Special Models for Animation - Computer Animation: Algorithms and Techniques - page 371

To solve the level set equations advecting in the normal direction, at a given point, get the point's
normal and scale it to form vector field. Common functions used to control the speed are curvature at
the point and a constant function. The interface can be updated by taking a Euler step in the direction of
its velocity. Once updated, the distance function needs to be updated as well. For purposes of effi-
ciency, the entire grid is not usually processed. Instead, just a band of grid values on either side of
the interface is updated [ 13 ] .
12.1.6 Summary
Although their display may be problematic for some graphic systems, implicit surfaces provide unique
and interesting opportunities for modeling and animating unusual shapes. They produce very organic-
looking shapes and, because of their indifference to changes in genus of the implicitly defined surface,
lend themselves to the modeling and animating of fluids and elastic material.
12.2 Plants
The modeling and animation of plants represent an interesting and challenging area for computer ani-
mation. Plants seem to exhibit arbitrary complexity while possessing a constrained branching structure.
They grow from a single source point, developing a branching structure over time while the individual
structural elements elongate. Plants have been modeled using particle systems, fractals, and L-systems.
There has been much work on modeling the static representations of various plants (e.g., [ 1 ][ 2 ] [ 8 ][ 12 ]
[ 15 ][ 17 ] [ 18 ] ). The intent here is not to delve into the botanically correct modeling of particular plants
but rather to explain those aspects of modeling plants that make the animation of the growth process
challenging. The representational issues of synthetic plants are discussed in just enough detail to
uncover these aspects. Prusinkiewicz and Lindenmayer [ 14 ] [ 16 ] provide more information on all
aspects of modeling and animating plants.
The topology 1 of a plant is characterized by a recursive branching structure. To this extent, plants
share with fractals the characteristics of self-similarity under scale. The two-dimensional branching
structures typically of interest are shown in Figure 12.9 . The three-dimensional branching structures
are analogous.
An encoding of the branching structure of a given plant is one of the objectives of plant modeling.
Plants are immensely varied, yet most share many common characteristics. These shared characteris-
tics allow efficient representations to be formed by abstracting out the features that are common to
plants of interest. But the representation of the static structure of a mature plant is only part of the story.
Because a plant is a living thing, it is subject to changes due to growth. The modeling and animation of
the growth process is the subject of this section.
12.2.1 A little bit of botany
Botany is, of course, useful when trying to model and animate realistic-looking plants. For computer
graphics and animation, it is only useful to the extent that it addresses the visual characteristics of the
plant. Thus, the structural components and surface elements of plants are briefly reviewed here.
1 The term topology , as applied to describing the form of plants, refers to the number and arrangement of convex regions of the
plant delineated by concave areas of attachment to other convex regions.