Special Models for Animation - Computer Animation: Algorithms and Techniques - page 366

(a)

(b) (c)

FIGURE 12.2
Overlapping metaball density functions. (a) Schematic showing overlapping density functions. (b) Surface
constructed when positive weight are associated with density functions. (c) Surface constructed when one
positive weight and one negative weight are associated with density functions.

(a) (b) (c) (d)

FIGURE 12.3
Various surfaces extracted from implicit distance-based functions. (a) Distance-based implicit primitive based on
a single polygon. (b) Distance-based implicit primitive based on a single convex polyhedron. (c) Distance-based
implicit primitive based on a single concave polyhedron. (d) Compound implicitly defined object.

point, a primitive can be defined that uses a line segment, a triangle, a convex polyhedron, or even
a concave polyhedron. Any central element for which there is an associated well-defined distance
function can be used. The drawback to using more complex central elements, such as a concave poly-
hedron, is that the distance function is more computationally expensive. Other primitives, which are not
strictly offset surfaces but which are still distance based, are the cone-sphere and the ellipse. See
Figure 12.3a-c for examples of distance-based primitives. As with metaballs, these implicit primitives
can be combined to create interesting compound density functions whose isosurfaces can be extracted
and displayed ( Figure 12.3d ) .

12.1.2 Animation using implicitly defined objects
In Bloomenthal's book [ 3 ], Wyvill discussed several animation effects that can be produced by mod-
ifying the shape of implicit surfaces. The most obvious way to achieve these modifications is to control
the movement of the underlying central elements. Topological changes are handled nicely by the
implicit surface formulation. The points that define a collection of metaballs can be controlled by a
simple particle system, and the resulting implicit surface can be used to model water, taffy, or clouds,
depending on the display attributes and the number of particles. Central elements consisting of lines can
be articulated as a jointed hierarchy.