Graphics Reference
In-Depth Information
FIGURE 4.23
Cylindrical grid.
Composite FFDs—sequential and hierarchical
FFDs can be composed sequentially or hierarchically. In a sequential composition an object is modeled
by progressing through a sequence of FFDs, each of which imparts a particular feature to the object. In
this way, various detail elements can be added to an object in stages as opposed to trying to create one
mammoth, complex FFD designed to do everything at once. For example, if a bulge is desired on a bent
tube, then one FFD can be used to impart the bulge on the surface while a second is designed to bend the
object ( Figure 4.24 ) .
Organizing FFDs hierarchically allows the user to work at various levels of detail. Finer-resolution
FFDs, usually localized, are embedded inside FFDs higher in the hierarchy. 1 As a coarser-level FFD is
used to modify the object's vertices, it also modifies the control points of any of its children FFDs that
are within the space affected by the deformation. A modification made at a finer level in the hierarchy
will remain well defined even as the animator works at a coarser level by modifying an FFD grid higher
up in the hierarchy [ 18 ] ( Figure 4.25 ) .
If an FFD encases only part of an object, then the default assumption is that only those object ver-
tices that are inside the initial FFD grid are changed by the modified FFD grid. Because the finer-level
FFDs are typically used to work on a local area of an object, it is useful for the animator to be able to
specify the part of the object that is subject to modification by a particular FFD. Otherwise, the rect-
angular nature of the FFD's grid can make it difficult to delimit the area that the animator actually
wants to affect.
Animated FFDs
Thus far FFDs have been considered as a method to modify the shape of an object by repositioning its
vertices. Animation would be performed by, for example, linear interpolation of the object's vertices
on a vertex-by-vertex basis. However, FFDs can be used to control the animation in a more direct
1 For this discussion, the hierarchy is conceptualized with the root node at the top, representing the coarsest level. More local-
ized nodes with finer resolution are found lower in the hierarchy.
 
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