid shells, so the visuals associated with flying into a cloud are not supported.
In addition to clouds, Gardner also used this approach, with suitable modification to the texture func-
tion, to model other environmental features such as trees and hills as in Figure 8.12 .
The surface texturing function is based on the sum of two weighted sums of sine waves,
defined to produce a pseudorandom cloud-like texture. The two sets of sine waves are orthogonal
to each other. In each set, each frequency is twice the frequency of its predecessor and has an
amplitude of one over radical two times its predecessor. In addition, the phase shift of each fre-
quency is based on its position in the other dimension. A user-defined threshold is set so that