Special Models for Animation - Computer Animation: Algorithms and Techniques - page 368

Sample points on
surface of polyhedron

Polygonal object
Collection of implicit surfaces
used to approximate polyhedron

FIGURE 12.5
Using implicit surfaces for detecting collisions between polyhedral objects.

Undeformed implicit surfaces

F j ( p ) 0

F i ( p ) 0

Object i Object j

Penetration region Propagation region

FIGURE 12.6
Penetrating implicit surfaces.

penetration region . An additional region just outside the penetration region is called the propagation
region ( Figure 12.6 ) .
The density function of each object is modified by the overlapping density function of the other
object to deform the implicitly defined surface of both objects so that they coincide in the region of
overlap, thus creating a contact surface ( Figure 12.7 ) . As shown in the example in Figure 12.7 , a defor-
mation term is added to F i as a function of Object j 's overlap with Object i , G ij , to form the contact
surface. Similarly, a deformation term is added to F j as a function of Object i 's overlap with Object j ,
G ji . The deformation functions are defined so that the isosurface of the modified density functions,