Graphics Reference
In-Depth Information
Figure 5.30.
Surface midpoint displacements.
the midpoint of the edge
AB
to
X
and
X
¢ with respect to the triangles
ABC
and
ABC
¢,
respectively. One has to make sure that one uses the same random number and normal
when offsetting an edge with respect to both triangles that have it in common.
Some good references on fractals are [Mand83] and [DevK89].
Iterated Function Systems.
Iterated function systems are an elegant way to gen-
erate fractals. We refer the reader to Section 22.4 for a brief discussion. [Barn88] is
a good reference.
Grammar-Based Models.
Building on work of Lindenmayer ([Lind68]) on
parallel
graph grammars
, Smith ([Smit84]) described a class of plant models that he called
graftals
. The modeling involved two stages: first one generates a formal string from
an initial string using production rules and then the image is generated by interpret-
ing this string as a geometric tree in a suitable way. Graftals were not necessarily frac-
tals, but were very similar in that one could generate as much detail as desired. Very
realistic plants and trees could be generated using botanical laws.
Particle Systems.
Particle systems, introduced in [Reev83], were good at modeling
phenomena that was “fluid-like” and changed over time by flowing or spattering, such
as clouds, smoke, fire, water falls, and water spray. Typical particles were spheres and
ellipsoids. They would be created in a random way with respect to size, position,
shape, and other properties and then randomly deleted. During their lifetime their
paths, which could be controlled by specified physical forces, would be rendered in
appropriate colors. See also [ReBl85].
Most models above are what are called
procedural models
. We have more to say
about this later in Sections 5.6 and 5.11.
5.5
Physically Based Modeling
The kind of modeling we have discussed so far has dealt mostly with static objects.
Allowing for animation would not change that since animation is nothing but a matter
of generating a sequence of views of static objects (rather than a single view). This
static modeling is what the traditional CAD systems do and is quite adequate in aiding
